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PROPN iajs-2479 4 1 33 33 NUM iajs-2479 4 2 ( ( PUNCT iajs-2479 4 3 3 3 NUM iajs-2479 4 4 ) ) PUNCT iajs-2479 4 5 2020 2020 NUM iajs-2479 4 6             SPACE iajs-2479 4 7 exact exact ADJ iajs-2479 4 8 solutions solution NOUN iajs-2479 4 9 for for ADP iajs-2479 4 10 minimizing minimize VERB iajs-2479 4 11 cost cost NOUN iajs-2479 4 12 function function NOUN iajs-2479 4 13 with with ADP iajs-2479 4 14 five five NUM iajs-2479 4 15 criteria criterion NOUN iajs-2479 4 16 and and CCONJ iajs-2479 4 17 release release VERB iajs-2479 4 18 dates date NOUN iajs-2479 4 19 on on ADP iajs-2479 4 20 single single ADJ iajs-2479 4 21 machine machine NOUN iajs-2479 4 22 hanan hanan PROPN iajs-2479 4 23 ali ali PROPN iajs-2479 4 24 chachan chachan PROPN iajs-2479 4 25 hussein hussein PROPN iajs-2479 4 26 abdullah abdullah PROPN iajs-2479 4 27 jaafar jaafar PROPN iajs-2479 4 28 mustansireah mustansireah PROPN iajs-2479 4 29 university university NOUN iajs-2479 4 30 , , PUNCT iajs-2479 4 31 iraq.-department iraq.-department PROPN iajs-2479 4 32 of of ADP iajs-2479 4 33 mathematics mathematic NOUN iajs-2479 4 34 , , PUNCT iajs-2479 4 35 college college NOUN iajs-2479 4 36 of of ADP iajs-2479 4 37 sciences sciences PROPN iajs-2479 4 38 , , PUNCT iajs-2479 4 39 al al PROPN iajs-2479 4 40 alhassen237@gmail.com alhassen237@gmail.com PROPN iajs-2479 4 41 altaai@yahoo.com altaai@yahoo.com PROPN iajs-2479 4 42 - - PUNCT iajs-2479 4 43 hanan hanan PROPN iajs-2479 4 44                           SPACE iajs-2479 4 45 abstract abstract NOUN iajs-2479 4 46 : : PUNCT iajs-2479 4 47 in in ADP iajs-2479 4 48 this this DET iajs-2479 4 49 paper paper NOUN iajs-2479 4 50 , , PUNCT iajs-2479 4 51 we we PRON iajs-2479 4 52 present present VERB iajs-2479 4 53 a a DET iajs-2479 4 54 branch branch NOUN iajs-2479 4 55 and and CCONJ iajs-2479 4 56 bound bound ADJ iajs-2479 4 57 ( ( PUNCT iajs-2479 4 58 b&b b&b PROPN iajs-2479 4 59 ) ) PUNCT iajs-2479 4 60 algorithm algorithm NOUN iajs-2479 4 61 of of ADP iajs-2479 4 62 scheduling scheduling NOUN iajs-2479 4 63 ( ( PUNCT iajs-2479 4 64 n n CCONJ iajs-2479 4 65 ) ) PUNCT iajs-2479 4 66 jobs job NOUN iajs-2479 4 67 on on ADP iajs-2479 4 68 a a DET iajs-2479 4 69 single single ADJ iajs-2479 4 70 machine machine NOUN iajs-2479 4 71 to to PART iajs-2479 4 72 minimize minimize VERB iajs-2479 4 73 the the DET iajs-2479 4 74 sum sum NOUN iajs-2479 4 75 total total ADJ iajs-2479 4 76 completion completion NOUN iajs-2479 4 77 time time NOUN iajs-2479 4 78 , , PUNCT iajs-2479 4 79 total total ADJ iajs-2479 4 80 tardiness tardiness NOUN iajs-2479 4 81 , , PUNCT iajs-2479 4 82 total total ADJ iajs-2479 4 83 earliness earliness NOUN iajs-2479 4 84 , , PUNCT iajs-2479 4 85 number number NOUN iajs-2479 4 86 of of ADP iajs-2479 4 87 tardy tardy ADJ iajs-2479 4 88 jobs job NOUN iajs-2479 4 89 and and CCONJ iajs-2479 4 90 total total ADJ iajs-2479 4 91 late late ADJ iajs-2479 4 92 work work NOUN iajs-2479 4 93 with with ADP iajs-2479 4 94 unequal unequal ADJ iajs-2479 4 95 release release NOUN iajs-2479 4 96 dates date NOUN iajs-2479 4 97 . . 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PUNCT iajs-2479 10 1 key key ADJ iajs-2479 10 2 words word NOUN iajs-2479 10 3 : : PUNCT iajs-2479 10 4 branch branch NOUN iajs-2479 10 5 and and CCONJ iajs-2479 10 6 bound bind VERB iajs-2479 10 7 method method NOUN iajs-2479 10 8 ( ( PUNCT iajs-2479 10 9 b&b b&b PROPN iajs-2479 10 10 ) ) PUNCT iajs-2479 10 11 , , PUNCT iajs-2479 10 12 upper upper ADJ iajs-2479 10 13 bound bound ADJ iajs-2479 10 14 ( ( PUNCT iajs-2479 10 15 ub ub PROPN iajs-2479 10 16 ) ) PUNCT iajs-2479 10 17 , , PUNCT iajs-2479 10 18 lower lower ADV iajs-2479 10 19 bound bound ADJ iajs-2479 10 20 ( ( PUNCT iajs-2479 10 21 lb lb NOUN iajs-2479 10 22 ) ) PUNCT iajs-2479 10 23 , , PUNCT iajs-2479 10 24 multi multi ADJ iajs-2479 10 25 - - ADJ iajs-2479 10 26 objective objective ADJ iajs-2479 10 27 problems problem NOUN iajs-2479 10 28 . . PUNCT iajs-2479 11 1 1 1 X iajs-2479 11 2 . . X iajs-2479 11 3 introduction introduction NOUN iajs-2479 11 4 a a DET iajs-2479 11 5 scheduling scheduling NOUN iajs-2479 11 6 problem problem NOUN iajs-2479 11 7 is be AUX iajs-2479 11 8 defined define VERB iajs-2479 11 9 as as ADP iajs-2479 11 10 a a DET iajs-2479 11 11 problem problem NOUN iajs-2479 11 12 of of ADP iajs-2479 11 13 assigning assign VERB iajs-2479 11 14 a a DET iajs-2479 11 15 set set NOUN iajs-2479 11 16 of of ADP iajs-2479 11 17 tasks task NOUN iajs-2479 11 18 or or CCONJ iajs-2479 11 19 jobs job NOUN iajs-2479 11 20 to to ADP iajs-2479 11 21 a a DET iajs-2479 11 22 set set NOUN iajs-2479 11 23 of of ADP iajs-2479 11 24 resources resource NOUN iajs-2479 11 25 or or CCONJ iajs-2479 11 26 machines machine NOUN iajs-2479 11 27 in in ADP iajs-2479 11 28 a a DET iajs-2479 11 29 specific specific ADJ iajs-2479 11 30 time time NOUN iajs-2479 11 31 . . PUNCT iajs-2479 12 1 common common ADJ iajs-2479 12 2 performance performance NOUN iajs-2479 12 3 measures measure NOUN iajs-2479 12 4 criteria criterion NOUN iajs-2479 12 5 are be AUX iajs-2479 12 6 usually usually ADV iajs-2479 12 7 in in ADP iajs-2479 12 8 the the DET iajs-2479 12 9 form form NOUN iajs-2479 12 10 ∑fj ∑fj PUNCT iajs-2479 12 11 and and CCONJ iajs-2479 12 12 fmax fmax PROPN iajs-2479 12 13 = = SYM iajs-2479 12 14 max{fj max{fj X iajs-2479 12 15 } } PUNCT iajs-2479 12 16 most most ADJ iajs-2479 12 17 of of ADP iajs-2479 12 18 the the DET iajs-2479 12 19 studies study NOUN iajs-2479 12 20 that that PRON iajs-2479 12 21 were be AUX iajs-2479 12 22 introduced introduce VERB iajs-2479 12 23 in in ADP iajs-2479 12 24 the the DET iajs-2479 12 25 early early ADJ iajs-2479 12 26 years year NOUN iajs-2479 12 27 of of ADP iajs-2479 12 28 the the DET iajs-2479 12 29 discovery discovery NOUN iajs-2479 12 30 of of ADP iajs-2479 12 31 the the DET iajs-2479 12 32 theory theory NOUN iajs-2479 12 33 of of ADP iajs-2479 12 34 scheduling scheduling NOUN iajs-2479 12 35 focused focus VERB iajs-2479 12 36 on on ADP iajs-2479 12 37 a a DET iajs-2479 12 38 single single ADJ iajs-2479 12 39 performance performance NOUN iajs-2479 12 40 measuring measure VERB iajs-2479 12 41 criterion criterion NOUN iajs-2479 12 42 . . PUNCT iajs-2479 13 1 however however ADV iajs-2479 13 2 , , PUNCT iajs-2479 13 3 in in ADP iajs-2479 13 4 practice practice NOUN iajs-2479 13 5 , , PUNCT iajs-2479 13 6 a a DET iajs-2479 13 7 manager manager NOUN iajs-2479 13 8 may may AUX iajs-2479 13 9 need need VERB iajs-2479 13 10 to to PART iajs-2479 13 11 find find VERB iajs-2479 13 12 an an DET iajs-2479 13 13 acceptable acceptable ADJ iajs-2479 13 14 schedule schedule NOUN iajs-2479 13 15 which which PRON iajs-2479 13 16 can can AUX iajs-2479 13 17 simultaneously simultaneously ADV iajs-2479 13 18 meet meet VERB iajs-2479 13 19 the the DET iajs-2479 13 20 requirements requirement NOUN iajs-2479 13 21 for for ADP iajs-2479 13 22 several several ADJ iajs-2479 13 23 criteria criterion NOUN iajs-2479 13 24 [ [ X iajs-2479 13 25 1 1 NUM iajs-2479 13 26 ] ] PUNCT iajs-2479 13 27 . . PUNCT iajs-2479 14 1 in in ADP iajs-2479 14 2 this this DET iajs-2479 14 3 paper paper NOUN iajs-2479 14 4 , , PUNCT iajs-2479 14 5 we we PRON iajs-2479 14 6 examine examine VERB iajs-2479 14 7 the the DET iajs-2479 14 8 problem problem NOUN iajs-2479 14 9 of of ADP iajs-2479 14 10 scheduling scheduling NOUN iajs-2479 14 11 with with ADP iajs-2479 14 12 five five NUM iajs-2479 14 13 criteria criterion NOUN iajs-2479 14 14 ( ( PUNCT iajs-2479 14 15 referred refer VERB iajs-2479 14 16 to to ADP iajs-2479 14 17 above above ADV iajs-2479 14 18 ) ) PUNCT iajs-2479 14 19 for for ADP iajs-2479 14 20 measuring measure VERB iajs-2479 14 21 performance performance NOUN iajs-2479 14 22 with with ADP iajs-2479 14 23 the the DET iajs-2479 14 24 release release NOUN iajs-2479 14 25 times time NOUN iajs-2479 14 26 , , PUNCT iajs-2479 14 27 and and CCONJ iajs-2479 14 28 to to ADP iajs-2479 14 29 the the DET iajs-2479 14 30 best good ADJ iajs-2479 14 31 of of ADP iajs-2479 14 32 our our PRON iajs-2479 14 33 knowledge knowledge NOUN iajs-2479 14 34 , , PUNCT iajs-2479 14 35 this this DET iajs-2479 14 36 problem problem NOUN iajs-2479 14 37 was be AUX iajs-2479 14 38 not not PART iajs-2479 14 39 studied study VERB iajs-2479 14 40 before before ADV iajs-2479 14 41 . . PUNCT iajs-2479 15 1 here here ADV iajs-2479 15 2 , , PUNCT iajs-2479 15 3 we we PRON iajs-2479 15 4 found find VERB iajs-2479 15 5 it it PRON iajs-2479 15 6 necessary necessary ADJ iajs-2479 15 7 to to PART iajs-2479 15 8 present present VERB iajs-2479 15 9 some some DET iajs-2479 15 10 research research NOUN iajs-2479 15 11 from from ADP iajs-2479 15 12 the the DET iajs-2479 15 13 literature literature NOUN iajs-2479 15 14 which which PRON iajs-2479 15 15 included include VERB iajs-2479 15 16 machine machine NOUN iajs-2479 15 17 scheduling scheduling NOUN iajs-2479 15 18 problems problem NOUN iajs-2479 15 19 with with ADP iajs-2479 15 20 one one NUM iajs-2479 15 21 or or CCONJ iajs-2479 15 22 more more ADJ iajs-2479 15 23 of of ADP iajs-2479 15 24 the the DET iajs-2479 15 25 performance performance NOUN iajs-2479 15 26 criteria criterion NOUN iajs-2479 15 27 contained contain VERB iajs-2479 15 28 in in ADP iajs-2479 15 29 our our PRON iajs-2479 15 30 problem problem NOUN iajs-2479 15 31 . . PUNCT iajs-2479 16 1 ibn ibn PROPN iajs-2479 16 2 al al PROPN iajs-2479 16 3 haitham haitham PROPN iajs-2479 16 4 journal journal PROPN iajs-2479 16 5 for for ADP iajs-2479 16 6 pure pure ADJ iajs-2479 16 7 and and CCONJ iajs-2479 16 8 applied apply VERB iajs-2479 16 9 science science NOUN iajs-2479 16 10 journal journal PROPN iajs-2479 16 11 homepage homepage NOUN iajs-2479 16 12 : : PUNCT iajs-2479 16 13 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index NOUN iajs-2479 16 14 doi doi NOUN iajs-2479 16 15 : : PUNCT iajs-2479 16 16 10.30526/33.3.2479 10.30526/33.3.2479 PROPN iajs-2479 16 17 article article NOUN iajs-2479 16 18 history history NOUN iajs-2479 16 19 : : PUNCT iajs-2479 16 20 received receive VERB iajs-2479 16 21 28 28 NUM iajs-2479 16 22 september september PROPN iajs-2479 16 23 2019 2019 NUM iajs-2479 16 24 , , PUNCT iajs-2479 16 25 accepted accept VERB iajs-2479 16 26 4 4 NUM iajs-2479 16 27 december december PROPN iajs-2479 16 28 2019 2019 NUM iajs-2479 16 29 , , PUNCT iajs-2479 16 30 published publish VERB iajs-2479 16 31 in in ADP iajs-2479 16 32 july july PROPN iajs-2479 16 33 2020 2020 NUM iajs-2479 16 34 . . PUNCT iajs-2479 16 35     SPACE iajs-2479 17 1 141 141 NUM iajs-2479 17 2     SPACE iajs-2479 17 3 ibn ibn PROPN iajs-2479 17 4 al al PROPN iajs-2479 17 5 - - PUNCT iajs-2479 17 6 haitham haitham PROPN iajs-2479 17 7 jour jour X iajs-2479 17 8 . . PROPN iajs-2479 17 9 for for ADP iajs-2479 17 10 pure pure ADJ iajs-2479 17 11 & & CCONJ iajs-2479 17 12 appl appl PROPN iajs-2479 17 13 . . PUNCT iajs-2479 18 1 sci sci PROPN iajs-2479 18 2 . . PROPN iajs-2479 19 1 33 33 NUM iajs-2479 19 2 ( ( PUNCT iajs-2479 19 3 3 3 NUM iajs-2479 19 4 ) ) PUNCT iajs-2479 19 5 2020 2020 NUM iajs-2479 19 6 the the DET iajs-2479 19 7 completion completion NOUN iajs-2479 19 8 time time NOUN iajs-2479 19 9 : : PUNCT iajs-2479 19 10 this this DET iajs-2479 19 11 criterion criterion NOUN iajs-2479 19 12 has have AUX iajs-2479 19 13 been be AUX iajs-2479 19 14 extensively extensively ADV iajs-2479 19 15 studied study VERB iajs-2479 19 16 in in ADP iajs-2479 19 17 the the DET iajs-2479 19 18 literature literature NOUN iajs-2479 19 19 . . PUNCT iajs-2479 20 1 for for ADP iajs-2479 20 2 1 1 NUM iajs-2479 20 3 / / SYM iajs-2479 20 4 rj/∑cj rj/∑cj PROPN iajs-2479 20 5 is be AUX iajs-2479 20 6 nphard nphard ADJ iajs-2479 20 7 in in ADP iajs-2479 20 8 the the DET iajs-2479 20 9 strong strong ADJ iajs-2479 20 10 sense sense NOUN iajs-2479 20 11 by by ADP iajs-2479 20 12 lenstra lenstra NOUN iajs-2479 20 13 , , PUNCT iajs-2479 20 14 rinnooy rinnooy VERB iajs-2479 20 15 kan kan PROPN iajs-2479 20 16 and and CCONJ iajs-2479 20 17 bruker bruker VERB iajs-2479 21 1 [ [ X iajs-2479 21 2 2 2 NUM iajs-2479 21 3 ] ] PUNCT iajs-2479 21 4 . . PUNCT iajs-2479 22 1 this this DET iajs-2479 22 2 problem problem NOUN iajs-2479 22 3 with with ADP iajs-2479 22 4 equal equal ADJ iajs-2479 22 5 release release NOUN iajs-2479 22 6 date date NOUN iajs-2479 22 7 solved solve VERB iajs-2479 22 8 by by ADP iajs-2479 22 9 " " PUNCT iajs-2479 22 10 shortestprocessingtime shortestprocessingtime ADJ iajs-2479 22 11 ( ( PUNCT iajs-2479 22 12 spt)-rule spt)-rule NOUN iajs-2479 22 13 " " PUNCT iajs-2479 22 14 of of ADP iajs-2479 22 15 smith smith NOUN iajs-2479 23 1 [ [ X iajs-2479 23 2 3 3 NUM iajs-2479 23 3 ] ] PUNCT iajs-2479 23 4 . . PUNCT iajs-2479 24 1 also also ADV iajs-2479 24 2 , , PUNCT iajs-2479 24 3 the the DET iajs-2479 24 4 problem problem NOUN iajs-2479 24 5 1 1 NUM iajs-2479 24 6 / / SYM iajs-2479 24 7 rj rj PROPN iajs-2479 24 8 , , PUNCT iajs-2479 24 9 pmtn pmtn NOUN iajs-2479 24 10 /∑cj /∑cj PUNCT iajs-2479 24 11 is be AUX iajs-2479 24 12 possible possible ADJ iajs-2479 24 13 to to PART iajs-2479 24 14 solve solve VERB iajs-2479 24 15 by by ADP iajs-2479 24 16 the the DET iajs-2479 24 17 " " PUNCT iajs-2479 24 18 shortest short ADJ iajs-2479 24 19 remainingprocessingtime remainingprocessingtime NOUN iajs-2479 24 20 ( ( PUNCT iajs-2479 24 21 srpt)-rule srpt)-rule NOUN iajs-2479 24 22 " " PUNCT iajs-2479 24 23 of of ADP iajs-2479 24 24 schrage schrage NOUN iajs-2479 24 25 [ [ X iajs-2479 24 26 4 4 NUM iajs-2479 24 27 ] ] PUNCT iajs-2479 24 28 . . PUNCT iajs-2479 25 1 several several ADJ iajs-2479 25 2 branch branch NOUN iajs-2479 25 3 and and CCONJ iajs-2479 25 4 bound bind VERB iajs-2479 25 5 algorithms algorithm NOUN iajs-2479 25 6 for for ADP iajs-2479 25 7 the the DET iajs-2479 25 8 problem problem NOUN iajs-2479 25 9 1 1 NUM iajs-2479 25 10 / / SYM iajs-2479 25 11 rj/∑cj rj/∑cj PROPN iajs-2479 25 12 , , PUNCT iajs-2479 25 13 depend depend VERB iajs-2479 25 14 extensively extensively ADV iajs-2479 25 15 on on ADP iajs-2479 25 16 the the DET iajs-2479 25 17 " " PUNCT iajs-2479 25 18 dominance dominance NOUN iajs-2479 25 19 rules rule NOUN iajs-2479 25 20 ( ( PUNCT iajs-2479 25 21 dr dr PROPN iajs-2479 25 22 ) ) PUNCT iajs-2479 25 23 " " PUNCT iajs-2479 25 24 derived derive VERB iajs-2479 25 25 by by ADP iajs-2479 25 26 chandra chandra PROPN iajs-2479 25 27 [ [ X iajs-2479 25 28 5 5 NUM iajs-2479 25 29 ] ] PUNCT iajs-2479 25 30 . . PUNCT iajs-2479 26 1 dessouky dessouky NOUN iajs-2479 26 2 and and CCONJ iajs-2479 26 3 deogun deogun VERB iajs-2479 26 4 [ [ PUNCT iajs-2479 26 5 6 6 NUM iajs-2479 26 6 ] ] PUNCT iajs-2479 26 7 . . PUNCT iajs-2479 27 1 and and CCONJ iajs-2479 27 2 others other NOUN iajs-2479 27 3 . . PUNCT iajs-2479 28 1 for for ADP iajs-2479 28 2 this this DET iajs-2479 28 3 problem problem NOUN iajs-2479 28 4 , , PUNCT iajs-2479 28 5 ahmadi ahmadi NOUN iajs-2479 28 6 and and CCONJ iajs-2479 28 7 bghchi bghchi VERB iajs-2479 29 1 [ [ X iajs-2479 29 2 7 7 NUM iajs-2479 29 3 ] ] PUNCT iajs-2479 29 4 . . PUNCT iajs-2479 30 1 display display VERB iajs-2479 30 2 that that SCONJ iajs-2479 30 3 the the DET iajs-2479 30 4 lower lower ADV iajs-2479 30 5 bound bound ADJ iajs-2479 30 6 which which PRON iajs-2479 30 7 is be AUX iajs-2479 30 8 symbolized symbolize VERB iajs-2479 30 9 by by ADP iajs-2479 30 10 ( ( PUNCT iajs-2479 30 11 srptlb srptlb NOUN iajs-2479 30 12 ) ) PUNCT iajs-2479 30 13 obtained obtain VERB iajs-2479 30 14 by by ADP iajs-2479 30 15 using use VERB iajs-2479 30 16 the the DET iajs-2479 30 17 ( ( PUNCT iajs-2479 30 18 srpt)rule srpt)rule PROPN iajs-2479 30 19 to to PART iajs-2479 30 20 solve solve VERB iajs-2479 30 21 the the DET iajs-2479 30 22 problem problem NOUN iajs-2479 30 23 1 1 NUM iajs-2479 30 24 / / SYM iajs-2479 30 25 rj rj PROPN iajs-2479 30 26 , , PUNCT iajs-2479 30 27 pumt/∑cj pumt/∑cj ADV iajs-2479 30 28 best good ADJ iajs-2479 30 29 ( ( PUNCT iajs-2479 30 30 lb lb X iajs-2479 30 31 ) ) PUNCT iajs-2479 30 32 in in ADP iajs-2479 30 33 comparison comparison NOUN iajs-2479 30 34 other other ADJ iajs-2479 30 35 know know NOUN iajs-2479 30 36 bounds bound NOUN iajs-2479 30 37 . . PUNCT iajs-2479 31 1 also also ADV iajs-2479 31 2 , , PUNCT iajs-2479 31 3 chu chu PROPN iajs-2479 32 1 [ [ X iajs-2479 32 2 8 8 NUM iajs-2479 32 3 ] ] PUNCT iajs-2479 32 4 . . PUNCT iajs-2479 33 1 uses use VERB iajs-2479 33 2 this this PRON iajs-2479 33 3 ( ( PUNCT iajs-2479 33 4 srpt srpt NOUN iajs-2479 33 5 - - PUNCT iajs-2479 33 6 lb lb NOUN iajs-2479 33 7 ) ) PUNCT iajs-2479 33 8 in in ADP iajs-2479 33 9 ( ( PUNCT iajs-2479 33 10 b&b b&b PROPN iajs-2479 33 11 ) ) PUNCT iajs-2479 33 12 algorithm algorithm NOUN iajs-2479 33 13 that that PRON iajs-2479 33 14 is be AUX iajs-2479 33 15 effective effective ADJ iajs-2479 33 16 in in ADP iajs-2479 33 17 solving solve VERB iajs-2479 33 18 problems problem NOUN iajs-2479 33 19 , , PUNCT iajs-2479 33 20 when when SCONJ iajs-2479 33 21 n n PRON iajs-2479 33 22 ≤ ≤ ADV iajs-2479 33 23 100 100 NUM iajs-2479 33 24 jobs job NOUN iajs-2479 33 25 . . PUNCT iajs-2479 34 1 the the DET iajs-2479 34 2 tardiness tardiness ADJ iajs-2479 34 3 time time NOUN iajs-2479 34 4 : : PUNCT iajs-2479 34 5 minimizing minimize VERB iajs-2479 34 6 the the DET iajs-2479 34 7 total total ADJ iajs-2479 34 8 tardiness tardiness NOUN iajs-2479 34 9 is be AUX iajs-2479 34 10 the the DET iajs-2479 34 11 other other ADJ iajs-2479 34 12 one one NUM iajs-2479 34 13 of of ADP iajs-2479 34 14 the the DET iajs-2479 34 15 most most ADV iajs-2479 34 16 important important ADJ iajs-2479 34 17 criteria criterion NOUN iajs-2479 34 18 in in ADP iajs-2479 34 19 practice practice NOUN iajs-2479 34 20 . . PUNCT iajs-2479 35 1 for for ADP iajs-2479 35 2 1 1 NUM iajs-2479 35 3 / / SYM iajs-2479 35 4 rj/∑tj rj/∑tj PROPN iajs-2479 35 5 is be AUX iajs-2479 35 6 known know VERB iajs-2479 35 7 to to PART iajs-2479 35 8 be be AUX iajs-2479 35 9 nphard nphard ADJ iajs-2479 35 10 in in ADP iajs-2479 35 11 the the DET iajs-2479 35 12 strong strong ADJ iajs-2479 35 13 sense sense NOUN iajs-2479 35 14 by by ADP iajs-2479 35 15 rinnooy rinnooy NOUN iajs-2479 36 1 [ [ X iajs-2479 36 2 9 9 NUM iajs-2479 36 3 ] ] PUNCT iajs-2479 36 4 . . PUNCT iajs-2479 36 5     SPACE iajs-2479 36 6 chu chu PROPN iajs-2479 37 1 [ [ X iajs-2479 37 2 10 10 NUM iajs-2479 37 3 ] ] PUNCT iajs-2479 37 4 . . PUNCT iajs-2479 38 1 proposes propose VERB iajs-2479 38 2 a a DET iajs-2479 38 3 ( ( PUNCT iajs-2479 38 4 bab bab PROPN iajs-2479 38 5 ) ) PUNCT iajs-2479 38 6 algorithm algorithm NOUN iajs-2479 38 7 and and CCONJ iajs-2479 38 8 proves prove VERB iajs-2479 38 9 some some DET iajs-2479 38 10 dominance dominance NOUN iajs-2479 38 11 properties property NOUN iajs-2479 38 12 . . PUNCT iajs-2479 38 13     SPACE iajs-2479 39 1 also also ADV iajs-2479 39 2 suggested suggest VERB iajs-2479 39 3 , , PUNCT iajs-2479 39 4 ( ( PUNCT iajs-2479 39 5 lb lb X iajs-2479 39 6 ) ) PUNCT iajs-2479 39 7 depends depend VERB iajs-2479 39 8 on on ADP iajs-2479 39 9 constructing construct VERB iajs-2479 39 10 a a DET iajs-2479 39 11 schedule schedule NOUN iajs-2479 39 12 in in ADP iajs-2479 39 13 which which PRON iajs-2479 39 14 the the DET iajs-2479 39 15 jobs job NOUN iajs-2479 39 16 are be AUX iajs-2479 39 17 scheduled schedule VERB iajs-2479 39 18 according accord VERB iajs-2479 39 19 to to ADP iajs-2479 39 20 ( ( PUNCT iajs-2479 39 21 srpt)-rule srpt)-rule NOUN iajs-2479 39 22 ( ( PUNCT iajs-2479 39 23 schrage schrage NOUN iajs-2479 39 24 [ [ X iajs-2479 39 25 4 4 NUM iajs-2479 39 26 ] ] PUNCT iajs-2479 39 27 . . PUNCT iajs-2479 39 28 ) ) PUNCT iajs-2479 40 1 by by ADP iajs-2479 40 2 restful restful ADJ iajs-2479 40 3 the the DET iajs-2479 40 4 problem problem NOUN iajs-2479 40 5 under under ADP iajs-2479 40 6 the the DET iajs-2479 40 7 presumption presumption NOUN iajs-2479 40 8 that that SCONJ iajs-2479 40 9 the the DET iajs-2479 40 10 jobs job NOUN iajs-2479 40 11 are be AUX iajs-2479 40 12 preemptive preemptive ADJ iajs-2479 40 13 . . PUNCT iajs-2479 41 1 the the DET iajs-2479 41 2 proposed propose VERB iajs-2479 41 3 algorithm algorithm NOUN iajs-2479 41 4 contributed contribute VERB iajs-2479 41 5 to to PART iajs-2479 41 6 solve solve VERB iajs-2479 41 7 problems problem NOUN iajs-2479 41 8 , , PUNCT iajs-2479 41 9 when when SCONJ iajs-2479 41 10 n n DET iajs-2479 41 11 ≤ ≤ NUM iajs-2479 41 12 260 260 NUM iajs-2479 41 13 jobs job NOUN iajs-2479 41 14 . . PUNCT iajs-2479 41 15     SPACE iajs-2479 42 1 philippe philippe PROPN iajs-2479 42 2 et et PROPN iajs-2479 42 3 al al PROPN iajs-2479 43 1 [ [ X iajs-2479 43 2 11 11 NUM iajs-2479 43 3 ] ] PUNCT iajs-2479 43 4 . . PUNCT iajs-2479 44 1 presented present VERB iajs-2479 44 2 a a DET iajs-2479 44 3 ( ( PUNCT iajs-2479 44 4 b&b b&b PROPN iajs-2479 44 5 ) ) PUNCT iajs-2479 44 6 algorithm algorithm NOUN iajs-2479 44 7 with with ADP iajs-2479 44 8 new new ADJ iajs-2479 44 9 lower low ADJ iajs-2479 44 10 bounds bound NOUN iajs-2479 44 11 ( ( PUNCT iajs-2479 44 12 nlb nlb PROPN iajs-2479 44 13 ) ) PUNCT iajs-2479 44 14 depending depend VERB iajs-2479 44 15 on on ADP iajs-2479 44 16 improve improve NOUN iajs-2479 44 17 ( ( PUNCT iajs-2479 44 18 lb lb NOUN iajs-2479 44 19 ) ) PUNCT iajs-2479 44 20 of of ADP iajs-2479 44 21 chu chu PROPN iajs-2479 45 1 [ [ X iajs-2479 45 2 10 10 NUM iajs-2479 45 3 ] ] PUNCT iajs-2479 45 4 . . PUNCT iajs-2479 46 1 and and CCONJ iajs-2479 46 2 generalization generalization NOUN iajs-2479 46 3 some some DET iajs-2479 46 4 well well ADV iajs-2479 46 5 – – PUNCT iajs-2479 46 6 known know VERB iajs-2479 46 7 dominance dominance NOUN iajs-2479 46 8 properties property NOUN iajs-2479 46 9 to to PART iajs-2479 46 10 solve solve VERB iajs-2479 46 11 this this DET iajs-2479 46 12 1 1 NUM iajs-2479 46 13 / / SYM iajs-2479 46 14 rj/∑tj rj/∑tj PROPN iajs-2479 46 15 problem problem NOUN iajs-2479 46 16 . . PUNCT iajs-2479 47 1 the the DET iajs-2479 47 2 cases case NOUN iajs-2479 47 3 handled handle VERB iajs-2479 47 4 by by ADP iajs-2479 47 5 this this DET iajs-2479 47 6 procedure procedure NOUN iajs-2479 47 7 are be AUX iajs-2479 47 8 as as ADP iajs-2479 47 9 500 500 NUM iajs-2479 47 10 jobs job NOUN iajs-2479 47 11 . . PUNCT iajs-2479 48 1 the the DET iajs-2479 48 2 earliness earliness ADJ iajs-2479 48 3 time time NOUN iajs-2479 48 4 : : PUNCT iajs-2479 48 5 in in ADP iajs-2479 48 6 general general ADJ iajs-2479 48 7 , , PUNCT iajs-2479 48 8 earliness earliness ADJ iajs-2479 48 9 criterion criterion NOUN iajs-2479 48 10 is be AUX iajs-2479 48 11 one one NUM iajs-2479 48 12 of of ADP iajs-2479 48 13 the the DET iajs-2479 48 14 scheduling scheduling NOUN iajs-2479 48 15 objectives objective NOUN iajs-2479 48 16 studied study VERB iajs-2479 48 17 by by ADP iajs-2479 48 18 few few ADJ iajs-2479 48 19 number number NOUN iajs-2479 48 20 of of ADP iajs-2479 48 21 researchers researcher NOUN iajs-2479 48 22 , , PUNCT iajs-2479 48 23 because because SCONJ iajs-2479 48 24 for for ADP iajs-2479 48 25 many many ADJ iajs-2479 48 26 years year NOUN iajs-2479 48 27 , , PUNCT iajs-2479 48 28 researchers researcher NOUN iajs-2479 48 29 focused focus VERB iajs-2479 48 30 on on ADP iajs-2479 48 31 one one NUM iajs-2479 48 32 - - PUNCT iajs-2479 48 33 criterion criterion NOUN iajs-2479 48 34 regular regular ADJ iajs-2479 48 35 performance performance NOUN iajs-2479 48 36 measures measure NOUN iajs-2479 48 37 ( ( PUNCT iajs-2479 48 38 i.e. i.e. X iajs-2479 48 39 no no DET iajs-2479 48 40 decreasing decrease VERB iajs-2479 48 41 in in ADP iajs-2479 48 42 cj cj NOUN iajs-2479 48 43 for for ADP iajs-2479 48 44 all all DET iajs-2479 48 45 j j NOUN iajs-2479 48 46 ) ) PUNCT iajs-2479 49 1 [ [ X iajs-2479 49 2 12 12 NUM iajs-2479 49 3 ] ] PUNCT iajs-2479 49 4 . . PUNCT iajs-2479 50 1 and and CCONJ iajs-2479 50 2 most most ADJ iajs-2479 50 3 research research NOUN iajs-2479 50 4 that that PRON iajs-2479 50 5 considers consider VERB iajs-2479 50 6 earliness earliness NOUN iajs-2479 50 7 as as ADP iajs-2479 50 8 an an DET iajs-2479 50 9 optimality optimality NOUN iajs-2479 50 10 criterion criterion NOUN iajs-2479 50 11 also also ADV iajs-2479 50 12 includes include VERB iajs-2479 50 13 a a DET iajs-2479 50 14 tardiness tardiness ADJ iajs-2479 50 15 component component NOUN iajs-2479 50 16 . . PUNCT iajs-2479 51 1 the the DET iajs-2479 51 2 first first ADJ iajs-2479 51 3 study study NOUN iajs-2479 51 4 on on ADP iajs-2479 51 5 earliness earliness NOUN iajs-2479 51 6 and and CCONJ iajs-2479 51 7 tardiness tardiness NOUN iajs-2479 51 8 ( ( PUNCT iajs-2479 51 9 e e NOUN iajs-2479 51 10 / / SYM iajs-2479 51 11 t t NOUN iajs-2479 51 12 ) ) PUNCT iajs-2479 51 13 penalties penalty NOUN iajs-2479 51 14 was be AUX iajs-2479 51 15 by by ADP iajs-2479 51 16 sidney sidney NOUN iajs-2479 52 1 [ [ X iajs-2479 52 2 13 13 NUM iajs-2479 52 3 ] ] PUNCT iajs-2479 52 4 . . PUNCT iajs-2479 53 1 who who PRON iajs-2479 53 2 developed develop VERB iajs-2479 53 3 a a DET iajs-2479 53 4 polynomial polynomial ADJ iajs-2479 53 5 - - PUNCT iajs-2479 53 6 algorithm algorithm NOUN iajs-2479 53 7 to to PART iajs-2479 53 8 minimize minimize VERB iajs-2479 53 9 maximum maximum ADJ iajs-2479 53 10 of of ADP iajs-2479 53 11 ( ( PUNCT iajs-2479 53 12 e e PROPN iajs-2479 53 13 / / SYM iajs-2479 53 14 t t PROPN iajs-2479 53 15 ) ) PUNCT iajs-2479 53 16 for for ADP iajs-2479 53 17 a a DET iajs-2479 53 18 single single ADJ iajs-2479 53 19 machine machine NOUN iajs-2479 53 20 problem problem NOUN iajs-2479 53 21 . . PUNCT iajs-2479 54 1 one one NUM iajs-2479 54 2 of of ADP iajs-2479 54 3 the the DET iajs-2479 54 4 studies study NOUN iajs-2479 54 5 presented present VERB iajs-2479 54 6 in in ADP iajs-2479 54 7 recent recent ADJ iajs-2479 54 8 years year NOUN iajs-2479 54 9 was be AUX iajs-2479 54 10 by by ADP iajs-2479 54 11 mehdi mehdi NOUN iajs-2479 54 12 and and CCONJ iajs-2479 54 13 ghasem ghasem PROPN iajs-2479 55 1 [ [ X iajs-2479 55 2 14 14 NUM iajs-2479 55 3 ] ] PUNCT iajs-2479 55 4 . . PUNCT iajs-2479 56 1 who who PRON iajs-2479 56 2     SPACE iajs-2479 56 3 studied study VERB iajs-2479 56 4 this this DET iajs-2479 56 5 problem problem NOUN iajs-2479 56 6 1 1 NUM iajs-2479 56 7 / / SYM iajs-2479 56 8 rj rj PROPN iajs-2479 56 9 / / SYM iajs-2479 56 10 emax emax PROPN iajs-2479 57 1 + + ADV iajs-2479 57 2 tmax tmax ADJ iajs-2479 57 3 . . PUNCT iajs-2479 58 1 a a DET iajs-2479 58 2 ( ( PUNCT iajs-2479 58 3 b&b b&b PROPN iajs-2479 58 4 ) ) PUNCT iajs-2479 58 5 algorithm algorithm NOUN iajs-2479 58 6 is be AUX iajs-2479 58 7 proposed propose VERB iajs-2479 58 8 , , PUNCT iajs-2479 58 9 the the DET iajs-2479 58 10 algorithm algorithm NOUN iajs-2479 58 11 extensively extensively ADV iajs-2479 58 12 uses use VERB iajs-2479 58 13 efficient efficient ADJ iajs-2479 58 14 dominance dominance NOUN iajs-2479 58 15 rules rule NOUN iajs-2479 58 16 . . PUNCT iajs-2479 59 1 in in ADP iajs-2479 59 2 the the DET iajs-2479 59 3 ( ( PUNCT iajs-2479 59 4 b&b b&b PROPN iajs-2479 59 5 ) ) PUNCT iajs-2479 59 6 algorithm algorithm NOUN iajs-2479 59 7 , , PUNCT iajs-2479 59 8 a a DET iajs-2479 59 9 ( ( PUNCT iajs-2479 59 10 lb lb NOUN iajs-2479 59 11 ) ) PUNCT iajs-2479 59 12 , , PUNCT iajs-2479 59 13 is be AUX iajs-2479 59 14 obtained obtain VERB iajs-2479 59 15 by by ADP iajs-2479 59 16 relaxing relax VERB iajs-2479 59 17 the the DET iajs-2479 59 18 assumption assumption NOUN iajs-2479 59 19 of of ADP iajs-2479 59 20 the the DET iajs-2479 59 21 non non NOUN iajs-2479 59 22 - - NOUN iajs-2479 59 23 preemption preemption NOUN iajs-2479 59 24 , , PUNCT iajs-2479 59 25 and and CCONJ iajs-2479 59 26 divided divide VERB iajs-2479 59 27 the the DET iajs-2479 59 28 problem problem NOUN iajs-2479 59 29 into into ADP iajs-2479 59 30 two two NUM iajs-2479 59 31 sub sub NOUN iajs-2479 59 32 - - NOUN iajs-2479 59 33 problems problem NOUN iajs-2479 59 34 of of ADP iajs-2479 59 35 ( ( PUNCT iajs-2479 59 36 1 1 NUM iajs-2479 59 37 / / SYM iajs-2479 59 38 rj rj PROPN iajs-2479 59 39 , , PUNCT iajs-2479 59 40 pmtn pmtn NOUN iajs-2479 59 41 / / SYM iajs-2479 59 42 tmax tmax PRON iajs-2479 59 43 ) ) PUNCT iajs-2479 59 44 and and CCONJ iajs-2479 59 45 ( ( PUNCT iajs-2479 59 46 1 1 NUM iajs-2479 59 47 / / SYM iajs-2479 59 48 rj rj PROPN iajs-2479 59 49 , , PUNCT iajs-2479 59 50 pmtn pmtn NOUN iajs-2479 59 51 / / SYM iajs-2479 59 52 emax emax NOUN iajs-2479 59 53 ) ) PUNCT iajs-2479 59 54 . . PUNCT iajs-2479 60 1 the the DET iajs-2479 60 2 two two NUM iajs-2479 60 3 problems problem NOUN iajs-2479 60 4 are be AUX iajs-2479 60 5 then then ADV iajs-2479 60 6 resolved resolve VERB iajs-2479 60 7 by by ADP iajs-2479 60 8 applying apply VERB iajs-2479 60 9 some some DET iajs-2479 60 10 procedures procedure NOUN iajs-2479 60 11 derived derive VERB iajs-2479 60 12 from from ADP iajs-2479 60 13 the the DET iajs-2479 60 14 two two NUM iajs-2479 60 15 rules rule NOUN iajs-2479 60 16 , , PUNCT iajs-2479 60 17 ( ( PUNCT iajs-2479 60 18 edd edd PROPN iajs-2479 60 19 ) ) PUNCT iajs-2479 60 20 and and CCONJ iajs-2479 60 21 ( ( PUNCT iajs-2479 60 22 mst mst PROPN iajs-2479 60 23 ) ) PUNCT iajs-2479 60 24 . . PUNCT iajs-2479 61 1 computational computational ADJ iajs-2479 61 2 experiments experiment NOUN iajs-2479 61 3 showed show VERB iajs-2479 61 4 the the DET iajs-2479 61 5 efficiency efficiency NOUN iajs-2479 61 6 of of ADP iajs-2479 61 7 the the DET iajs-2479 61 8 proposed propose VERB iajs-2479 61 9 procedure procedure NOUN iajs-2479 61 10 of of ADP iajs-2479 61 11 solving solve VERB iajs-2479 61 12 problems problem NOUN iajs-2479 61 13 with with ADP iajs-2479 61 14 up up ADP iajs-2479 61 15 to to PART iajs-2479 61 16 1000 1000 NUM iajs-2479 61 17 jobs job NOUN iajs-2479 61 18 . . PUNCT iajs-2479 62 1 the the DET iajs-2479 62 2 late late ADJ iajs-2479 62 3 work work NOUN iajs-2479 62 4 : : PUNCT iajs-2479 62 5 is be AUX iajs-2479 62 6 the the DET iajs-2479 62 7 quantity quantity NOUN iajs-2479 62 8 of of ADP iajs-2479 62 9 processing processing NOUN iajs-2479 62 10 performed perform VERB iajs-2479 62 11 after after ADP iajs-2479 62 12 its its PRON iajs-2479 62 13 due due ADJ iajs-2479 62 14 date date NOUN iajs-2479 62 15 , , PUNCT iajs-2479 62 16 and and CCONJ iajs-2479 62 17 is be AUX iajs-2479 62 18 denoted denote VERB iajs-2479 62 19 by by ADP iajs-2479 62 20 ( ( PUNCT iajs-2479 62 21 vj vj INTJ iajs-2479 62 22 ) ) PUNCT iajs-2479 62 23 . . PUNCT iajs-2479 63 1 at at ADP iajs-2479 63 2 first first ADV iajs-2479 63 3 , , PUNCT iajs-2479 63 4 this this DET iajs-2479 63 5 problem problem NOUN iajs-2479 63 6 was be AUX iajs-2479 63 7 known know VERB iajs-2479 63 8 as as ADP iajs-2479 63 9 information information NOUN iajs-2479 63 10 loss loss NOUN iajs-2479 63 11 by by ADP iajs-2479 63 12 blazewicz blazewicz NOUN iajs-2479 63 13 [ [ X iajs-2479 63 14 15 15 NUM iajs-2479 63 15 ] ] PUNCT iajs-2479 63 16 . . PUNCT iajs-2479 64 1 potts potts PROPN iajs-2479 64 2 and and CCONJ iajs-2479 64 3 van van PROPN iajs-2479 64 4 [ [ PUNCT iajs-2479 64 5 16 16 NUM iajs-2479 64 6 , , PUNCT iajs-2479 64 7 17 17 NUM iajs-2479 64 8 ] ] PUNCT iajs-2479 64 9 . . PUNCT iajs-2479 65 1 suggested suggest VERB iajs-2479 65 2 the the DET iajs-2479 65 3 term term NOUN iajs-2479 65 4 ( ( PUNCT iajs-2479 65 5 total total ADJ iajs-2479 65 6 late late ADJ iajs-2479 65 7 work work NOUN iajs-2479 65 8 ) ) PUNCT iajs-2479 65 9 . . PUNCT iajs-2479 66 1 for for ADP iajs-2479 66 2 the the DET iajs-2479 66 3 problem problem NOUN iajs-2479 66 4 1 1 NUM iajs-2479 66 5 / / SYM iajs-2479 66 6 pmtn/∑vj pmtn/∑vj NUM iajs-2479 66 7 , , PUNCT iajs-2479 66 8 they they PRON iajs-2479 66 9 showed show VERB iajs-2479 66 10 that that SCONJ iajs-2479 66 11 the the DET iajs-2479 66 12 minimum minimum NOUN iajs-2479 66 13 ( ( PUNCT iajs-2479 66 14 1//∑vj 1//∑vj NUM iajs-2479 66 15 ) ) PUNCT iajs-2479 66 16 ≤ ≤ NOUN iajs-2479 67 1 [ [ X iajs-2479 67 2 ( ( PUNCT iajs-2479 67 3 tmax tmax NOUN iajs-2479 67 4 ) ) PUNCT iajs-2479 67 5 for for ADP iajs-2479 67 6 the the DET iajs-2479 67 7 ( ( PUNCT iajs-2479 67 8 edd)-rule edd)-rule ADJ iajs-2479 67 9 sequence sequence NOUN iajs-2479 67 10 ] ] PUNCT iajs-2479 67 11 . . PUNCT iajs-2479 68 1 while while SCONJ iajs-2479 68 2 the the DET iajs-2479 68 3 problem problem NOUN iajs-2479 68 4 1//∑vj 1//∑vj NUM iajs-2479 68 5 is be AUX iajs-2479 68 6 np np INTJ iajs-2479 68 7 - - PUNCT iajs-2479 68 8 hard hard ADJ iajs-2479 68 9 by by ADP iajs-2479 68 10 potts pott NOUN iajs-2479 68 11 and and CCONJ iajs-2479 68 12 van van PROPN iajs-2479 68 13 [ [ X iajs-2479 68 14 17 17 NUM iajs-2479 68 15 ] ] PUNCT iajs-2479 68 16 . . PUNCT iajs-2479 69 1 bryan bryan PROPN iajs-2479 69 2 and and CCONJ iajs-2479 69 3 bahram bahram PROPN iajs-2479 70 1 [ [ X iajs-2479 70 2 18 18 NUM iajs-2479 70 3 ] ] PUNCT iajs-2479 70 4 . . PUNCT iajs-2479 71 1 in in ADP iajs-2479 71 2 this this DET iajs-2479 71 3 research research NOUN iajs-2479 71 4 , , PUNCT iajs-2479 71 5 considering consider VERB iajs-2479 71 6 1//∑ 1//∑ NUM iajs-2479 71 7 wj wj PROPN iajs-2479 71 8 vj vj PROPN iajs-2479 71 9 the the DET iajs-2479 71 10 total total NOUN iajs-2479 71 11 weighted weight VERB iajs-2479 71 12 late late ADJ iajs-2479 71 13 work work NOUN iajs-2479 71 14 , , PUNCT iajs-2479 71 15 with with ADP iajs-2479 71 16 the the DET iajs-2479 71 17 condition condition NOUN iajs-2479 71 18 that that SCONJ iajs-2479 71 19 all all DET iajs-2479 71 20 jobs job NOUN iajs-2479 71 21 arrived arrive VERB iajs-2479 71 22 at at ADP iajs-2479 71 23 the the DET iajs-2479 71 24 same same ADJ iajs-2479 71 25 time time NOUN iajs-2479 71 26 ( ( PUNCT iajs-2479 71 27 i.e. i.e. X iajs-2479 71 28 the the DET iajs-2479 71 29 release release NOUN iajs-2479 71 30 date date NOUN iajs-2479 71 31 rj= rj= NOUN iajs-2479 71 32 0 0 PUNCT iajs-2479 71 33 for for ADP iajs-2479 71 34 all all DET iajs-2479 71 35 jobs job NOUN iajs-2479 71 36 ) ) PUNCT iajs-2479 71 37 . . PUNCT iajs-2479 72 1 this this DET iajs-2479 72 2 function function NOUN iajs-2479 72 3 is be AUX iajs-2479 72 4 a a DET iajs-2479 72 5 more more ADV iajs-2479 72 6 general general ADJ iajs-2479 72 7 form form NOUN iajs-2479 72 8 than than ADP iajs-2479 72 9 the the DET iajs-2479 72 10 formula formula NOUN iajs-2479 72 11 potts pott NOUN iajs-2479 72 12 and and CCONJ iajs-2479 72 13 van van PROPN iajs-2479 72 14 [ [ PUNCT iajs-2479 72 15 16 16 NUM iajs-2479 72 16 , , PUNCT iajs-2479 72 17 17 17 NUM iajs-2479 72 18 ] ] PUNCT iajs-2479 72 19 . . PUNCT iajs-2479 73 1 abdul abdul PROPN iajs-2479 73 2 razaq razaq PROPN iajs-2479 73 3 et et PROPN iajs-2479 73 4 al al PROPN iajs-2479 74 1 [ [ X iajs-2479 74 2 19 19 NUM iajs-2479 74 3 ] ] PUNCT iajs-2479 74 4 . . PUNCT iajs-2479 74 5     SPACE iajs-2479 75 1 142 142 NUM iajs-2479 75 2     SPACE iajs-2479 75 3 ibn ibn PROPN iajs-2479 75 4 al al PROPN iajs-2479 75 5 - - PUNCT iajs-2479 75 6 haitham haitham PROPN iajs-2479 75 7 jour jour X iajs-2479 75 8 . . PROPN iajs-2479 75 9 for for ADP iajs-2479 75 10 pure pure ADJ iajs-2479 75 11 & & CCONJ iajs-2479 75 12 appl appl PROPN iajs-2479 75 13 . . PUNCT iajs-2479 76 1 sci sci PROPN iajs-2479 76 2 . . PROPN iajs-2479 77 1 33 33 NUM iajs-2479 77 2 ( ( PUNCT iajs-2479 77 3 3 3 NUM iajs-2479 77 4 ) ) PUNCT iajs-2479 77 5 2020 2020 NUM iajs-2479 77 6 studied study VERB iajs-2479 77 7 this this DET iajs-2479 77 8 1 1 NUM iajs-2479 77 9 / / SYM iajs-2479 77 10 rj/∑wjvj rj/∑wjvj ADJ iajs-2479 77 11 problem problem NOUN iajs-2479 77 12 , , PUNCT iajs-2479 77 13 using use VERB iajs-2479 77 14 unequal unequal ADJ iajs-2479 77 15 release release NOUN iajs-2479 77 16 dates date NOUN iajs-2479 77 17 , , PUNCT iajs-2479 77 18 to to PART iajs-2479 77 19 solve solve VERB iajs-2479 77 20 this this DET iajs-2479 77 21 problem problem NOUN iajs-2479 77 22 some some DET iajs-2479 77 23 special special ADJ iajs-2479 77 24 cases case NOUN iajs-2479 77 25 were be AUX iajs-2479 77 26 proofed proof VERB iajs-2479 77 27 and and CCONJ iajs-2479 77 28 using use VERB iajs-2479 77 29 a a DET iajs-2479 77 30 branch branch NOUN iajs-2479 77 31 and and CCONJ iajs-2479 77 32 bound bind VERB iajs-2479 77 33 algorithm algorithm NOUN iajs-2479 77 34 with with ADP iajs-2479 77 35 up up ADP iajs-2479 77 36 to to PART iajs-2479 77 37 30 30 NUM iajs-2479 77 38 jobs job NOUN iajs-2479 77 39 . . PUNCT iajs-2479 78 1 also also ADV iajs-2479 78 2 five five NUM iajs-2479 78 3 local local ADJ iajs-2479 78 4 search search NOUN iajs-2479 78 5 methods method NOUN iajs-2479 78 6 to to PART iajs-2479 78 7 solve solve VERB iajs-2479 78 8 this this DET iajs-2479 78 9 problem problem NOUN iajs-2479 78 10 were be AUX iajs-2479 78 11 applied apply VERB iajs-2479 78 12 and and CCONJ iajs-2479 78 13 performance performance NOUN iajs-2479 78 14 is be AUX iajs-2479 78 15 evaluated evaluate VERB iajs-2479 78 16 to to ADP iajs-2479 78 17 it it PRON iajs-2479 78 18 with with ADP iajs-2479 78 19 up up ADP iajs-2479 78 20 to to PART iajs-2479 78 21 60000 60000 NUM iajs-2479 78 22 jobs job NOUN iajs-2479 78 23 , , PUNCT iajs-2479 78 24 and and CCONJ iajs-2479 78 25 who who PRON iajs-2479 78 26 showed show VERB iajs-2479 78 27 this this DET iajs-2479 78 28 problem problem NOUN iajs-2479 78 29 its its PRON iajs-2479 78 30 np np INTJ iajs-2479 78 31 - - PUNCT iajs-2479 78 32 hard hard ADJ iajs-2479 78 33 . . PUNCT iajs-2479 79 1 the the DET iajs-2479 79 2 unit unit NOUN iajs-2479 79 3 penalty penalty NOUN iajs-2479 79 4 : : PUNCT iajs-2479 79 5 for for ADP iajs-2479 79 6 the the DET iajs-2479 79 7 1//∑uj 1//∑uj NUM iajs-2479 79 8 , , PUNCT iajs-2479 79 9 moore moore PROPN iajs-2479 80 1 [ [ X iajs-2479 80 2 20 20 NUM iajs-2479 80 3 ] ] PUNCT iajs-2479 80 4 . . PUNCT iajs-2479 81 1 study study NOUN iajs-2479 81 2 was be AUX iajs-2479 81 3 among among ADP iajs-2479 81 4 the the DET iajs-2479 81 5 earliest early ADJ iajs-2479 81 6 to to PART iajs-2479 81 7 consider consider VERB iajs-2479 81 8 scheduling scheduling NOUN iajs-2479 81 9 to to PART iajs-2479 81 10 minimize minimize VERB iajs-2479 81 11 this this DET iajs-2479 81 12 problem problem NOUN iajs-2479 81 13 by by ADP iajs-2479 81 14 an an DET iajs-2479 81 15 algorithm algorithm NOUN iajs-2479 81 16 known know VERB iajs-2479 81 17 as as ADP iajs-2479 81 18 moor moor PROPN iajs-2479 81 19 algorithm algorithm NOUN iajs-2479 81 20 “ " PUNCT iajs-2479 81 21 sometimes sometimes ADV iajs-2479 81 22 known know VERB iajs-2479 81 23 as as ADP iajs-2479 81 24 hudgson hudgson NOUN iajs-2479 81 25 's 's PART iajs-2479 81 26 algorithm algorithm NOUN iajs-2479 81 27 " " PUNCT iajs-2479 81 28 that that PRON iajs-2479 81 29 solved solve VERB iajs-2479 81 30 the the DET iajs-2479 81 31 problem problem NOUN iajs-2479 81 32 optimally optimally ADV iajs-2479 81 33 . . PUNCT iajs-2479 82 1 with with ADP iajs-2479 82 2 release release NOUN iajs-2479 82 3 dates date NOUN iajs-2479 82 4 , , PUNCT iajs-2479 82 5 the the DET iajs-2479 82 6 problem problem NOUN iajs-2479 82 7 1 1 X iajs-2479 82 8 / / SYM iajs-2479 82 9 rj/∑uj rj/∑uj VERB iajs-2479 82 10 is be AUX iajs-2479 82 11 strongly strongly ADV iajs-2479 82 12 nphard nphard ADJ iajs-2479 82 13 by by ADP iajs-2479 82 14 lenstra lenstra PROPN iajs-2479 82 15 et et PROPN iajs-2479 82 16 al al PROPN iajs-2479 83 1 [ [ X iajs-2479 83 2 2 2 NUM iajs-2479 83 3 ] ] PUNCT iajs-2479 83 4 . . PUNCT iajs-2479 84 1 dauzereperes dauzerepere NOUN iajs-2479 85 1 [ [ X iajs-2479 85 2 21 21 NUM iajs-2479 85 3 ] ] PUNCT iajs-2479 85 4 . . PUNCT iajs-2479 86 1 studied study VERB iajs-2479 86 2 this1 this1 NOUN iajs-2479 86 3 / / SYM iajs-2479 86 4 rj/∑uj rj/∑uj VERB iajs-2479 86 5 problem problem NOUN iajs-2479 86 6 , , PUNCT iajs-2479 86 7 and and CCONJ iajs-2479 86 8 determined determine VERB iajs-2479 86 9 a a DET iajs-2479 86 10 lower lower ADV iajs-2479 86 11 bound bind VERB iajs-2479 86 12 depending depend VERB iajs-2479 86 13 on on ADP iajs-2479 86 14 the the DET iajs-2479 86 15 relaxation relaxation NOUN iajs-2479 86 16 of of ADP iajs-2479 86 17 a a DET iajs-2479 86 18 " " PUNCT iajs-2479 86 19 mixed mixed ADJ iajs-2479 86 20 - - PUNCT iajs-2479 86 21 integerlinearprogramming integerlinearprogramming ADJ iajs-2479 86 22 " " PUNCT iajs-2479 86 23 formulation formulation NOUN iajs-2479 86 24 , , PUNCT iajs-2479 86 25 presented present VERB iajs-2479 86 26 a a DET iajs-2479 86 27 heuristic heuristic ADJ iajs-2479 86 28 method method NOUN iajs-2479 86 29 to to PART iajs-2479 86 30 solve solve VERB iajs-2479 86 31 the the DET iajs-2479 86 32 problem problem NOUN iajs-2479 86 33 . . PUNCT iajs-2479 87 1 a a DET iajs-2479 87 2 large large ADJ iajs-2479 87 3 sample sample NOUN iajs-2479 87 4 of of ADP iajs-2479 87 5 problems problem NOUN iajs-2479 87 6 has have AUX iajs-2479 87 7 been be AUX iajs-2479 87 8 tested test VERB iajs-2479 87 9 with with ADP iajs-2479 87 10 up up ADP iajs-2479 87 11 to to PART iajs-2479 87 12 50 50 NUM iajs-2479 87 13 jobs job NOUN iajs-2479 87 14 . . PUNCT iajs-2479 88 1 the the DET iajs-2479 88 2 calculations calculation NOUN iajs-2479 88 3 showed show VERB iajs-2479 88 4 the the DET iajs-2479 88 5 efficiency efficiency NOUN iajs-2479 88 6 of of ADP iajs-2479 88 7 the the DET iajs-2479 88 8 proposed propose VERB iajs-2479 88 9 approach approach NOUN iajs-2479 88 10 by by ADP iajs-2479 88 11 comparison comparison NOUN iajs-2479 88 12 with with ADP iajs-2479 88 13 the the DET iajs-2479 88 14 lower low ADJ iajs-2479 88 15 bound bind VERB iajs-2479 88 16 . . PUNCT iajs-2479 89 1 philippe philippe PROPN iajs-2479 89 2 et et PROPN iajs-2479 89 3 al al PROPN iajs-2479 90 1 [ [ X iajs-2479 90 2 22 22 NUM iajs-2479 90 3 ] ] PUNCT iajs-2479 90 4 . . PUNCT iajs-2479 91 1 to to PART iajs-2479 91 2 solved solved VERB iajs-2479 91 3 this this DET iajs-2479 91 4 1 1 NUM iajs-2479 91 5 / / SYM iajs-2479 91 6 rj/∑uj rj/∑uj VERB iajs-2479 91 7 problem problem NOUN iajs-2479 91 8 , , PUNCT iajs-2479 91 9 who who PRON iajs-2479 91 10 suggesting suggest VERB iajs-2479 91 11 ( ( PUNCT iajs-2479 91 12 b&b b&b PROPN iajs-2479 91 13 ) ) PUNCT iajs-2479 91 14 algorithm algorithm NOUN iajs-2479 91 15 , , PUNCT iajs-2479 91 16 with with ADP iajs-2479 91 17 lower low ADJ iajs-2479 91 18 bounds bound NOUN iajs-2479 91 19 based base VERB iajs-2479 91 20 on on ADP iajs-2479 91 21 a a DET iajs-2479 91 22 " " PUNCT iajs-2479 91 23 lagrangian lagrangian ADJ iajs-2479 91 24 relaxation relaxation NOUN iajs-2479 91 25 " " PUNCT iajs-2479 91 26 . . PUNCT iajs-2479 92 1 also also ADV iajs-2479 92 2 , , PUNCT iajs-2479 92 3 they they PRON iajs-2479 92 4 used use VERB iajs-2479 92 5 dominance dominance NOUN iajs-2479 92 6 rules rule NOUN iajs-2479 92 7 to to PART iajs-2479 92 8 reduce reduce VERB iajs-2479 92 9 the the DET iajs-2479 92 10 search search NOUN iajs-2479 92 11 space space NOUN iajs-2479 92 12 , , PUNCT iajs-2479 92 13 suggested suggest VERB iajs-2479 92 14 techniques technique NOUN iajs-2479 92 15 are be AUX iajs-2479 92 16 showed show VERB iajs-2479 92 17 solve solve NOUN iajs-2479 92 18 to to ADP iajs-2479 92 19 optimality optimality NOUN iajs-2479 92 20 cases case NOUN iajs-2479 92 21 with with ADP iajs-2479 92 22 up up ADP iajs-2479 92 23 to to PART iajs-2479 92 24 200 200 NUM iajs-2479 92 25 jobs job NOUN iajs-2479 92 26 . . PUNCT iajs-2479 93 1 cyril cyril PROPN iajs-2479 93 2 and and CCONJ iajs-2479 93 3 samia samia PROPN iajs-2479 94 1 [ [ X iajs-2479 94 2 23 23 NUM iajs-2479 94 3 ] ] PUNCT iajs-2479 94 4 . . PUNCT iajs-2479 95 1 in in ADP iajs-2479 95 2 this this DET iajs-2479 95 3 study study NOUN iajs-2479 95 4 showed show VERB iajs-2479 95 5 how how SCONJ iajs-2479 95 6 good good ADJ iajs-2479 95 7 – – PUNCT iajs-2479 95 8 quality quality NOUN iajs-2479 95 9 lower low ADJ iajs-2479 95 10 and and CCONJ iajs-2479 95 11 upper upper ADJ iajs-2479 95 12 bounds bound NOUN iajs-2479 95 13 that that PRON iajs-2479 95 14 can can AUX iajs-2479 95 15 be be AUX iajs-2479 95 16 calculated calculate VERB iajs-2479 95 17 for for ADP iajs-2479 95 18 the the DET iajs-2479 95 19 problem1 problem1 NOUN iajs-2479 95 20 / / SYM iajs-2479 95 21 rj/∑uj rj/∑uj VERB iajs-2479 95 22 , , PUNCT iajs-2479 95 23 using use VERB iajs-2479 95 24 an an DET iajs-2479 95 25 original original ADJ iajs-2479 95 26 mathematical mathematical ADJ iajs-2479 95 27 integer integer NOUN iajs-2479 95 28 programming programming NOUN iajs-2479 95 29 formulation formulation NOUN iajs-2479 95 30 . . PUNCT iajs-2479 96 1 numerical numerical ADJ iajs-2479 96 2 experiences experience NOUN iajs-2479 96 3 showed show VERB iajs-2479 96 4 the the DET iajs-2479 96 5 assessing assessing NOUN iajs-2479 96 6 of of ADP iajs-2479 96 7 the the DET iajs-2479 96 8 proposed propose VERB iajs-2479 96 9 approach approach NOUN iajs-2479 96 10 it it PRON iajs-2479 96 11 up up ADP iajs-2479 96 12 to to PART iajs-2479 96 13 160 160 NUM iajs-2479 96 14 jobs job NOUN iajs-2479 96 15 . . PUNCT iajs-2479 97 1 al al PROPN iajs-2479 97 2 zuwaini zuwaini PROPN iajs-2479 97 3 and and CCONJ iajs-2479 97 4 mohanned mohanne VERB iajs-2479 97 5 [ [ X iajs-2479 97 6 24 24 NUM iajs-2479 97 7 , , PUNCT iajs-2479 97 8 25 25 NUM iajs-2479 97 9 ] ] PUNCT iajs-2479 97 10 . . PUNCT iajs-2479 97 11 studied study VERB iajs-2479 97 12 the the DET iajs-2479 97 13 problem problem NOUN iajs-2479 97 14 1 1 NUM iajs-2479 97 15 / / SYM iajs-2479 97 16 rj/∑(fj rj/∑(fj NOUN iajs-2479 97 17 + + CCONJ iajs-2479 97 18 uj uj NOUN iajs-2479 97 19 ) ) PUNCT iajs-2479 97 20 , , PUNCT iajs-2479 97 21 and and CCONJ iajs-2479 97 22 presented present VERB iajs-2479 97 23 a a DET iajs-2479 97 24 ( ( PUNCT iajs-2479 97 25 b&b b&b PROPN iajs-2479 97 26 ) ) PUNCT iajs-2479 97 27 algorithm algorithm NOUN iajs-2479 97 28 , , PUNCT iajs-2479 97 29 and and CCONJ iajs-2479 97 30 application application NOUN iajs-2479 97 31 of of ADP iajs-2479 97 32 some some DET iajs-2479 97 33 dominance dominance NOUN iajs-2479 97 34 rules rule NOUN iajs-2479 97 35 to to PART iajs-2479 97 36 solve solve VERB iajs-2479 97 37 this this DET iajs-2479 97 38 problem problem NOUN iajs-2479 97 39 , , PUNCT iajs-2479 97 40 finding find VERB iajs-2479 97 41 lower lower ADV iajs-2479 97 42 bound bind VERB iajs-2479 97 43 by by ADP iajs-2479 97 44 using use VERB iajs-2479 97 45 ( ( PUNCT iajs-2479 97 46 spt)-rule spt)-rule NOUN iajs-2479 97 47 and and CCONJ iajs-2479 97 48 moor moor NOUN iajs-2479 97 49 's 's PART iajs-2479 97 50 algorithm algorithm NOUN iajs-2479 97 51 . . PUNCT iajs-2479 98 1 computational computational ADJ iajs-2479 98 2 experience experience NOUN iajs-2479 98 3 with with ADP iajs-2479 98 4 instances instance NOUN iajs-2479 98 5 having have VERB iajs-2479 98 6 up up ADP iajs-2479 98 7 to to PART iajs-2479 98 8 40 40 NUM iajs-2479 98 9 jobs job NOUN iajs-2479 98 10 showed show VERB iajs-2479 98 11 that that SCONJ iajs-2479 98 12 the the DET iajs-2479 98 13 lower lower ADV iajs-2479 98 14 bound bind VERB iajs-2479 98 15 was be AUX iajs-2479 98 16 effective effective ADJ iajs-2479 98 17 in in ADP iajs-2479 98 18 restricting restrict VERB iajs-2479 98 19 the the DET iajs-2479 98 20 search search NOUN iajs-2479 98 21 . . PUNCT iajs-2479 99 1 scheduling scheduling NOUN iajs-2479 99 2 problems problem NOUN iajs-2479 99 3 of of ADP iajs-2479 99 4 multiple multiple ADJ iajs-2479 99 5 performance performance NOUN iajs-2479 99 6 measures measure NOUN iajs-2479 99 7 ( ( PUNCT iajs-2479 99 8 three three NUM iajs-2479 99 9 or or CCONJ iajs-2479 99 10 more more ADJ iajs-2479 99 11 ) ) PUNCT iajs-2479 99 12 with with ADP iajs-2479 99 13 release release NOUN iajs-2479 99 14 date date NOUN iajs-2479 99 15 , , PUNCT iajs-2479 99 16 to to ADP iajs-2479 99 17 the the DET iajs-2479 99 18 moments moment NOUN iajs-2479 99 19 of of ADP iajs-2479 99 20 writing write VERB iajs-2479 99 21 this this DET iajs-2479 99 22 paper paper NOUN iajs-2479 99 23 . . PUNCT iajs-2479 100 1 we we PRON iajs-2479 100 2 did do AUX iajs-2479 100 3 not not PART iajs-2479 100 4 find find VERB iajs-2479 100 5 any any DET iajs-2479 100 6 study study NOUN iajs-2479 100 7 submitted submit VERB iajs-2479 100 8 to to PART iajs-2479 100 9 discuss discuss VERB iajs-2479 100 10 this this DET iajs-2479 100 11 subject subject NOUN iajs-2479 100 12 . . PUNCT iajs-2479 101 1 from from ADP iajs-2479 101 2 the the DET iajs-2479 101 3 above above NOUN iajs-2479 101 4 , , PUNCT iajs-2479 101 5 we we PRON iajs-2479 101 6 can can AUX iajs-2479 101 7 say say VERB iajs-2479 101 8 that that SCONJ iajs-2479 101 9 scheduling scheduling NOUN iajs-2479 101 10 problem problem NOUN iajs-2479 101 11 often often ADV iajs-2479 101 12 increases increase VERB iajs-2479 101 13 complexity complexity NOUN iajs-2479 101 14 by by ADP iajs-2479 101 15 increasing increase VERB iajs-2479 101 16 the the DET iajs-2479 101 17 number number NOUN iajs-2479 101 18 of of ADP iajs-2479 101 19 performance performance NOUN iajs-2479 101 20 measures measure NOUN iajs-2479 101 21 with with ADP iajs-2479 101 22 release release NOUN iajs-2479 101 23 date date NOUN iajs-2479 101 24 . . PUNCT iajs-2479 102 1 also also ADV iajs-2479 102 2 , , PUNCT iajs-2479 102 3 we we PRON iajs-2479 102 4 can can AUX iajs-2479 102 5 say say VERB iajs-2479 102 6 that that SCONJ iajs-2479 102 7 our our PRON iajs-2479 102 8 problem problem NOUN iajs-2479 102 9 ( ( PUNCT iajs-2479 102 10 p p NOUN iajs-2479 102 11 ) ) PUNCT iajs-2479 102 12 is be AUX iajs-2479 102 13 the the DET iajs-2479 102 14 first first ADJ iajs-2479 102 15 study study NOUN iajs-2479 102 16 to to PART iajs-2479 102 17 address address VERB iajs-2479 102 18 scheduling scheduling NOUN iajs-2479 102 19 problem problem NOUN iajs-2479 102 20 with with ADP iajs-2479 102 21 five five NUM iajs-2479 102 22 criteria criterion NOUN iajs-2479 102 23 and and CCONJ iajs-2479 102 24 with with ADP iajs-2479 102 25 release release NOUN iajs-2479 102 26 date date NOUN iajs-2479 102 27 . . PUNCT iajs-2479 103 1 in in ADP iajs-2479 103 2 this this DET iajs-2479 103 3 paper paper NOUN iajs-2479 103 4 , , PUNCT iajs-2479 103 5 we we PRON iajs-2479 103 6 describe describe VERB iajs-2479 103 7 the the DET iajs-2479 103 8 problem problem NOUN iajs-2479 103 9 of of ADP iajs-2479 103 10 scheduling scheduling NOUN iajs-2479 103 11 of of ADP iajs-2479 103 12 ( ( PUNCT iajs-2479 103 13 n n CCONJ iajs-2479 103 14 ) ) PUNCT iajs-2479 103 15 jobs job NOUN iajs-2479 103 16 on on ADP iajs-2479 103 17 onemachine onemachine NOUN iajs-2479 103 18 with with ADP iajs-2479 103 19 multiple multiple ADJ iajs-2479 103 20 performance performance NOUN iajs-2479 103 21 measures measure NOUN iajs-2479 103 22 and and CCONJ iajs-2479 103 23 release release VERB iajs-2479 103 24 date date NOUN iajs-2479 103 25 , , PUNCT iajs-2479 103 26 with with ADP iajs-2479 103 27 a a DET iajs-2479 103 28 view view NOUN iajs-2479 103 29 to to ADP iajs-2479 103 30 minimizing minimize VERB iajs-2479 103 31 the the DET iajs-2479 103 32 sum sum NOUN iajs-2479 103 33 total total ADJ iajs-2479 103 34 completion completion NOUN iajs-2479 103 35 time time NOUN iajs-2479 103 36 , , PUNCT iajs-2479 103 37 total total ADJ iajs-2479 103 38 tardiness tardiness NOUN iajs-2479 103 39 , , PUNCT iajs-2479 103 40 total total ADJ iajs-2479 103 41 earliness earliness NOUN iajs-2479 103 42 , , PUNCT iajs-2479 103 43 number number NOUN iajs-2479 103 44 of of ADP iajs-2479 103 45 tardy tardy ADJ iajs-2479 103 46 jobs job NOUN iajs-2479 103 47 and and CCONJ iajs-2479 103 48 total total ADJ iajs-2479 103 49 late late ADJ iajs-2479 103 50 work work NOUN iajs-2479 103 51 , , PUNCT iajs-2479 103 52 this this DET iajs-2479 103 53 problem problem NOUN iajs-2479 103 54 is be AUX iajs-2479 103 55 denoted denote VERB iajs-2479 103 56 by by ADP iajs-2479 103 57 1/𝑟 1/𝑟 NUM iajs-2479 103 58 / / SYM iajs-2479 103 59 ∑ ∑ PUNCT iajs-2479 103 60 𝐶 𝐶 PROPN iajs-2479 103 61 𝑇 𝑇 PROPN iajs-2479 103 62 𝐸 𝐸 PROPN iajs-2479 103 63 𝑈 𝑈 PROPN iajs-2479 103 64 𝑉 𝑉 PROPN iajs-2479 103 65 … … PUNCT iajs-2479 103 66 ( ( PUNCT iajs-2479 103 67 p p NOUN iajs-2479 103 68 ) ) PUNCT iajs-2479 103 69 , , PUNCT iajs-2479 103 70 from from ADP iajs-2479 103 71 used used ADJ iajs-2479 103 72 form form NOUN iajs-2479 103 73 3field 3field NUM iajs-2479 103 74 α α NOUN iajs-2479 103 75 ∕ ∕ NOUN iajs-2479 103 76 β β NOUN iajs-2479 103 77 ∕ ∕ NOUN iajs-2479 103 78 𝛾 𝛾 X iajs-2479 103 79 by by ADP iajs-2479 103 80 graham graham PROPN iajs-2479 103 81 et et PROPN iajs-2479 103 82 al al PROPN iajs-2479 104 1 [ [ X iajs-2479 104 2 26 26 NUM iajs-2479 104 3 ] ] PUNCT iajs-2479 104 4 . . PUNCT iajs-2479 105 1 this this DET iajs-2479 105 2 paper paper NOUN iajs-2479 105 3 is be AUX iajs-2479 105 4 organized organize VERB iajs-2479 105 5 as as SCONJ iajs-2479 105 6 follows follow VERB iajs-2479 105 7 : : PUNCT iajs-2479 105 8 in in ADP iajs-2479 105 9 next next ADJ iajs-2479 105 10 section section NOUN iajs-2479 105 11 begins begin VERB iajs-2479 105 12 with with ADP iajs-2479 105 13 some some DET iajs-2479 105 14 notation notation NOUN iajs-2479 105 15 and and CCONJ iajs-2479 105 16 basic basic ADJ iajs-2479 105 17 concepts concept NOUN iajs-2479 105 18 of of ADP iajs-2479 105 19 one one NUM iajs-2479 105 20 - - PUNCT iajs-2479 105 21 machine machine NOUN iajs-2479 105 22 scheduling scheduling NOUN iajs-2479 105 23 . . PUNCT iajs-2479 106 1 formulation formulation NOUN iajs-2479 106 2 of of ADP iajs-2479 106 3 the the DET iajs-2479 106 4 problem problem NOUN iajs-2479 106 5 and and CCONJ iajs-2479 106 6 decomposition decomposition NOUN iajs-2479 106 7 into into ADP iajs-2479 106 8 three three NUM iajs-2479 106 9 sub sub NOUN iajs-2479 106 10 - - NOUN iajs-2479 106 11 problem problem NOUN iajs-2479 106 12 are be AUX iajs-2479 106 13 given give VERB iajs-2479 106 14 in in ADP iajs-2479 106 15 section section NOUN iajs-2479 106 16 3 3 NUM iajs-2479 106 17 . . PUNCT iajs-2479 107 1 some some DET iajs-2479 107 2 algorithms algorithm NOUN iajs-2479 107 3 are be AUX iajs-2479 107 4 given give VERB iajs-2479 107 5 in in ADP iajs-2479 107 6 section section NOUN iajs-2479 107 7 4 4 NUM iajs-2479 107 8 . . PUNCT iajs-2479 108 1 also also ADV iajs-2479 108 2 , , PUNCT iajs-2479 108 3 three three NUM iajs-2479 108 4 special special ADJ iajs-2479 108 5 cases case NOUN iajs-2479 108 6 were be AUX iajs-2479 108 7 presented present VERB iajs-2479 108 8 in in ADP iajs-2479 108 9 section section NOUN iajs-2479 108 10 5 5 NUM iajs-2479 108 11 . . PUNCT iajs-2479 109 1 in in ADP iajs-2479 109 2 section section NOUN iajs-2479 109 3 6 6 NUM iajs-2479 109 4 , , PUNCT iajs-2479 109 5 the the DET iajs-2479 109 6 ( ( PUNCT iajs-2479 109 7 b&b b&b PROPN iajs-2479 109 8 ) ) PUNCT iajs-2479 109 9 algorithm algorithm NOUN iajs-2479 109 10 was be AUX iajs-2479 109 11 discussed discuss VERB iajs-2479 109 12 , , PUNCT iajs-2479 109 13 an an DET iajs-2479 109 14 account account NOUN iajs-2479 109 15 the the DET iajs-2479 109 16 upper upper ADJ iajs-2479 109 17 bound bind VERB iajs-2479 109 18 and and CCONJ iajs-2479 109 19 the the DET iajs-2479 109 20 derivation derivation NOUN iajs-2479 109 21 of of ADP iajs-2479 109 22 a a DET iajs-2479 109 23 lower lower ADV iajs-2479 109 24 bound bind VERB iajs-2479 109 25 , , PUNCT iajs-2479 109 26 and and CCONJ iajs-2479 109 27 some some DET iajs-2479 109 28 dominance dominance NOUN iajs-2479 109 29 rules rule NOUN iajs-2479 109 30 in in ADP iajs-2479 109 31 section section NOUN iajs-2479 109 32 7 7 NUM iajs-2479 109 33 . . PUNCT iajs-2479 109 34 computational computational ADJ iajs-2479 109 35 results result NOUN iajs-2479 109 36 are be AUX iajs-2479 109 37 presented present VERB iajs-2479 109 38 in in ADP iajs-2479 109 39 section section NOUN iajs-2479 109 40 8 8 NUM iajs-2479 109 41 . . PUNCT iajs-2479 109 42     SPACE iajs-2479 110 1 143 143 NUM iajs-2479 110 2     SPACE iajs-2479 110 3 ibn ibn PROPN iajs-2479 110 4 al al PROPN iajs-2479 110 5 - - PUNCT iajs-2479 110 6 haitham haitham PROPN iajs-2479 110 7 jour jour X iajs-2479 110 8 . . PROPN iajs-2479 110 9 for for ADP iajs-2479 110 10 pure pure ADJ iajs-2479 110 11 & & CCONJ iajs-2479 110 12 appl appl PROPN iajs-2479 110 13 . . PUNCT iajs-2479 111 1 sci sci PROPN iajs-2479 111 2 . . PROPN iajs-2479 112 1 33 33 NUM iajs-2479 112 2 ( ( PUNCT iajs-2479 112 3 3 3 NUM iajs-2479 112 4 ) ) PUNCT iajs-2479 112 5 2020 2020 NUM iajs-2479 112 6 2 2 NUM iajs-2479 112 7 . . PUNCT iajs-2479 113 1 notation notation VERB iajs-2479 113 2 the the DET iajs-2479 113 3 following follow VERB iajs-2479 113 4 notations notation NOUN iajs-2479 113 5 are be AUX iajs-2479 113 6 used use VERB iajs-2479 113 7 in in ADP iajs-2479 113 8 this this DET iajs-2479 113 9 paper paper NOUN iajs-2479 113 10 : : PUNCT iajs-2479 113 11 j j NOUN iajs-2479 113 12 : : PUNCT iajs-2479 113 13 job job NOUN iajs-2479 113 14 index index NOUN iajs-2479 113 15 . . PUNCT iajs-2479 114 1 n̅ n̅ NOUN iajs-2479 114 2 : : PUNCT iajs-2479 114 3 the the DET iajs-2479 114 4 set set NOUN iajs-2479 114 5 of of ADP iajs-2479 114 6 all all DET iajs-2479 114 7 n n PRON iajs-2479 114 8 jobs job NOUN iajs-2479 114 9 . . PUNCT iajs-2479 115 1 n n X iajs-2479 115 2 : : PUNCT iajs-2479 115 3 number number NOUN iajs-2479 115 4 of of ADP iajs-2479 115 5 jobs job NOUN iajs-2479 115 6 . . PUNCT iajs-2479 116 1 pj pj NOUN iajs-2479 116 2 : : PUNCT iajs-2479 117 1 processing process VERB iajs-2479 117 2 time time NOUN iajs-2479 117 3 for for ADP iajs-2479 117 4 job job NOUN iajs-2479 117 5 j j PROPN iajs-2479 117 6 . . PUNCT iajs-2479 118 1 dj dj X iajs-2479 118 2 : : PUNCT iajs-2479 118 3 due due ADJ iajs-2479 118 4 date date NOUN iajs-2479 118 5 for for ADP iajs-2479 118 6 job job NOUN iajs-2479 118 7 j j PROPN iajs-2479 118 8 . . PUNCT iajs-2479 119 1 rj rj PROPN iajs-2479 119 2 : : PUNCT iajs-2479 119 3 release release VERB iajs-2479 119 4 date date NOUN iajs-2479 119 5 for for ADP iajs-2479 119 6 job job NOUN iajs-2479 119 7 j j PROPN iajs-2479 119 8 . . PUNCT iajs-2479 120 1 cj cj X iajs-2479 120 2 : : PUNCT iajs-2479 121 1 completion completion NOUN iajs-2479 121 2 time time NOUN iajs-2479 121 3 of of ADP iajs-2479 121 4 job job NOUN iajs-2479 121 5 j j PROPN iajs-2479 121 6 . . PUNCT iajs-2479 122 1 ∑cj ∑cj PUNCT iajs-2479 122 2 : : PUNCT iajs-2479 123 1 the the DET iajs-2479 123 2 total total ADJ iajs-2479 123 3 completion completion NOUN iajs-2479 123 4 times time NOUN iajs-2479 123 5 . . PUNCT iajs-2479 124 1 tj tj INTJ iajs-2479 124 2 : : PUNCT iajs-2479 124 3 the the DET iajs-2479 124 4 tardiness tardiness NOUN iajs-2479 124 5 of of ADP iajs-2479 124 6 job job NOUN iajs-2479 124 7 j. j. PROPN iajs-2479 124 8 ∑tj ∑tj PROPN iajs-2479 124 9 : : PUNCT iajs-2479 124 10 the the DET iajs-2479 124 11 total total ADJ iajs-2479 124 12 tardiness tardiness NOUN iajs-2479 124 13 . . PUNCT iajs-2479 125 1 ej ej X iajs-2479 125 2 : : PUNCT iajs-2479 126 1 the the DET iajs-2479 126 2 earliness earliness NOUN iajs-2479 126 3 of of ADP iajs-2479 126 4 job job NOUN iajs-2479 126 5 j j PROPN iajs-2479 126 6 . . PUNCT iajs-2479 127 1 ∑ej ∑ej PUNCT iajs-2479 128 1 : : PUNCT iajs-2479 129 1 the the DET iajs-2479 129 2 total total ADJ iajs-2479 129 3 earliness earliness NOUN iajs-2479 129 4 . . PUNCT iajs-2479 130 1 vj vj INTJ iajs-2479 130 2 : : PUNCT iajs-2479 130 3 the the DET iajs-2479 130 4 late late ADJ iajs-2479 130 5 work work NOUN iajs-2479 130 6 of of ADP iajs-2479 130 7 job job NOUN iajs-2479 130 8 j j PROPN iajs-2479 130 9 . . PUNCT iajs-2479 131 1 ∑vj ∑vj PUNCT iajs-2479 131 2 : : PUNCT iajs-2479 132 1 the the DET iajs-2479 132 2 total total ADJ iajs-2479 132 3 late late ADJ iajs-2479 132 4 work work NOUN iajs-2479 132 5 . . PUNCT iajs-2479 133 1 uj uj NOUN iajs-2479 133 2 : : PUNCT iajs-2479 133 3 the the DET iajs-2479 133 4 unit unit NOUN iajs-2479 133 5 penalty penalty NOUN iajs-2479 133 6 of of ADP iajs-2479 133 7 job job NOUN iajs-2479 133 8 j j PROPN iajs-2479 133 9 . . PUNCT iajs-2479 133 10 ∑uj ∑uj PROPN iajs-2479 134 1 : : PUNCT iajs-2479 134 2 the the DET iajs-2479 134 3 number number NOUN iajs-2479 134 4 of of ADP iajs-2479 134 5 tardy tardy ADJ iajs-2479 134 6 jobs job NOUN iajs-2479 134 7 . . PUNCT iajs-2479 135 1 ( ( PUNCT iajs-2479 135 2 b&b b&b PROPN iajs-2479 135 3 ) ) PUNCT iajs-2479 135 4 : : PUNCT iajs-2479 135 5 branch branch NOUN iajs-2479 135 6 and and CCONJ iajs-2479 135 7 bound bind VERB iajs-2479 135 8 . . PUNCT iajs-2479 136 1 up up ADP iajs-2479 136 2 : : PUNCT iajs-2479 136 3 upper upper ADJ iajs-2479 136 4 bound bind VERB iajs-2479 136 5 . . PUNCT iajs-2479 137 1 lb lb X iajs-2479 137 2 : : PUNCT iajs-2479 137 3 lower lower ADV iajs-2479 137 4 bound bind VERB iajs-2479 137 5 . . PUNCT iajs-2479 138 1 ( ( PUNCT iajs-2479 138 2 sc sc PROPN iajs-2479 138 3 ) ) PUNCT iajs-2479 138 4 : : PUNCT iajs-2479 138 5 special special ADJ iajs-2479 138 6 cases case NOUN iajs-2479 138 7 . . PUNCT iajs-2479 139 1 ( ( PUNCT iajs-2479 139 2 dr dr PROPN iajs-2479 139 3 ) ) PUNCT iajs-2479 139 4 : : PUNCT iajs-2479 139 5 dominance dominance NOUN iajs-2479 139 6 rules rule NOUN iajs-2479 139 7 . . PUNCT iajs-2479 140 1 3 3 X iajs-2479 140 2 . . X iajs-2479 140 3 the the DET iajs-2479 140 4 mathematical mathematical ADJ iajs-2479 140 5 formulation formulation NOUN iajs-2479 140 6 the the DET iajs-2479 140 7 problem problem NOUN iajs-2479 140 8 ( ( PUNCT iajs-2479 140 9 p p NOUN iajs-2479 140 10 ) ) PUNCT iajs-2479 140 11 considered consider VERB iajs-2479 140 12 in in ADP iajs-2479 140 13 this this DET iajs-2479 140 14 paper paper NOUN iajs-2479 140 15 is be AUX iajs-2479 140 16 to to PART iajs-2479 140 17 schedule schedule VERB iajs-2479 140 18 a a DET iajs-2479 140 19 set set NOUN iajs-2479 140 20 n̅ n̅ NOUN iajs-2479 140 21 of of ADP iajs-2479 140 22 n n PRON iajs-2479 140 23 jobs job NOUN iajs-2479 140 24 , , PUNCT iajs-2479 140 25 n̅={1, n̅={1, ADP iajs-2479 140 26 … … X iajs-2479 140 27 ,n ,n NOUN iajs-2479 140 28 } } PUNCT iajs-2479 140 29 on on ADP iajs-2479 140 30 an an DET iajs-2479 140 31 onemachine onemachine NOUN iajs-2479 140 32 . . 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PUNCT iajs-2479 142 1 given give VERB iajs-2479 142 2 a a DET iajs-2479 142 3 schedule schedule NOUN iajs-2479 142 4 σ σ PROPN iajs-2479 142 5 =( =( NOUN iajs-2479 142 6 1, 1, NUM iajs-2479 142 7 … … PUNCT iajs-2479 142 8 ,n ,n NOUN iajs-2479 142 9 ) ) PUNCT iajs-2479 142 10 , , PUNCT iajs-2479 142 11 then then ADV iajs-2479 142 12 for for ADP iajs-2479 142 13 each each DET iajs-2479 142 14 job job NOUN iajs-2479 142 15 j j NOUN iajs-2479 142 16 we we PRON iajs-2479 142 17 calculate calculate VERB iajs-2479 142 18 the the DET iajs-2479 142 19 completion completion NOUN iajs-2479 142 20 time time NOUN iajs-2479 142 21 by by ADP iajs-2479 142 22 c1 c1 NOUN iajs-2479 142 23 = = PROPN iajs-2479 142 24 r1 r1 PROPN iajs-2479 142 25 + + CCONJ iajs-2479 142 26 p1 p1 PROPN iajs-2479 142 27 , , PUNCT iajs-2479 142 28 cj= cj= PROPN iajs-2479 142 29 max max PROPN iajs-2479 142 30 { { PUNCT iajs-2479 142 31 rj rj PROPN iajs-2479 142 32 , , PUNCT iajs-2479 142 33 cj cj NOUN iajs-2479 142 34 } } PUNCT iajs-2479 142 35 + + CCONJ iajs-2479 142 36 pj pj PROPN iajs-2479 142 37 for for ADP iajs-2479 142 38 j=2, j=2, PROPN iajs-2479 142 39 … … X iajs-2479 142 40 ,n ,n NOUN iajs-2479 142 41 . . PUNCT iajs-2479 143 1 the the DET iajs-2479 143 2 tardiness tardiness NOUN iajs-2479 143 3 of of ADP iajs-2479 143 4 job job NOUN iajs-2479 143 5 j j PROPN iajs-2479 143 6 is be AUX iajs-2479 143 7 defined define VERB iajs-2479 143 8 by by ADP iajs-2479 143 9 tj tj NOUN iajs-2479 143 10 = = NOUN iajs-2479 143 11 max{cj max{cj NOUN iajs-2479 143 12 – – PUNCT iajs-2479 143 13 dj dj NOUN iajs-2479 143 14 , , PUNCT iajs-2479 143 15 0 0 NUM iajs-2479 143 16 } } PUNCT iajs-2479 143 17 , , PUNCT iajs-2479 143 18 and and CCONJ iajs-2479 143 19 earliness earliness NOUN iajs-2479 143 20 by by ADP iajs-2479 143 21 ej ej PROPN iajs-2479 143 22 = = NOUN iajs-2479 143 23 max{dj max{dj X iajs-2479 143 24 – – PUNCT iajs-2479 143 25 cj cj NUM iajs-2479 143 26 , , PUNCT iajs-2479 143 27 0 0 NUM iajs-2479 143 28 } } PUNCT iajs-2479 143 29 . . PUNCT iajs-2479 144 1 the the DET iajs-2479 144 2 unit unit NOUN iajs-2479 144 3 penalty penalty NOUN iajs-2479 144 4 of of ADP iajs-2479 144 5 job job NOUN iajs-2479 144 6 j j PROPN iajs-2479 144 7 is be AUX iajs-2479 144 8 defined define VERB iajs-2479 144 9 by by ADP iajs-2479 144 10 uj uj PROPN iajs-2479 144 11 = = PROPN iajs-2479 144 12 1 1 NUM iajs-2479 144 13 , , PUNCT iajs-2479 144 14 if if SCONJ iajs-2479 144 15 cj cj X iajs-2479 144 16 > > X iajs-2479 144 17 dj dj PROPN iajs-2479 144 18 ; ; PUNCT iajs-2479 144 19 o.w o.w PROPN iajs-2479 144 20 , , PUNCT iajs-2479 144 21 uj=0.the uj=0.the PRON iajs-2479 144 22 late late ADJ iajs-2479 144 23 work work NOUN iajs-2479 144 24 of of ADP iajs-2479 144 25 job job NOUN iajs-2479 144 26 j j NOUN iajs-2479 144 27 given give VERB iajs-2479 144 28 by by ADP iajs-2479 144 29 vj vj X iajs-2479 144 30 = = SYM iajs-2479 144 31 min{tj min{tj X iajs-2479 144 32 , , PUNCT iajs-2479 144 33 pj pj PROPN iajs-2479 144 34 } } PUNCT iajs-2479 144 35 . . PUNCT iajs-2479 145 1 let let VERB iajs-2479 145 2 𝛿 𝛿 PRON iajs-2479 145 3 be be AUX iajs-2479 145 4 a a DET iajs-2479 145 5 set set NOUN iajs-2479 145 6 of of ADP iajs-2479 145 7 all all DET iajs-2479 145 8 feasible feasible ADJ iajs-2479 145 9 solutions solution NOUN iajs-2479 145 10 , , PUNCT iajs-2479 145 11 and and CCONJ iajs-2479 145 12 σ σ PROPN iajs-2479 145 13 is be AUX iajs-2479 145 14 a a DET iajs-2479 145 15 schedule schedule NOUN iajs-2479 145 16 in in ADP iajs-2479 145 17 𝛿 𝛿 PROPN iajs-2479 145 18 . . PUNCT iajs-2479 146 1 the the DET iajs-2479 146 2 mathematical mathematical ADJ iajs-2479 146 3 form form NOUN iajs-2479 146 4 of of ADP iajs-2479 146 5 our our PRON iajs-2479 146 6 problem problem NOUN iajs-2479 146 7 ( ( PUNCT iajs-2479 146 8 p p X iajs-2479 146 9 ) ) PUNCT iajs-2479 146 10 can can AUX iajs-2479 146 11 be be AUX iajs-2479 146 12 written write VERB iajs-2479 146 13 as as ADP iajs-2479 146 14 : : PUNCT iajs-2479 146 15 m m PROPN iajs-2479 146 16 = = NOUN iajs-2479 146 17 min min NOUN iajs-2479 146 18 f(σ)=min f(σ)=min NOUN iajs-2479 146 19 { { PUNCT iajs-2479 146 20 ∑ ∑ PUNCT iajs-2479 146 21 𝐶 𝐶 PROPN iajs-2479 146 22 𝑇 𝑇 PROPN iajs-2479 146 23 𝐸 𝐸 PROPN iajs-2479 146 24 𝑈 𝑈 PROPN iajs-2479 146 25 𝑉 𝑉 PROPN iajs-2479 146 26 subject subject NOUN iajs-2479 146 27 to to ADP iajs-2479 146 28 : : PUNCT iajs-2479 146 29 cσ(1)=rσ(1 cσ(1)=rσ(1 NUM iajs-2479 146 30 ) ) PUNCT iajs-2479 147 1 + + SYM iajs-2479 147 2 pσ(1 pσ(1 NOUN iajs-2479 147 3 ) ) PUNCT iajs-2479 147 4 cσ cσ PROPN iajs-2479 147 5 ( ( PUNCT iajs-2479 147 6 j j PROPN iajs-2479 147 7 ) ) PUNCT iajs-2479 148 1 = = SYM iajs-2479 148 2 max max PROPN iajs-2479 148 3 { { PUNCT iajs-2479 148 4 rj rj PROPN iajs-2479 148 5 , , PUNCT iajs-2479 148 6 cj-1 cj-1 ADV iajs-2479 148 7 } } PUNCT iajs-2479 148 8 + + CCONJ iajs-2479 148 9 pj pj PROPN iajs-2479 148 10 j j PROPN iajs-2479 148 11 = = SYM iajs-2479 148 12 2 2 NUM iajs-2479 148 13 , , PUNCT iajs-2479 148 14 … … PUNCT iajs-2479 148 15 , , PUNCT iajs-2479 148 16 n n PRON iajs-2479 148 17 … … PUNCT iajs-2479 148 18 .(p .(p SYM iajs-2479 148 19 ) ) PUNCT iajs-2479 148 20 tσ(j tσ(j NOUN iajs-2479 148 21 ) ) PUNCT iajs-2479 148 22 = = SYM iajs-2479 148 23 max{cσ(j max{cσ(j X iajs-2479 148 24 ) ) PUNCT iajs-2479 148 25 – – PUNCT iajs-2479 148 26 dσ(j dσ(j NOUN iajs-2479 148 27 ) ) PUNCT iajs-2479 148 28 , , PUNCT iajs-2479 148 29 0 0 NUM iajs-2479 148 30 } } PUNCT iajs-2479 148 31 j= j= VERB iajs-2479 148 32 1, 1, NUM iajs-2479 148 33 … … SYM iajs-2479 148 34 ,n ,n NOUN iajs-2479 148 35 eσ(j eσ(j NUM iajs-2479 148 36 ) ) PUNCT iajs-2479 148 37 = = SYM iajs-2479 148 38 max{dσ(j max{dσ(j X iajs-2479 148 39 ) ) PUNCT iajs-2479 148 40 – – PUNCT iajs-2479 148 41 cσ(j cσ(j X iajs-2479 148 42 ) ) PUNCT iajs-2479 148 43 , , PUNCT iajs-2479 148 44 0 0 X iajs-2479 148 45 } } PUNCT iajs-2479 148 46 j= j= X iajs-2479 148 47 1 1 NUM iajs-2479 148 48 , , PUNCT iajs-2479 148 49 … … PUNCT iajs-2479 148 50 , , PUNCT iajs-2479 148 51 n n PRON iajs-2479 148 52 uσ(j uσ(j X iajs-2479 148 53 ) ) PUNCT iajs-2479 148 54 = = SYM iajs-2479 148 55 1 1 NUM iajs-2479 148 56 if if SCONJ iajs-2479 148 57 c c PROPN iajs-2479 148 58 d d X iajs-2479 148 59 j j PROPN iajs-2479 148 60 1 1 NUM iajs-2479 148 61 , , PUNCT iajs-2479 148 62 … … PUNCT iajs-2479 148 63 , , PUNCT iajs-2479 148 64 n n NOUN iajs-2479 148 65 0 0 NUM iajs-2479 149 1 o. o. PROPN iajs-2479 149 2 w w PROPN iajs-2479 149 3     SPACE iajs-2479 149 4 144 144 NUM iajs-2479 149 5     SPACE iajs-2479 149 6 ibn ibn PROPN iajs-2479 149 7 al al PROPN iajs-2479 149 8 - - PUNCT iajs-2479 149 9 haitham haitham PROPN iajs-2479 149 10 jour jour X iajs-2479 149 11 . . PROPN iajs-2479 150 1 for for ADP iajs-2479 150 2 pure pure ADJ iajs-2479 150 3 & & CCONJ iajs-2479 150 4 appl appl PROPN iajs-2479 150 5 . . PUNCT iajs-2479 151 1 sci sci PROPN iajs-2479 151 2 . . PROPN iajs-2479 152 1 33 33 NUM iajs-2479 152 2 ( ( PUNCT iajs-2479 152 3 3 3 NUM iajs-2479 152 4 ) ) PUNCT iajs-2479 152 5 2020 2020 NUM iajs-2479 152 6 vσ(j vσ(j X iajs-2479 152 7 ) ) PUNCT iajs-2479 152 8 = = SYM iajs-2479 152 9 min min PROPN iajs-2479 152 10 { { PUNCT iajs-2479 152 11 tσ tσ PROPN iajs-2479 152 12 ( ( PUNCT iajs-2479 152 13 j j PROPN iajs-2479 152 14 ) ) PUNCT iajs-2479 152 15 , , PUNCT iajs-2479 153 1 pσ pσ PROPN iajs-2479 153 2 ( ( PUNCT iajs-2479 153 3 j j PROPN iajs-2479 153 4 ) ) PUNCT iajs-2479 153 5 } } PUNCT iajs-2479 153 6 j j X iajs-2479 153 7 = = SYM iajs-2479 153 8 1 1 NUM iajs-2479 153 9 , , PUNCT iajs-2479 153 10 … … PUNCT iajs-2479 153 11 , , PUNCT iajs-2479 153 12 n n CCONJ iajs-2479 153 13 the the DET iajs-2479 153 14 objective objective NOUN iajs-2479 153 15 is be AUX iajs-2479 153 16 to to PART iajs-2479 153 17 find find VERB iajs-2479 153 18 a a DET iajs-2479 153 19 processing processing NOUN iajs-2479 153 20 order order NOUN iajs-2479 153 21 σ σ PROPN iajs-2479 153 22 =( =( PROPN iajs-2479 153 23 σ(1), σ(1), PROPN iajs-2479 153 24 … … SYM iajs-2479 153 25 ,σ(n ,σ(n PUNCT iajs-2479 153 26 ) ) PUNCT iajs-2479 153 27 ) ) PUNCT iajs-2479 153 28 for for SCONJ iajs-2479 153 29 the the DET iajs-2479 153 30 problem problem NOUN iajs-2479 153 31 ( ( PUNCT iajs-2479 153 32 p p NOUN iajs-2479 153 33 ) ) PUNCT iajs-2479 153 34 to to PART iajs-2479 153 35 minimize minimize VERB iajs-2479 153 36 the the DET iajs-2479 153 37 sum sum NOUN iajs-2479 153 38 of of ADP iajs-2479 153 39 the the DET iajs-2479 153 40 total total ADJ iajs-2479 153 41 completion completion NOUN iajs-2479 153 42 times time NOUN iajs-2479 153 43 , , PUNCT iajs-2479 153 44 the the DET iajs-2479 153 45 total total ADJ iajs-2479 153 46 tardiness tardiness NOUN iajs-2479 153 47 , , PUNCT iajs-2479 153 48 the the DET iajs-2479 153 49 total total ADJ iajs-2479 153 50 earliness earliness NOUN iajs-2479 153 51 , , PUNCT iajs-2479 153 52 the the DET iajs-2479 153 53 number number NOUN iajs-2479 153 54 of of ADP iajs-2479 153 55 tardy tardy NOUN iajs-2479 153 56 , , PUNCT iajs-2479 153 57 and and CCONJ iajs-2479 153 58 the the DET iajs-2479 153 59 total total ADJ iajs-2479 153 60 late late ADJ iajs-2479 153 61 work work NOUN iajs-2479 153 62 . . PUNCT iajs-2479 154 1 3.1 3.1 NUM iajs-2479 154 2 decomposition decomposition NOUN iajs-2479 154 3 of of ADP iajs-2479 154 4 problem problem NOUN iajs-2479 154 5 ( ( PUNCT iajs-2479 154 6 p p NOUN iajs-2479 154 7 ) ) PUNCT iajs-2479 154 8 in in ADP iajs-2479 154 9 order order NOUN iajs-2479 154 10 to to PART iajs-2479 154 11 have have AUX iajs-2479 154 12 a a DET iajs-2479 154 13 less less ADV iajs-2479 154 14 complex complex ADJ iajs-2479 154 15 structure structure NOUN iajs-2479 154 16 of of ADP iajs-2479 154 17 the the DET iajs-2479 154 18 problem problem NOUN iajs-2479 154 19 ( ( PUNCT iajs-2479 154 20 p p NOUN iajs-2479 154 21 ) ) PUNCT iajs-2479 154 22 , , PUNCT iajs-2479 154 23 can can AUX iajs-2479 154 24 be be AUX iajs-2479 154 25 decomposed decompose VERB iajs-2479 154 26 into into ADP iajs-2479 154 27 three three NUM iajs-2479 154 28 sub sub NOUN iajs-2479 154 29 problems problem NOUN iajs-2479 154 30 ( ( PUNCT iajs-2479 154 31 p1 p1 PROPN iajs-2479 154 32 ) ) PUNCT iajs-2479 154 33 , , PUNCT iajs-2479 154 34 ( ( PUNCT iajs-2479 154 35 p2 p2 PROPN iajs-2479 154 36 ) ) PUNCT iajs-2479 154 37 and and CCONJ iajs-2479 154 38 ( ( PUNCT iajs-2479 154 39 p3 p3 PROPN iajs-2479 154 40 ) ) PUNCT iajs-2479 154 41 , , PUNCT iajs-2479 154 42 as as ADP iajs-2479 154 43 following follow VERB iajs-2479 154 44 : : PUNCT iajs-2479 154 45 m1= m1= NOUN iajs-2479 154 46 min min PROPN iajs-2479 154 47 { { PUNCT iajs-2479 154 48 ∑ ∑ PUNCT iajs-2479 154 49 𝐶 𝐶 PROPN iajs-2479 154 50 𝑇 𝑇 PROPN iajs-2479 154 51 𝐸 𝐸 PROPN iajs-2479 154 52 subject subject NOUN iajs-2479 154 53 to to ADP iajs-2479 154 54 : : PUNCT iajs-2479 154 55 cσ(1)=rσ(1 cσ(1)=rσ(1 NUM iajs-2479 154 56 ) ) PUNCT iajs-2479 154 57 + + SYM iajs-2479 154 58 pσ(1 pσ(1 NOUN iajs-2479 154 59 ) ) PUNCT iajs-2479 154 60 cσ cσ PROPN iajs-2479 154 61 ( ( PUNCT iajs-2479 154 62 j j PROPN iajs-2479 154 63 ) ) PUNCT iajs-2479 155 1 = = NOUN iajs-2479 155 2 max max X iajs-2479 155 3 { { PUNCT iajs-2479 155 4 rσ(j rσ(j X iajs-2479 155 5 ) ) PUNCT iajs-2479 155 6 , , PUNCT iajs-2479 155 7 cσ(j-1 cσ(j-1 NOUN iajs-2479 155 8 ) ) PUNCT iajs-2479 155 9 } } PUNCT iajs-2479 156 1 + + CCONJ iajs-2479 156 2 pσ(j pσ(j NOUN iajs-2479 156 3 ) ) PUNCT iajs-2479 156 4 j j NOUN iajs-2479 156 5 = = SYM iajs-2479 156 6 2, 2, NUM iajs-2479 156 7 … … PUNCT iajs-2479 156 8 ,n ,n NOUN iajs-2479 156 9 … … PUNCT iajs-2479 156 10 .. .. PUNCT iajs-2479 156 11 ( ( PUNCT iajs-2479 156 12 p1 p1 NOUN iajs-2479 156 13 ) ) PUNCT iajs-2479 156 14 tσ(j tσ(j NOUN iajs-2479 156 15 ) ) PUNCT iajs-2479 156 16 = = SYM iajs-2479 156 17 max{cσ(j max{cσ(j X iajs-2479 156 18 ) ) PUNCT iajs-2479 156 19 – – PUNCT iajs-2479 156 20 dσ(j dσ(j NOUN iajs-2479 156 21 ) ) PUNCT iajs-2479 156 22 , , PUNCT iajs-2479 156 23 0 0 NUM iajs-2479 156 24 } } PUNCT iajs-2479 156 25 j= j= VERB iajs-2479 156 26 1, 1, NUM iajs-2479 156 27 … … SYM iajs-2479 156 28 ,n ,n NOUN iajs-2479 156 29 eσ(j eσ(j NUM iajs-2479 156 30 ) ) PUNCT iajs-2479 156 31 = = SYM iajs-2479 156 32 max{dσ(j max{dσ(j X iajs-2479 156 33 ) ) PUNCT iajs-2479 156 34 – – PUNCT iajs-2479 156 35 cσ(j cσ(j X iajs-2479 156 36 ) ) PUNCT iajs-2479 156 37 , , PUNCT iajs-2479 156 38 0 0 X iajs-2479 156 39 } } PUNCT iajs-2479 156 40 j= j= X iajs-2479 156 41 1 1 NUM iajs-2479 156 42 , , PUNCT iajs-2479 156 43 … … PUNCT iajs-2479 156 44 , , PUNCT iajs-2479 156 45 n n PRON iajs-2479 156 46 m2 m2 PROPN iajs-2479 156 47 = = SYM iajs-2479 156 48 min min PROPN iajs-2479 156 49 ∑ ∑ PROPN iajs-2479 156 50 𝑈 𝑈 PROPN iajs-2479 156 51 ) ) PUNCT iajs-2479 156 52 subject subject ADJ iajs-2479 156 53 to to ADP iajs-2479 156 54 : : PUNCT iajs-2479 156 55 𝑈 𝑈 NOUN iajs-2479 156 56 = = PUNCT iajs-2479 156 57 1 1 NUM iajs-2479 156 58 if if SCONJ iajs-2479 156 59 c c PROPN iajs-2479 156 60 d d X iajs-2479 156 61 j j PROPN iajs-2479 156 62 1 1 NUM iajs-2479 156 63 , , PUNCT iajs-2479 156 64 … … PUNCT iajs-2479 156 65 , , PUNCT iajs-2479 156 66 n n NOUN iajs-2479 156 67 0 0 NUM iajs-2479 157 1 o. o. NOUN iajs-2479 157 2 w w PROPN iajs-2479 157 3 … … PUNCT iajs-2479 157 4 .(p2 .(p2 NOUN iajs-2479 157 5 ) ) PUNCT iajs-2479 157 6 cσ(1)= cσ(1)= PROPN iajs-2479 157 7 rσ(1 rσ(1 PROPN iajs-2479 157 8 ) ) PUNCT iajs-2479 158 1 + + SYM iajs-2479 158 2 pσ(1 pσ(1 NOUN iajs-2479 158 3 ) ) PUNCT iajs-2479 159 1 cσ cσ PROPN iajs-2479 159 2 ( ( PUNCT iajs-2479 159 3 j j PROPN iajs-2479 159 4 ) ) PUNCT iajs-2479 160 1 = = NOUN iajs-2479 160 2 max max X iajs-2479 160 3 { { PUNCT iajs-2479 160 4 rσ(j rσ(j X iajs-2479 160 5 ) ) PUNCT iajs-2479 160 6 , , PUNCT iajs-2479 160 7 cσ(j-1 cσ(j-1 NOUN iajs-2479 160 8 ) ) PUNCT iajs-2479 160 9 } } PUNCT iajs-2479 161 1 + + CCONJ iajs-2479 161 2 pσ(j pσ(j NOUN iajs-2479 161 3 ) ) PUNCT iajs-2479 161 4 j j NOUN iajs-2479 161 5 = = SYM iajs-2479 161 6 2, 2, NUM iajs-2479 161 7 … … PUNCT iajs-2479 161 8 ,n ,n PUNCT iajs-2479 161 9 m3 m3 PROPN iajs-2479 161 10 = = SYM iajs-2479 161 11 min min PROPN iajs-2479 161 12 ( ( PUNCT iajs-2479 161 13 ∑ ∑ PUNCT iajs-2479 161 14 𝑉 𝑉 PROPN iajs-2479 161 15 ) ) PUNCT iajs-2479 161 16 subject subject NOUN iajs-2479 161 17 to to ADP iajs-2479 161 18 : : PUNCT iajs-2479 161 19 vσ vσ PROPN iajs-2479 161 20 ( ( PUNCT iajs-2479 161 21 j j PROPN iajs-2479 161 22 ) ) PUNCT iajs-2479 161 23 = = SYM iajs-2479 161 24 min min PROPN iajs-2479 161 25 { { PUNCT iajs-2479 161 26 tσ tσ PROPN iajs-2479 161 27 ( ( PUNCT iajs-2479 161 28 j j PROPN iajs-2479 161 29 ) ) PUNCT iajs-2479 161 30 , , PUNCT iajs-2479 161 31 pσ pσ PROPN iajs-2479 161 32 ( ( PUNCT iajs-2479 161 33 j j PROPN iajs-2479 161 34 ) ) PUNCT iajs-2479 161 35 } } PUNCT iajs-2479 161 36 j j X iajs-2479 162 1 = = SYM iajs-2479 162 2 1, 1, NUM iajs-2479 162 3 … … SYM iajs-2479 162 4 ,n ,n X iajs-2479 162 5 … … PUNCT iajs-2479 162 6 .. .. PUNCT iajs-2479 162 7 ( ( PUNCT iajs-2479 162 8 p3 p3 PROPN iajs-2479 162 9 ) ) PUNCT iajs-2479 162 10 tσ tσ PROPN iajs-2479 162 11 ( ( PUNCT iajs-2479 162 12 j j PROPN iajs-2479 162 13 ) ) PUNCT iajs-2479 162 14 ≥ ≥ PROPN iajs-2479 162 15 0 0 NUM iajs-2479 163 1 j j PROPN iajs-2479 163 2 = = SYM iajs-2479 163 3 1, 1, NUM iajs-2479 163 4 … … SYM iajs-2479 163 5 ,n ,n SYM iajs-2479 163 6 pσ pσ PROPN iajs-2479 163 7 ( ( PUNCT iajs-2479 163 8 j j PROPN iajs-2479 163 9 ) ) PUNCT iajs-2479 163 10 ≥ ≥ PROPN iajs-2479 163 11 0 0 NUM iajs-2479 164 1 j j PROPN iajs-2479 164 2 = = SYM iajs-2479 164 3 1, 1, NUM iajs-2479 164 4 … … PUNCT iajs-2479 164 5 ,n ,n PUNCT iajs-2479 164 6 theorem theorem VERB iajs-2479 164 7 1 1 NUM iajs-2479 165 1 [ [ X iajs-2479 165 2 26 26 NUM iajs-2479 165 3 ] ] PUNCT iajs-2479 165 4 . . PUNCT iajs-2479 166 1 m1 m1 PROPN iajs-2479 166 2 + + CCONJ iajs-2479 166 3 m2 m2 PROPN iajs-2479 166 4 + + CCONJ iajs-2479 166 5 m3 m3 PROPN iajs-2479 166 6 ≤ ≤ NUM iajs-2479 166 7 m m VERB iajs-2479 166 8 where where SCONJ iajs-2479 166 9 m1 m1 PROPN iajs-2479 166 10 , , PUNCT iajs-2479 166 11 m2 m2 PROPN iajs-2479 166 12 , , PUNCT iajs-2479 166 13 m3 m3 PROPN iajs-2479 166 14 and and CCONJ iajs-2479 166 15 m m PROPN iajs-2479 166 16 are be AUX iajs-2479 166 17 the the DET iajs-2479 166 18 min min ADJ iajs-2479 166 19 - - ADJ iajs-2479 166 20 objective objective ADJ iajs-2479 166 21 function function NOUN iajs-2479 166 22 values value NOUN iajs-2479 166 23 of of ADP iajs-2479 166 24 ( ( PUNCT iajs-2479 166 25 p1 p1 PROPN iajs-2479 166 26 ) ) PUNCT iajs-2479 166 27 , , PUNCT iajs-2479 166 28 ( ( PUNCT iajs-2479 166 29 p2),(p3 p2),(p3 NOUN iajs-2479 166 30 ) ) PUNCT iajs-2479 166 31 and and CCONJ iajs-2479 166 32 ( ( PUNCT iajs-2479 166 33 p p NOUN iajs-2479 166 34 ) ) PUNCT iajs-2479 166 35 respectively respectively ADV iajs-2479 166 36 . . PUNCT iajs-2479 166 37     SPACE iajs-2479 167 1 145 145 NUM iajs-2479 167 2     SPACE iajs-2479 167 3 ibn ibn PROPN iajs-2479 167 4 al al PROPN iajs-2479 167 5 - - PUNCT iajs-2479 167 6 haitham haitham PROPN iajs-2479 167 7 jour jour X iajs-2479 167 8 . . PROPN iajs-2479 167 9 for for ADP iajs-2479 167 10 pure pure ADJ iajs-2479 167 11 & & CCONJ iajs-2479 167 12 appl appl PROPN iajs-2479 167 13 . . PUNCT iajs-2479 168 1 sci sci PROPN iajs-2479 168 2 . . PROPN iajs-2479 169 1 33 33 NUM iajs-2479 169 2 ( ( PUNCT iajs-2479 169 3 3 3 NUM iajs-2479 169 4 ) ) PUNCT iajs-2479 169 5 2020 2020 NUM iajs-2479 169 6 4 4 NUM iajs-2479 169 7 . . X iajs-2479 170 1 two two NUM iajs-2479 170 2 important important ADJ iajs-2479 170 3 algorithms algorithm NOUN iajs-2479 170 4 4.1 4.1 NUM iajs-2479 170 5 . . PUNCT iajs-2479 171 1 lawler lawler PROPN iajs-2479 171 2 algorithm algorithm PROPN iajs-2479 171 3 ( ( PUNCT iajs-2479 171 4 la la NOUN iajs-2479 171 5 ) ) PUNCT iajs-2479 172 1 [ [ X iajs-2479 172 2 27 27 NUM iajs-2479 172 3 ] ] PUNCT iajs-2479 172 4 . . PUNCT iajs-2479 173 1 step step NOUN iajs-2479 173 2 ( ( PUNCT iajs-2479 173 3 1 1 NUM iajs-2479 173 4 ): ): PUNCT iajs-2479 173 5 let let VERB iajs-2479 173 6 n̅={1, n̅={1, ADP iajs-2479 173 7 … … X iajs-2479 173 8 ,n ,n NOUN iajs-2479 173 9 } } PUNCT iajs-2479 173 10 , , PUNCT iajs-2479 173 11 ω=(∅ ω=(∅ PROPN iajs-2479 173 12 ) ) PUNCT iajs-2479 173 13 and and CCONJ iajs-2479 173 14 m m AUX iajs-2479 173 15 be be AUX iajs-2479 173 16 " " PUNCT iajs-2479 173 17 the the DET iajs-2479 173 18 set set NOUN iajs-2479 173 19 of of ADP iajs-2479 173 20 all all DET iajs-2479 173 21 jobs job NOUN iajs-2479 173 22 with with ADP iajs-2479 173 23 no no DET iajs-2479 173 24 successors successor NOUN iajs-2479 173 25 " " PUNCT iajs-2479 173 26 . . PUNCT iajs-2479 174 1 step step NOUN iajs-2479 174 2 ( ( PUNCT iajs-2479 174 3 2 2 NUM iajs-2479 174 4 ): ): PUNCT iajs-2479 174 5 let let VERB iajs-2479 174 6 [ [ X iajs-2479 174 7 j j X iajs-2479 174 8 * * X iajs-2479 174 9 ] ] X iajs-2479 174 10 such such ADJ iajs-2479 174 11 that that SCONJ iajs-2479 174 12 [ [ X iajs-2479 174 13 fj fj X iajs-2479 174 14 * * X iajs-2479 174 15 ( ( PUNCT iajs-2479 174 16 σjϵn̅ σjϵn̅ X iajs-2479 174 17 pj)= pj)= PROPN iajs-2479 174 18 minjϵm minjϵm NOUN iajs-2479 174 19 { { PUNCT iajs-2479 174 20 fj fj PROPN iajs-2479 174 21 ( ( PUNCT iajs-2479 174 22 σjϵn̅ σjϵn̅ PROPN iajs-2479 174 23 pj pj PROPN iajs-2479 174 24 ) ) PUNCT iajs-2479 174 25 } } PUNCT iajs-2479 174 26 ] ] PUNCT iajs-2479 174 27 , , PUNCT iajs-2479 174 28 j∈ j∈ PROPN iajs-2479 174 29 m m AUX iajs-2479 174 30 set set VERB iajs-2479 174 31 n n PROPN iajs-2479 174 32 = = SYM iajs-2479 174 33 n̅- n̅- PROPN iajs-2479 174 34 { { PUNCT iajs-2479 174 35 j j NOUN iajs-2479 174 36 * * PROPN iajs-2479 174 37 } } PUNCT iajs-2479 174 38 and and CCONJ iajs-2479 174 39 sequence sequence VERB iajs-2479 174 40 the the DET iajs-2479 174 41 job job NOUN iajs-2479 174 42 [ [ PUNCT iajs-2479 174 43 j j NOUN iajs-2479 174 44 * * X iajs-2479 174 45 ] ] X iajs-2479 174 46 in in ADP iajs-2479 174 47 the the DET iajs-2479 174 48 last last ADJ iajs-2479 174 49 position position NOUN iajs-2479 174 50 of of ADP iajs-2479 174 51 ω ω PROPN iajs-2479 174 52 . . PUNCT iajs-2479 175 1 modify modify VERB iajs-2479 175 2 m m PRON iajs-2479 175 3 to to PART iajs-2479 175 4 represent represent VERB iajs-2479 175 5 the the DET iajs-2479 175 6 new new ADJ iajs-2479 175 7 set set NOUN iajs-2479 175 8 of of ADP iajs-2479 175 9 the the DET iajs-2479 175 10 schedule schedule NOUN iajs-2479 175 11 jobs job NOUN iajs-2479 175 12 . . PUNCT iajs-2479 176 1 step step NOUN iajs-2479 176 2 ( ( PUNCT iajs-2479 176 3 3 3 NUM iajs-2479 176 4 ): ): PUNCT iajs-2479 176 5 if if SCONJ iajs-2479 176 6 n̅ n̅ NOUN iajs-2479 176 7 = = SYM iajs-2479 176 8 ∅ ∅ NOUN iajs-2479 176 9 stop stop NOUN iajs-2479 176 10 , , PUNCT iajs-2479 176 11 o.w o.w PROPN iajs-2479 176 12 go go VERB iajs-2479 176 13 to to PART iajs-2479 176 14 step step VERB iajs-2479 176 15 ( ( PUNCT iajs-2479 176 16 2 2 NUM iajs-2479 176 17 ) ) PUNCT iajs-2479 176 18 . . PUNCT iajs-2479 177 1 this this DET iajs-2479 177 2 algorithm algorithm NOUN iajs-2479 177 3 , , PUNCT iajs-2479 177 4 which which PRON iajs-2479 177 5 solves solve VERB iajs-2479 177 6 the the DET iajs-2479 177 7 [ [ X iajs-2479 177 8 1 1 NUM iajs-2479 177 9 / / SYM iajs-2479 177 10 prec prec X iajs-2479 177 11 / / SYM iajs-2479 177 12 fmax fmax PROPN iajs-2479 177 13 p p PROPN iajs-2479 177 14 or or CCONJ iajs-2479 177 15 1//fmax 1//fmax PROPN iajs-2479 177 16 ] ] PUNCT iajs-2479 177 17 problems problem NOUN iajs-2479 177 18 , , PUNCT iajs-2479 177 19 where where SCONJ iajs-2479 177 20 fmax fmax PROPN iajs-2479 177 21 ϵ ϵ X iajs-2479 177 22 { { PUNCT iajs-2479 177 23 cmax cmax NOUN iajs-2479 177 24 , , PUNCT iajs-2479 177 25 lmax lmax NOUN iajs-2479 177 26 , , PUNCT iajs-2479 177 27 tmax tmax ADV iajs-2479 177 28 , , PUNCT iajs-2479 177 29 vmax vmax X iajs-2479 177 30 } } PUNCT iajs-2479 177 31 . . PUNCT iajs-2479 178 1 4.2 4.2 NUM iajs-2479 178 2 moore moore PROPN iajs-2479 178 3 algorithm algorithm PROPN iajs-2479 178 4 ( ( PUNCT iajs-2479 178 5 ma ma PROPN iajs-2479 178 6 ) ) PUNCT iajs-2479 179 1 [ [ X iajs-2479 179 2 21 21 NUM iajs-2479 179 3 ] ] PUNCT iajs-2479 179 4 . . PUNCT iajs-2479 180 1 step step NOUN iajs-2479 180 2 1 1 NUM iajs-2479 180 3 : : PUNCT iajs-2479 180 4 order order VERB iajs-2479 180 5 the the DET iajs-2479 180 6 jobs job NOUN iajs-2479 180 7 in in ADP iajs-2479 180 8 ( ( PUNCT iajs-2479 180 9 edd)-rule edd)-rule ADV iajs-2479 180 10 , , PUNCT iajs-2479 180 11 let let VERB iajs-2479 180 12 e e NOUN iajs-2479 180 13 = = VERB iajs-2479 180 14 l l NOUN iajs-2479 180 15 = = NOUN iajs-2479 180 16 ø ø X iajs-2479 180 17 , , PUNCT iajs-2479 180 18 and and CCONJ iajs-2479 180 19 let let VERB iajs-2479 180 20 t= t= PRON iajs-2479 180 21 k=0 k=0 PROPN iajs-2479 180 22 . . PUNCT iajs-2479 181 1 step step NOUN iajs-2479 181 2 2 2 NUM iajs-2479 181 3 : : PUNCT iajs-2479 181 4 k k X iajs-2479 181 5 = = X iajs-2479 181 6 k+1 k+1 X iajs-2479 181 7 , , PUNCT iajs-2479 181 8 if if SCONJ iajs-2479 181 9 k k PROPN iajs-2479 181 10 ˃ ˃ PROPN iajs-2479 181 11 n n CCONJ iajs-2479 181 12 then then ADV iajs-2479 181 13 go go VERB iajs-2479 181 14 to to PART iajs-2479 181 15 step step VERB iajs-2479 181 16 ( ( PUNCT iajs-2479 181 17 4 4 NUM iajs-2479 181 18 ) ) PUNCT iajs-2479 181 19 . . PUNCT iajs-2479 182 1 step step NOUN iajs-2479 182 2 3 3 NUM iajs-2479 182 3 : : PUNCT iajs-2479 182 4 set set VERB iajs-2479 182 5 t t PROPN iajs-2479 182 6 = = PROPN iajs-2479 182 7 t t PROPN iajs-2479 182 8 + + PROPN iajs-2479 182 9 pk pk NOUN iajs-2479 182 10 , , PUNCT iajs-2479 182 11 e e PROPN iajs-2479 182 12 = = NOUN iajs-2479 182 13 e∪ e∪ PROPN iajs-2479 182 14 𝑘 𝑘 PART iajs-2479 182 15 𝑖𝑓 𝑖𝑓 NOUN iajs-2479 182 16 𝑡 𝑡 PROPN iajs-2479 182 17 𝑑 𝑑 PROPN iajs-2479 182 18 . . PUNCT iajs-2479 183 1 then then ADV iajs-2479 183 2 go go VERB iajs-2479 183 3 to to PART iajs-2479 183 4 step step NOUN iajs-2479 183 5 ( ( PUNCT iajs-2479 183 6 2 2 NUM iajs-2479 183 7 ) ) PUNCT iajs-2479 183 8 . . PUNCT iajs-2479 184 1 otherwise otherwise ADV iajs-2479 184 2 if if SCONJ iajs-2479 184 3 ( ( PUNCT iajs-2479 184 4 t t NOUN iajs-2479 184 5 ˃ ˃ NOUN iajs-2479 184 6 dk dk NOUN iajs-2479 184 7 ) ) PUNCT iajs-2479 184 8 then then ADV iajs-2479 184 9 find find VERB iajs-2479 184 10 a a DET iajs-2479 184 11 job job NOUN iajs-2479 184 12 j j PROPN iajs-2479 184 13 ∈ ∈ PROPN iajs-2479 184 14 𝐸 𝐸 PROPN iajs-2479 184 15 , , PUNCT iajs-2479 184 16 with with ADP iajs-2479 184 17 pj pj PROPN iajs-2479 184 18 is be AUX iajs-2479 184 19 as as ADV iajs-2479 184 20 large large ADJ iajs-2479 184 21 as as ADP iajs-2479 184 22 possible possible ADJ iajs-2479 184 23 and and CCONJ iajs-2479 184 24 set set VERB iajs-2479 184 25 e e NOUN iajs-2479 184 26 = = NOUN iajs-2479 184 27 e𝑗 e𝑗 X iajs-2479 184 28 , , PUNCT iajs-2479 184 29 l l X iajs-2479 184 30 = = NOUN iajs-2479 184 31 l∪ l∪ X iajs-2479 184 32 𝑗 𝑗 INTJ iajs-2479 184 33 , , PUNCT iajs-2479 184 34 and and CCONJ iajs-2479 184 35 t= t= PROPN iajs-2479 184 36 tpj tpj NOUN iajs-2479 184 37 , , PUNCT iajs-2479 184 38 go go VERB iajs-2479 184 39 to to PART iajs-2479 184 40 step step VERB iajs-2479 184 41 ( ( PUNCT iajs-2479 184 42 2 2 NUM iajs-2479 184 43 ) ) PUNCT iajs-2479 184 44 . . PUNCT iajs-2479 185 1 step step NOUN iajs-2479 185 2 4 4 NUM iajs-2479 185 3 : : PUNCT iajs-2479 185 4 e e X iajs-2479 185 5 is be AUX iajs-2479 185 6 the the DET iajs-2479 185 7 step step NOUN iajs-2479 185 8 of of ADP iajs-2479 185 9 early early ADJ iajs-2479 185 10 jobs job NOUN iajs-2479 185 11 , , PUNCT iajs-2479 185 12 l l NOUN iajs-2479 185 13 is be AUX iajs-2479 185 14 the the DET iajs-2479 185 15 step step NOUN iajs-2479 185 16 of of ADP iajs-2479 185 17 late late ADJ iajs-2479 185 18 jobs job NOUN iajs-2479 185 19 . . PUNCT iajs-2479 186 1 this this DET iajs-2479 186 2 algorithm algorithm NOUN iajs-2479 186 3 to to PART iajs-2479 186 4 solve solve VERB iajs-2479 186 5 the the DET iajs-2479 186 6 ( ( PUNCT iajs-2479 186 7 1//uj 1//uj NUM iajs-2479 186 8 ) ) PUNCT iajs-2479 186 9 problem problem NOUN iajs-2479 186 10 . . PUNCT iajs-2479 187 1 5 5 X iajs-2479 187 2 . . X iajs-2479 187 3 special special ADJ iajs-2479 187 4 cases case NOUN iajs-2479 187 5 ( ( PUNCT iajs-2479 187 6 sc sc NOUN iajs-2479 187 7 ) ) PUNCT iajs-2479 187 8 a a DET iajs-2479 187 9 special special ADJ iajs-2479 187 10 cases case NOUN iajs-2479 187 11 ( ( PUNCT iajs-2479 187 12 sc sc NOUN iajs-2479 187 13 ) ) PUNCT iajs-2479 187 14 for for ADP iajs-2479 187 15 scheduling scheduling NOUN iajs-2479 187 16 problem problem NOUN iajs-2479 187 17 means mean VERB iajs-2479 187 18 getting get VERB iajs-2479 187 19 an an DET iajs-2479 187 20 optimal optimal ADJ iajs-2479 187 21 schedule schedule NOUN iajs-2479 187 22 ( ( PUNCT iajs-2479 187 23 optimal optimal ADJ iajs-2479 187 24 solution solution NOUN iajs-2479 187 25 ) ) PUNCT iajs-2479 187 26 directly directly ADV iajs-2479 187 27 without without ADP iajs-2479 187 28 utilize utilize NOUN iajs-2479 187 29 ( ( PUNCT iajs-2479 187 30 b&b b&b PROPN iajs-2479 187 31 ) ) PUNCT iajs-2479 187 32 method method NOUN iajs-2479 187 33 or or CCONJ iajs-2479 187 34 ( ( PUNCT iajs-2479 187 35 dp dp NOUN iajs-2479 187 36 ) ) PUNCT iajs-2479 187 37 technique technique NOUN iajs-2479 187 38 [ [ X iajs-2479 187 39 28 28 NUM iajs-2479 187 40 ] ] PUNCT iajs-2479 187 41 . . PUNCT iajs-2479 188 1 in in ADP iajs-2479 188 2 this this DET iajs-2479 188 3 section section NOUN iajs-2479 188 4 we we PRON iajs-2479 188 5 present present VERB iajs-2479 188 6 two two NUM iajs-2479 188 7 ( ( PUNCT iajs-2479 188 8 sc sc PROPN iajs-2479 188 9 ) ) PUNCT iajs-2479 188 10 of of ADP iajs-2479 188 11 our our PRON iajs-2479 188 12 problem problem NOUN iajs-2479 188 13 ( ( PUNCT iajs-2479 188 14 p p NOUN iajs-2479 188 15 ) ) PUNCT iajs-2479 188 16 , , PUNCT iajs-2479 188 17 which which PRON iajs-2479 188 18 are be AUX iajs-2479 188 19 as as SCONJ iajs-2479 188 20 follows follow VERB iajs-2479 188 21 : : PUNCT iajs-2479 188 22 case case NOUN iajs-2479 188 23 1 1 X iajs-2479 188 24 . . PUNCT iajs-2479 189 1 if if SCONJ iajs-2479 189 2 cj= cj= PROPN iajs-2479 189 3 dj dj VERB iajs-2479 189 4 ∀ ∀ PUNCT iajs-2479 189 5 j j NOUN iajs-2479 189 6 in in ADP iajs-2479 189 7 a a DET iajs-2479 189 8 schedule schedule NOUN iajs-2479 189 9 s s NOUN iajs-2479 189 10 and and CCONJ iajs-2479 189 11 the the DET iajs-2479 189 12 preemptive preemptive NOUN iajs-2479 189 13 is be AUX iajs-2479 189 14 allowed allow VERB iajs-2479 189 15 then then ADV iajs-2479 189 16 s s AUX iajs-2479 189 17 given give VERB iajs-2479 189 18 an an DET iajs-2479 189 19 optimal optimal ADJ iajs-2479 189 20 schedule schedule NOUN iajs-2479 189 21 for for ADP iajs-2479 189 22 the the DET iajs-2479 189 23 problem problem NOUN iajs-2479 189 24 1/ 1/ PROPN iajs-2479 189 25 rj rj PROPN iajs-2479 189 26 , , PUNCT iajs-2479 189 27 pmtn pmtn NOUN iajs-2479 189 28 / / SYM iajs-2479 189 29 ∑ ∑ PUNCT iajs-2479 189 30 𝑪𝒋 𝑪𝒋 ADP iajs-2479 189 31 𝑻𝒋 𝑻𝒋 PROPN iajs-2479 189 32 𝑬𝒋 𝑬𝒋 PROPN iajs-2479 189 33 𝒏 𝒏 PROPN iajs-2479 189 34 𝒋 𝒋 X iajs-2479 189 35 𝟏 𝟏 NOUN iajs-2479 189 36 𝑼𝒋 𝑼𝒋 PROPN iajs-2479 189 37 𝑽𝒋 𝑽𝒋 PROPN iajs-2479 189 38 . . PUNCT iajs-2479 190 1 proof proof NOUN iajs-2479 190 2 : : PUNCT iajs-2479 190 3 from from ADP iajs-2479 190 4 cj cj NOUN iajs-2479 190 5 = = NOUN iajs-2479 190 6 dj dj NOUN iajs-2479 190 7 ∀ ∀ X iajs-2479 190 8 j j NOUN iajs-2479 190 9 in in ADP iajs-2479 190 10 s s PROPN iajs-2479 190 11 , , PUNCT iajs-2479 190 12 then then ADV iajs-2479 190 13 tj tj X iajs-2479 190 14 = = PUNCT iajs-2479 190 15 ej ej PROPN iajs-2479 190 16 = = SYM iajs-2479 190 17 uj uj PROPN iajs-2479 190 18 = = NOUN iajs-2479 191 1 vj vj PROPN iajs-2479 191 2 = = SYM iajs-2479 191 3 0 0 NUM iajs-2479 191 4 ∀ ∀ NOUN iajs-2479 191 5 j j NOUN iajs-2479 191 6 , , PUNCT iajs-2479 191 7 therefore therefore ADV iajs-2479 191 8 problem problem NOUN iajs-2479 191 9 ( ( PUNCT iajs-2479 191 10 p p NOUN iajs-2479 191 11 ) ) PUNCT iajs-2479 191 12 with with ADP iajs-2479 191 13 preemptive preemptive ADJ iajs-2479 191 14 reduced reduce VERB iajs-2479 191 15 to to ADP iajs-2479 191 16 1 1 NUM iajs-2479 191 17 / / SYM iajs-2479 191 18 rj rj PROPN iajs-2479 191 19 , , PUNCT iajs-2479 191 20 pmtn/∑cj pmtn/∑cj PROPN iajs-2479 191 21 , , PUNCT iajs-2479 191 22 but but CCONJ iajs-2479 191 23 this this DET iajs-2479 191 24 problem problem NOUN iajs-2479 191 25 solved solve VERB iajs-2479 191 26 in in ADP iajs-2479 191 27 " " PUNCT iajs-2479 191 28 shortest short ADJ iajs-2479 191 29 remaining remain VERB iajs-2479 191 30 processing processing NOUN iajs-2479 191 31 time time NOUN iajs-2479 191 32 ( ( PUNCT iajs-2479 191 33 srpt)-rule srpt)-rule NOUN iajs-2479 191 34 " " PUNCT iajs-2479 191 35 [ [ X iajs-2479 191 36 6 6 NUM iajs-2479 191 37 ] ] PUNCT iajs-2479 191 38 . . PUNCT iajs-2479 192 1 then then ADV iajs-2479 192 2 s s AUX iajs-2479 192 3 given give VERB iajs-2479 192 4 an an DET iajs-2479 192 5 optimal optimal ADJ iajs-2479 192 6     SPACE iajs-2479 192 7 schedule schedule NOUN iajs-2479 192 8 for for ADP iajs-2479 192 9 the the DET iajs-2479 192 10 problem problem NOUN iajs-2479 192 11 1/ 1/ PROPN iajs-2479 192 12 rj rj PROPN iajs-2479 192 13 , , PUNCT iajs-2479 192 14 pmtn pmtn NOUN iajs-2479 192 15 / / SYM iajs-2479 192 16 ∑ ∑ PUNCT iajs-2479 192 17 𝐶 𝐶 PROPN iajs-2479 192 18 𝑇 𝑇 PROPN iajs-2479 192 19 𝐸 𝐸 PROPN iajs-2479 192 20 𝑈 𝑈 PROPN iajs-2479 192 21 𝑉 𝑉 PROPN iajs-2479 192 22 . . PUNCT iajs-2479 192 23     SPACE iajs-2479 193 1 146 146 NUM iajs-2479 193 2     SPACE iajs-2479 193 3 ibn ibn PROPN iajs-2479 193 4 al al PROPN iajs-2479 193 5 - - PUNCT iajs-2479 193 6 haitham haitham PROPN iajs-2479 193 7 jour jour X iajs-2479 193 8 . . PROPN iajs-2479 193 9 for for ADP iajs-2479 193 10 pure pure ADJ iajs-2479 193 11 & & CCONJ iajs-2479 193 12 appl appl PROPN iajs-2479 193 13 . . PUNCT iajs-2479 194 1 sci sci PROPN iajs-2479 194 2 . . PROPN iajs-2479 195 1 33 33 NUM iajs-2479 195 2 ( ( PUNCT iajs-2479 195 3 3 3 NUM iajs-2479 195 4 ) ) PUNCT iajs-2479 195 5 2020 2020 NUM iajs-2479 195 6 case case NOUN iajs-2479 195 7 2 2 NUM iajs-2479 195 8 . . PUNCT iajs-2479 196 1 if if SCONJ iajs-2479 196 2 in in ADP iajs-2479 196 3 spt spt PROPN iajs-2479 196 4 schedule schedule NOUN iajs-2479 196 5 rj rj PROPN iajs-2479 196 6 = = NOUN iajs-2479 196 7 r r NOUN iajs-2479 196 8 ∀ ∀ X iajs-2479 196 9 j j NOUN iajs-2479 196 10 and and CCONJ iajs-2479 196 11 satisfy satisfy VERB iajs-2479 196 12 , , PUNCT iajs-2479 196 13 " " PUNCT iajs-2479 196 14 ( ( PUNCT iajs-2479 196 15 just just ADV iajs-2479 196 16 in in ADP iajs-2479 196 17 time time NOUN iajs-2479 196 18 ) ) PUNCT iajs-2479 196 19 ( ( PUNCT iajs-2479 196 20 jit jit PROPN iajs-2479 196 21 ) ) PUNCT iajs-2479 196 22 " " PUNCT iajs-2479 196 23 then then ADV iajs-2479 196 24 ( ( PUNCT iajs-2479 196 25 spt)rule spt)rule PROPN iajs-2479 196 26 given give VERB iajs-2479 196 27 an an DET iajs-2479 196 28 optimal optimal ADJ iajs-2479 196 29 schedule schedule NOUN iajs-2479 196 30 for for ADP iajs-2479 196 31 the the DET iajs-2479 196 32 problem problem NOUN iajs-2479 196 33 ( ( PUNCT iajs-2479 196 34 p p NOUN iajs-2479 196 35 ) ) PUNCT iajs-2479 196 36 . . PUNCT iajs-2479 197 1 proof proof NOUN iajs-2479 197 2 : : PUNCT iajs-2479 197 3 from from ADP iajs-2479 197 4 ( ( PUNCT iajs-2479 197 5 jit jit NOUN iajs-2479 197 6 ) ) PUNCT iajs-2479 197 7 we we PRON iajs-2479 197 8 get get VERB iajs-2479 197 9 cj cj NOUN iajs-2479 197 10 = = SYM iajs-2479 197 11 dj dj PROPN iajs-2479 197 12 , , PUNCT iajs-2479 197 13 then then ADV iajs-2479 197 14 tj tj X iajs-2479 197 15 = = PUNCT iajs-2479 197 16 ej ej PROPN iajs-2479 198 1 = = SYM iajs-2479 198 2 uj uj PROPN iajs-2479 198 3 = = NOUN iajs-2479 199 1 vj vj PROPN iajs-2479 199 2 = = SYM iajs-2479 199 3 0 0 NUM iajs-2479 199 4 ∀ ∀ NOUN iajs-2479 199 5 j j NOUN iajs-2479 199 6 , , PUNCT iajs-2479 199 7 therefore therefore ADV iajs-2479 199 8 problem problem NOUN iajs-2479 199 9 ( ( PUNCT iajs-2479 199 10 p p NOUN iajs-2479 199 11 ) ) PUNCT iajs-2479 199 12 reduced reduce VERB iajs-2479 199 13 to to ADP iajs-2479 199 14 1 1 NUM iajs-2479 199 15 / / SYM iajs-2479 199 16 rj/ rj/ PROPN iajs-2479 199 17 ∑ ∑ PROPN iajs-2479 199 18 𝐶 𝐶 PROPN iajs-2479 199 19 , , PUNCT iajs-2479 199 20 but but CCONJ iajs-2479 199 21 this this DET iajs-2479 199 22 problem problem NOUN iajs-2479 199 23 was be AUX iajs-2479 199 24 solved solve VERB iajs-2479 199 25 by by ADP iajs-2479 199 26 ( ( PUNCT iajs-2479 199 27 spt)-rule spt)-rule NOUN iajs-2479 199 28 . . PUNCT iajs-2479 200 1 then then ADV iajs-2479 200 2 ( ( PUNCT iajs-2479 200 3 spt)-rule spt)-rule NOUN iajs-2479 200 4 given give VERB iajs-2479 200 5 an an DET iajs-2479 200 6 optimal optimal ADJ iajs-2479 200 7 schedule schedule NOUN iajs-2479 200 8 for for ADP iajs-2479 200 9 the the DET iajs-2479 200 10 problem problem NOUN iajs-2479 200 11 ( ( PUNCT iajs-2479 200 12 p p NOUN iajs-2479 200 13 ) ) PUNCT iajs-2479 200 14 . . PUNCT iajs-2479 201 1 6 6 X iajs-2479 201 2 . . X iajs-2479 201 3 branch branch NOUN iajs-2479 201 4 and and CCONJ iajs-2479 201 5 bound bind VERB iajs-2479 201 6 ( ( PUNCT iajs-2479 201 7 b&b b&b PROPN iajs-2479 201 8 ) ) PUNCT iajs-2479 201 9 algorithm algorithm NOUN iajs-2479 201 10 in in ADP iajs-2479 201 11 this this DET iajs-2479 201 12 section section NOUN iajs-2479 201 13 , , PUNCT iajs-2479 201 14 we we PRON iajs-2479 201 15 apply apply VERB iajs-2479 201 16 ( ( PUNCT iajs-2479 201 17 b&b b&b PROPN iajs-2479 201 18 ) ) PUNCT iajs-2479 201 19 to to PART iajs-2479 201 20 get get VERB iajs-2479 201 21 an an DET iajs-2479 201 22 exact exact ADJ iajs-2479 201 23 solution solution NOUN iajs-2479 201 24 for for ADP iajs-2479 201 25 our our PRON iajs-2479 201 26 problem problem NOUN iajs-2479 201 27 ( ( PUNCT iajs-2479 201 28 p p NOUN iajs-2479 201 29 ) ) PUNCT iajs-2479 201 30 . . PUNCT iajs-2479 202 1 the the DET iajs-2479 202 2 ( ( PUNCT iajs-2479 202 3 b&b b&b PROPN iajs-2479 202 4 ) ) PUNCT iajs-2479 202 5 method method NOUN iajs-2479 202 6 is be AUX iajs-2479 202 7 strategy strategy NOUN iajs-2479 202 8 to to PART iajs-2479 202 9 explore explore VERB iajs-2479 202 10 the the DET iajs-2479 202 11 solution solution NOUN iajs-2479 202 12 space space NOUN iajs-2479 202 13 based base VERB iajs-2479 202 14 on on ADP iajs-2479 202 15 the the DET iajs-2479 202 16 implicit implicit ADJ iajs-2479 202 17 enumeration enumeration NOUN iajs-2479 202 18 of of ADP iajs-2479 202 19 the the DET iajs-2479 202 20 solution solution NOUN iajs-2479 202 21 . . PUNCT iajs-2479 203 1 this this DET iajs-2479 203 2 method method NOUN iajs-2479 203 3 is be AUX iajs-2479 203 4 based base VERB iajs-2479 203 5 on on ADP iajs-2479 203 6 the the DET iajs-2479 203 7 idea idea NOUN iajs-2479 203 8 of of ADP iajs-2479 203 9 calculate calculate NOUN iajs-2479 203 10 all all DET iajs-2479 203 11 feasible feasible ADJ iajs-2479 203 12 solutions solution NOUN iajs-2479 203 13 by by ADP iajs-2479 203 14 a a DET iajs-2479 203 15 special special ADJ iajs-2479 203 16 technique technique NOUN iajs-2479 203 17 , , PUNCT iajs-2479 203 18 which which PRON iajs-2479 203 19 among among ADP iajs-2479 203 20 them they PRON iajs-2479 203 21 research research NOUN iajs-2479 203 22 tree tree NOUN iajs-2479 203 23 technique technique NOUN iajs-2479 203 24 , , PUNCT iajs-2479 203 25 where where SCONJ iajs-2479 203 26 helps help VERB iajs-2479 203 27 to to PART iajs-2479 203 28 present present VERB iajs-2479 203 29 the the DET iajs-2479 203 30 procedures procedure NOUN iajs-2479 203 31 of of ADP iajs-2479 203 32 this this DET iajs-2479 203 33 method method NOUN iajs-2479 203 34 more more ADV iajs-2479 203 35 clearly clearly ADV iajs-2479 203 36 . . PUNCT iajs-2479 204 1 here here ADV iajs-2479 204 2 , , PUNCT iajs-2479 204 3 at at ADP iajs-2479 204 4 the the DET iajs-2479 204 5 root root NOUN iajs-2479 204 6 node node NOUN iajs-2479 204 7 of of ADP iajs-2479 204 8 the the DET iajs-2479 204 9 search search NOUN iajs-2479 204 10 tree tree NOUN iajs-2479 204 11 , , PUNCT iajs-2479 204 12 we we PRON iajs-2479 204 13 suggest suggest VERB iajs-2479 204 14 six six NUM iajs-2479 204 15 heuristic heuristic ADJ iajs-2479 204 16 methods method NOUN iajs-2479 204 17 to to PART iajs-2479 204 18 provide provide VERB iajs-2479 204 19 an an DET iajs-2479 204 20 upper upper ADJ iajs-2479 204 21 bound bind VERB iajs-2479 204 22 ( ( PUNCT iajs-2479 204 23 ub ub PROPN iajs-2479 204 24 ) ) PUNCT iajs-2479 204 25 on on ADP iajs-2479 204 26 the the DET iajs-2479 204 27 cost cost NOUN iajs-2479 204 28 of of ADP iajs-2479 204 29 the the DET iajs-2479 204 30 optimal optimal ADJ iajs-2479 204 31 schedule schedule NOUN iajs-2479 204 32 . . PUNCT iajs-2479 205 1 also also ADV iajs-2479 205 2 , , PUNCT iajs-2479 205 3 we we PRON iajs-2479 205 4 derive derive VERB iajs-2479 205 5 a a DET iajs-2479 205 6 especially especially ADV iajs-2479 205 7 formula formula NOUN iajs-2479 205 8 to to PART iajs-2479 205 9 ensure ensure VERB iajs-2479 205 10 an an DET iajs-2479 205 11 lower low ADJ iajs-2479 205 12 bound bind VERB iajs-2479 205 13 ( ( PUNCT iajs-2479 205 14 lb lb NOUN iajs-2479 205 15 ) ) PUNCT iajs-2479 205 16 , , PUNCT iajs-2479 205 17 as as ADP iajs-2479 205 18 following follow VERB iajs-2479 205 19 : : PUNCT iajs-2479 205 20 6.1 6.1 NUM iajs-2479 205 21 . . X iajs-2479 205 22 six six NUM iajs-2479 205 23 - - PUNCT iajs-2479 205 24 upper upper ADJ iajs-2479 205 25 bound bind VERB iajs-2479 205 26 ( ( PUNCT iajs-2479 205 27 6 6 NUM iajs-2479 205 28 - - PUNCT iajs-2479 205 29 ub ub NOUN iajs-2479 205 30 ) ) PUNCT iajs-2479 205 31 in in ADP iajs-2479 205 32 this this DET iajs-2479 205 33 section section NOUN iajs-2479 205 34 , , PUNCT iajs-2479 205 35 six six NUM iajs-2479 205 36 heuristic heuristic ADJ iajs-2479 205 37 techniques technique NOUN iajs-2479 205 38 are be AUX iajs-2479 205 39 used use VERB iajs-2479 205 40 for for ADP iajs-2479 205 41 arranging arrange VERB iajs-2479 205 42 the the DET iajs-2479 205 43 jobs job NOUN iajs-2479 205 44 and and CCONJ iajs-2479 205 45 valuation valuation NOUN iajs-2479 205 46 the the DET iajs-2479 205 47 cost cost NOUN iajs-2479 205 48 problem problem NOUN iajs-2479 205 49 ( ( PUNCT iajs-2479 205 50 p p NOUN iajs-2479 205 51 ) ) PUNCT iajs-2479 205 52 . . PUNCT iajs-2479 206 1 1 1 X iajs-2479 206 2 . . X iajs-2479 206 3 the the DET iajs-2479 206 4 first first ADJ iajs-2479 206 5 upper upper ADJ iajs-2479 206 6 bound bound ADJ iajs-2479 206 7 ( ( PUNCT iajs-2479 206 8 ub-1 ub-1 CCONJ iajs-2479 206 9 ) ) PUNCT iajs-2479 206 10 is be AUX iajs-2479 206 11 obtained obtain VERB iajs-2479 206 12 by by ADP iajs-2479 206 13 " " PUNCT iajs-2479 206 14 short short ADJ iajs-2479 206 15 release release NOUN iajs-2479 206 16 time time NOUN iajs-2479 206 17 ( ( PUNCT iajs-2479 206 18 srt)-rule srt)-rule NOUN iajs-2479 206 19 " " PUNCT iajs-2479 206 20 i.e. i.e. X iajs-2479 206 21 ( ( PUNCT iajs-2479 206 22 r1 r1 PROPN iajs-2479 206 23 ≤ ≤ NUM iajs-2479 206 24 … … SYM iajs-2479 206 25 ≤ ≤ NUM iajs-2479 206 26 rn rn NOUN iajs-2479 206 27 ) ) PUNCT iajs-2479 206 28 , , PUNCT iajs-2479 206 29 then then ADV iajs-2479 206 30 find find VERB iajs-2479 206 31 ; ; PUNCT iajs-2479 206 32 ub-1 ub-1 ADV iajs-2479 207 1 2 2 X iajs-2479 207 2 . . PUNCT iajs-2479 207 3 the the DET iajs-2479 207 4 second second ADJ iajs-2479 207 5 upper upper ADJ iajs-2479 207 6 bound bound ADJ iajs-2479 207 7 ( ( PUNCT iajs-2479 207 8 ub-2 ub-2 ADV iajs-2479 207 9 ) ) PUNCT iajs-2479 207 10 is be AUX iajs-2479 207 11 obtained obtain VERB iajs-2479 207 12 by by ADP iajs-2479 207 13 , , PUNCT iajs-2479 207 14 set set VERB iajs-2479 207 15 j1= j1= NOUN iajs-2479 207 16 min{rj min{rj PROPN iajs-2479 207 17 + + CCONJ iajs-2479 207 18 pj pj PROPN iajs-2479 207 19 } } PUNCT iajs-2479 207 20 , , PUNCT iajs-2479 207 21 then then ADV iajs-2479 207 22 order order VERB iajs-2479 207 23 all all DET iajs-2479 207 24 jobs job NOUN iajs-2479 207 25 by by ADP iajs-2479 207 26 ( ( PUNCT iajs-2479 207 27 srt srt NOUN iajs-2479 207 28 ) ) PUNCT iajs-2479 207 29 rule rule NOUN iajs-2479 207 30 , , PUNCT iajs-2479 207 31 where where SCONJ iajs-2479 207 32 j=2, j=2, PROPN iajs-2479 207 33 … … X iajs-2479 207 34 ,n ,n NOUN iajs-2479 207 35 . . PUNCT iajs-2479 208 1 then then ADV iajs-2479 208 2 find find VERB iajs-2479 208 3 ; ; PUNCT iajs-2479 208 4 ub-2 ub-2 X iajs-2479 208 5 3 3 X iajs-2479 208 6 . . X iajs-2479 209 1 the the DET iajs-2479 209 2 third third ADJ iajs-2479 209 3 upper upper ADJ iajs-2479 209 4 bound bound ADJ iajs-2479 209 5 ( ( PUNCT iajs-2479 209 6 ub-3 ub-3 X iajs-2479 209 7 ) ) PUNCT iajs-2479 209 8 is be AUX iajs-2479 209 9 obtained obtain VERB iajs-2479 209 10 by by ADP iajs-2479 209 11 order order NOUN iajs-2479 209 12 the the DET iajs-2479 209 13 jobs job NOUN iajs-2479 209 14 in in ADP iajs-2479 209 15 non non ADJ iajs-2479 209 16 - - ADJ iajs-2479 209 17 decreasing decrease VERB iajs-2479 209 18 of of ADP iajs-2479 209 19 the the DET iajs-2479 209 20 ( ( PUNCT iajs-2479 209 21 rj rj PROPN iajs-2479 209 22 + + PROPN iajs-2479 209 23 pj pj PROPN iajs-2479 209 24 ) ) PUNCT iajs-2479 209 25 i.e. i.e. X iajs-2479 209 26 ( ( PUNCT iajs-2479 209 27 r1 r1 NOUN iajs-2479 209 28 + + CCONJ iajs-2479 209 29 p1≤ p1≤ NUM iajs-2479 209 30 … … NUM iajs-2479 209 31 ≤ ≤ NUM iajs-2479 209 32 rn+ rn+ NOUN iajs-2479 209 33 pn pn PROPN iajs-2479 209 34 ) ) PUNCT iajs-2479 209 35 . . PUNCT iajs-2479 210 1 then then ADV iajs-2479 210 2 find find VERB iajs-2479 210 3 ; ; PUNCT iajs-2479 210 4 ub-3 ub-3 PROPN iajs-2479 210 5 4 4 NUM iajs-2479 210 6 . . PUNCT iajs-2479 211 1 the the DET iajs-2479 211 2 fourth fourth ADJ iajs-2479 211 3 upper upper ADJ iajs-2479 211 4 bound bound ADJ iajs-2479 211 5 ( ( PUNCT iajs-2479 211 6 ub-4 ub-4 NUM iajs-2479 211 7 ) ) PUNCT iajs-2479 211 8 is be AUX iajs-2479 211 9 obtained obtain VERB iajs-2479 211 10 by by ADP iajs-2479 211 11 , , PUNCT iajs-2479 211 12 set set VERB iajs-2479 211 13 j1 j1 PROPN iajs-2479 211 14 = = SYM iajs-2479 211 15 min{rj min{rj NOUN iajs-2479 211 16 + + ADJ iajs-2479 211 17 pj pj PROPN iajs-2479 211 18 } } PUNCT iajs-2479 211 19 , , PUNCT iajs-2479 211 20 then then ADV iajs-2479 211 21 order order VERB iajs-2479 211 22 all all DET iajs-2479 211 23 jobs job NOUN iajs-2479 211 24 by by ADP iajs-2479 211 25 ( ( PUNCT iajs-2479 211 26 spt spt ADJ iajs-2479 211 27 ) ) PUNCT iajs-2479 211 28 rule rule NOUN iajs-2479 211 29 , , PUNCT iajs-2479 211 30 i.e. i.e. X iajs-2479 211 31 ( ( PUNCT iajs-2479 211 32 p2≤ p2≤ NUM iajs-2479 211 33 … … SYM iajs-2479 211 34 ≤pn ≤pn NOUN iajs-2479 211 35 ) ) PUNCT iajs-2479 211 36 . . PUNCT iajs-2479 212 1 then then ADV iajs-2479 212 2 find find VERB iajs-2479 212 3 ; ; PUNCT iajs-2479 212 4 ub-4 ub-4 NUM iajs-2479 212 5 5 5 NUM iajs-2479 212 6 . . PUNCT iajs-2479 213 1 the the DET iajs-2479 213 2 fifth fifth ADJ iajs-2479 213 3 upper upper ADJ iajs-2479 213 4 bound bind VERB iajs-2479 213 5 ( ( PUNCT iajs-2479 213 6 ub-5 ub-5 NOUN iajs-2479 213 7 ) ) PUNCT iajs-2479 213 8 is be AUX iajs-2479 213 9 obtained obtain VERB iajs-2479 213 10 by by ADP iajs-2479 213 11 ( ( PUNCT iajs-2479 213 12 spt)-rule spt)-rule NOUN iajs-2479 213 13 . . PUNCT iajs-2479 214 1 then then ADV iajs-2479 214 2 find find VERB iajs-2479 214 3 ; ; PUNCT iajs-2479 214 4 ub-5 ub-5 NUM iajs-2479 214 5 6 6 NUM iajs-2479 214 6 . . PUNCT iajs-2479 215 1 the the DET iajs-2479 215 2 sixth sixth ADJ iajs-2479 215 3 upper upper ADJ iajs-2479 215 4 bound bind VERB iajs-2479 215 5 ( ( PUNCT iajs-2479 215 6 ub-6 ub-6 NUM iajs-2479 215 7 ) ) PUNCT iajs-2479 215 8 is be AUX iajs-2479 215 9 obtained obtain VERB iajs-2479 215 10 by by ADP iajs-2479 215 11 ( ( PUNCT iajs-2479 215 12 edd)-rule edd)-rule NOUN iajs-2479 215 13 . . PUNCT iajs-2479 216 1 then then ADV iajs-2479 216 2 find find VERB iajs-2479 216 3 ; ; PUNCT iajs-2479 216 4 ub-6 ub-6 ADJ iajs-2479 216 5 among among ADP iajs-2479 216 6 these these DET iajs-2479 216 7 sixheuristics sixheuristic NOUN iajs-2479 216 8 , , PUNCT iajs-2479 216 9 we we PRON iajs-2479 216 10 select select VERB iajs-2479 216 11 the the DET iajs-2479 216 12 lowest low ADJ iajs-2479 216 13 value value NOUN iajs-2479 216 14 to to PART iajs-2479 216 15 be be AUX iajs-2479 216 16 the the DET iajs-2479 216 17 an an DET iajs-2479 216 18 upper upper ADJ iajs-2479 216 19 bound bind VERB iajs-2479 216 20 , , PUNCT iajs-2479 216 21 ( ( PUNCT iajs-2479 216 22 i.e. i.e. X iajs-2479 216 23 ub= ub= PROPN iajs-2479 216 24 min min PROPN iajs-2479 216 25 { { PUNCT iajs-2479 216 26 ub-1 ub-1 ADV iajs-2479 216 27 , , PUNCT iajs-2479 216 28 ... ... PUNCT iajs-2479 216 29 , , PUNCT iajs-2479 216 30 ub-6 ub-6 ADJ iajs-2479 216 31 } } PUNCT iajs-2479 216 32 ) ) PUNCT iajs-2479 216 33 . . PUNCT iajs-2479 217 1 this this PRON iajs-2479 217 2 ub ub INTJ iajs-2479 217 3 is be AUX iajs-2479 217 4 then then ADV iajs-2479 217 5 used use VERB iajs-2479 217 6 in in ADP iajs-2479 217 7 a a DET iajs-2479 217 8 root root NOUN iajs-2479 217 9 node node NOUN iajs-2479 217 10 of of ADP iajs-2479 217 11 the the DET iajs-2479 217 12 search search NOUN iajs-2479 217 13 tree tree NOUN iajs-2479 217 14 in in ADP iajs-2479 217 15 ( ( PUNCT iajs-2479 217 16 bab bab PROPN iajs-2479 217 17 ) ) PUNCT iajs-2479 217 18 method method NOUN iajs-2479 217 19 . . PUNCT iajs-2479 218 1 6.2 6.2 NUM iajs-2479 218 2 . . PUNCT iajs-2479 219 1 lower lower ADV iajs-2479 219 2 bound bound ADJ iajs-2479 219 3 ( ( PUNCT iajs-2479 219 4 lb lb NOUN iajs-2479 219 5 ) ) PUNCT iajs-2479 219 6 finding find VERB iajs-2479 219 7 a a DET iajs-2479 219 8 lower low ADJ iajs-2479 219 9 bound bind VERB iajs-2479 219 10 ( ( PUNCT iajs-2479 219 11 lb lb NOUN iajs-2479 219 12 ) ) PUNCT iajs-2479 219 13 for for ADP iajs-2479 219 14 our our PRON iajs-2479 219 15 problem problem NOUN iajs-2479 219 16 ( ( PUNCT iajs-2479 219 17 p p NOUN iajs-2479 219 18 ) ) PUNCT iajs-2479 219 19 is be AUX iajs-2479 219 20 based base VERB iajs-2479 219 21 on on ADP iajs-2479 219 22 decomposing decompose VERB iajs-2479 219 23 problem problem NOUN iajs-2479 219 24 ( ( PUNCT iajs-2479 219 25 p p NOUN iajs-2479 219 26 ) ) PUNCT iajs-2479 219 27 into into ADP iajs-2479 219 28 three three NUM iajs-2479 219 29 sub sub NOUN iajs-2479 219 30 - - NOUN iajs-2479 219 31 problems problem NOUN iajs-2479 219 32 ( ( PUNCT iajs-2479 219 33 p1 p1 NOUN iajs-2479 219 34 ) ) PUNCT iajs-2479 219 35 , , PUNCT iajs-2479 219 36 ( ( PUNCT iajs-2479 219 37 p2 p2 PROPN iajs-2479 219 38 ) ) PUNCT iajs-2479 219 39 and and CCONJ iajs-2479 219 40 ( ( PUNCT iajs-2479 219 41 p3 p3 PROPN iajs-2479 219 42 ) ) PUNCT iajs-2479 219 43 . . PUNCT iajs-2479 220 1 then then ADV iajs-2479 220 2 calculate calculate VERB iajs-2479 220 3 m1 m1 PROPN iajs-2479 220 4 to to PART iajs-2479 220 5 be be AUX iajs-2479 220 6 ( ( PUNCT iajs-2479 220 7 lb-1 lb-1 NUM iajs-2479 220 8 ) ) PUNCT iajs-2479 220 9 for for ADP iajs-2479 220 10 ( ( PUNCT iajs-2479 220 11 p1 p1 PROPN iajs-2479 220 12 ) ) PUNCT iajs-2479 220 13 , , PUNCT iajs-2479 220 14 m2 m2 PROPN iajs-2479 220 15 to to PART iajs-2479 220 16 be be AUX iajs-2479 220 17 ( ( PUNCT iajs-2479 220 18 lb-2 lb-2 NOUN iajs-2479 220 19 ) ) PUNCT iajs-2479 220 20 for for ADP iajs-2479 220 21 ( ( PUNCT iajs-2479 220 22 p2 p2 NOUN iajs-2479 220 23 ) ) PUNCT iajs-2479 220 24 , , PUNCT iajs-2479 220 25 and and CCONJ iajs-2479 220 26 m3 m3 PROPN iajs-2479 220 27 to to PART iajs-2479 220 28 be be AUX iajs-2479 220 29 ( ( PUNCT iajs-2479 220 30 lb-3 lb-3 NOUN iajs-2479 220 31 ) ) PUNCT iajs-2479 220 32 for for ADP iajs-2479 220 33 ( ( PUNCT iajs-2479 220 34 p3 p3 PROPN iajs-2479 220 35 ) ) PUNCT iajs-2479 220 36 . . PUNCT iajs-2479 221 1 then then ADV iajs-2479 221 2 applying apply VERB iajs-2479 221 3 the the DET iajs-2479 221 4 theorem theorem NOUN iajs-2479 221 5 ( ( PUNCT iajs-2479 221 6 1 1 NUM iajs-2479 221 7 ): ): PUNCT iajs-2479 221 8   VERB iajs-2479 221 9 to to PART iajs-2479 221 10 get get VERB iajs-2479 221 11 a a DET iajs-2479 221 12 lower low ADJ iajs-2479 221 13 bound bind VERB iajs-2479 221 14 ( ( PUNCT iajs-2479 221 15 lb lb NOUN iajs-2479 221 16 ) ) PUNCT iajs-2479 221 17 for for ADP iajs-2479 221 18 problem problem NOUN iajs-2479 221 19 ( ( PUNCT iajs-2479 221 20 p1 p1 PROPN iajs-2479 221 21 ) ) PUNCT iajs-2479 221 22 ( ( PUNCT iajs-2479 221 23 lb-1 lb-1 NUM iajs-2479 221 24 ) ) PUNCT iajs-2479 221 25 . . PUNCT iajs-2479 222 1 we we PRON iajs-2479 222 2 modified modify VERB iajs-2479 222 3 the the DET iajs-2479 222 4 lower low ADJ iajs-2479 222 5 bound bind VERB iajs-2479 222 6 of of ADP iajs-2479 222 7 tariq tariq NOUN iajs-2479 222 8 and and CCONJ iajs-2479 222 9 hussam hussam PROPN iajs-2479 223 1 [ [ X iajs-2479 223 2 29 29 NUM iajs-2479 223 3 ] ] PUNCT iajs-2479 223 4 . . PUNCT iajs-2479 224 1 they they PRON iajs-2479 224 2 proved prove VERB iajs-2479 224 3 that that SCONJ iajs-2479 224 4 ( ( PUNCT iajs-2479 224 5 max max PROPN iajs-2479 224 6 { { PUNCT iajs-2479 224 7 ∑ ∑ PROPN iajs-2479 224 8 𝑑 𝑑 PROPN iajs-2479 224 9 , , PUNCT iajs-2479 224 10 ∑ ∑ ADV iajs-2479 224 11 𝑀𝑎𝑥 𝑀𝑎𝑥 PROPN iajs-2479 224 12 { { PUNCT iajs-2479 224 13 2cσ(j 2cσ(j NUM iajs-2479 224 14 ) ) PUNCT iajs-2479 224 15 – – PUNCT iajs-2479 224 16 dσ(j dσ(j NOUN iajs-2479 224 17 ) ) PUNCT iajs-2479 224 18 , , PUNCT iajs-2479 224 19 cσ(j cσ(j X iajs-2479 224 20 ) ) PUNCT iajs-2479 224 21 } } PUNCT iajs-2479 224 22 ) ) PUNCT iajs-2479 224 23 is be AUX iajs-2479 224 24 ( ( PUNCT iajs-2479 224 25 lb lb NOUN iajs-2479 224 26 ) ) PUNCT iajs-2479 224 27 for for ADP iajs-2479 224 28 the the DET iajs-2479 224 29 1//∑ 1//∑ PROPN iajs-2479 224 30 𝐶 𝐶 PROPN iajs-2479 224 31 𝑇 𝑇 PROPN iajs-2479 224 32 𝐸 𝐸 PROPN iajs-2479 224 33 problem problem NOUN iajs-2479 224 34 , , PUNCT iajs-2479 224 35 since since SCONJ iajs-2479 224 36 this this DET iajs-2479 224 37 problem problem NOUN iajs-2479 224 38 is be AUX iajs-2479 224 39 a a DET iajs-2479 224 40 special special ADJ iajs-2479 224 41 case case NOUN iajs-2479 224 42 of of ADP iajs-2479 224 43 our our PRON iajs-2479 224 44 problem problem NOUN iajs-2479 224 45 ( ( PUNCT iajs-2479 224 46 p1 p1 PROPN iajs-2479 224 47 ) ) PUNCT iajs-2479 224 48 , , PUNCT iajs-2479 224 49 then then ADV iajs-2479 224 50 ( ( PUNCT iajs-2479 224 51 max max PROPN iajs-2479 224 52 { { PUNCT iajs-2479 224 53 ∑ ∑ PROPN iajs-2479 224 54 𝑑 𝑑 PROPN iajs-2479 224 55 , , PUNCT iajs-2479 224 56 ∑ ∑ ADV iajs-2479 224 57 𝑀𝑎𝑥 𝑀𝑎𝑥 PROPN iajs-2479 224 58 { { PUNCT iajs-2479 224 59 2cσ(j 2cσ(j NUM iajs-2479 224 60 ) ) PUNCT iajs-2479 224 61 dσ(j dσ(j NOUN iajs-2479 224 62 ) ) PUNCT iajs-2479 224 63 , , PUNCT iajs-2479 224 64 cσ(j cσ(j X iajs-2479 224 65 ) ) PUNCT iajs-2479 224 66 } } PUNCT iajs-2479 224 67 ) ) PUNCT iajs-2479 224 68 is be AUX iajs-2479 224 69 also also ADV iajs-2479 224 70 ( ( PUNCT iajs-2479 224 71 lb lb X iajs-2479 224 72 ) ) PUNCT iajs-2479 224 73 of of ADP iajs-2479 224 74 our our PRON iajs-2479 224 75 problem problem NOUN iajs-2479 224 76 ( ( PUNCT iajs-2479 224 77 p1 p1 NOUN iajs-2479 224 78 ) ) PUNCT iajs-2479 224 79 . . PUNCT iajs-2479 225 1 but but CCONJ iajs-2479 225 2 this this PRON iajs-2479 225 3 ( ( PUNCT iajs-2479 225 4 lb lb NOUN iajs-2479 225 5 ) ) PUNCT iajs-2479 225 6 is be AUX iajs-2479 225 7 a a DET iajs-2479 225 8 weak weak ADJ iajs-2479 225 9 . . PUNCT iajs-2479 226 1 to to PART iajs-2479 226 2 improvement improvement VERB iajs-2479 226 3 this this DET iajs-2479 226 4 ( ( PUNCT iajs-2479 226 5 lb lb NOUN iajs-2479 226 6 ) ) PUNCT iajs-2479 226 7 , , PUNCT iajs-2479 226 8 we we PRON iajs-2479 226 9 suggest suggest VERB iajs-2479 226 10 the the DET iajs-2479 226 11 following follow VERB iajs-2479 226 12 : : PUNCT iajs-2479 226 13     SPACE iajs-2479 226 14 147 147 NUM iajs-2479 226 15     SPACE iajs-2479 226 16 ibn ibn PROPN iajs-2479 226 17 al al PROPN iajs-2479 226 18 - - PUNCT iajs-2479 226 19 haitham haitham PROPN iajs-2479 226 20 jour jour X iajs-2479 226 21 . . PROPN iajs-2479 226 22 for for ADP iajs-2479 226 23 pure pure ADJ iajs-2479 226 24 & & CCONJ iajs-2479 226 25 appl appl PROPN iajs-2479 226 26 . . PUNCT iajs-2479 227 1 sci sci PROPN iajs-2479 227 2 . . PROPN iajs-2479 228 1 33 33 NUM iajs-2479 228 2 ( ( PUNCT iajs-2479 228 3 3 3 NUM iajs-2479 228 4 ) ) PUNCT iajs-2479 228 5 2020 2020 NUM iajs-2479 229 1 ( ( PUNCT iajs-2479 229 2 lb-1)= lb-1)= NOUN iajs-2479 229 3 nr٭+𝜶 nr٭+𝜶 VERB iajs-2479 229 4 – – PUNCT iajs-2479 229 5 r r NOUN iajs-2479 229 6 ; ; PUNCT iajs-2479 229 7 where where SCONJ iajs-2479 229 8 : : PUNCT iajs-2479 229 9 n n NOUN iajs-2479 229 10 = = NOUN iajs-2479 229 11 number number NOUN iajs-2479 229 12 of of ADP iajs-2479 229 13 jobs job NOUN iajs-2479 229 14 . . PUNCT iajs-2479 230 1 r٭= r٭= PROPN iajs-2479 230 2 min min PROPN iajs-2479 230 3 rj rj PROPN iajs-2479 230 4 j=1, j=1, PROPN iajs-2479 230 5 … … PUNCT iajs-2479 230 6 ,n ,n NOUN iajs-2479 230 7 . . PUNCT iajs-2479 231 1 𝛼 𝛼 X iajs-2479 231 2 = = SYM iajs-2479 231 3 ( ( PUNCT iajs-2479 231 4 max max PROPN iajs-2479 231 5 { { PUNCT iajs-2479 231 6 ∑ ∑ PROPN iajs-2479 231 7 𝑑 𝑑 PROPN iajs-2479 231 8 , , PUNCT iajs-2479 231 9 ∑ ∑ ADV iajs-2479 231 10 𝑀𝑎𝑥 𝑀𝑎𝑥 PROPN iajs-2479 231 11 { { PUNCT iajs-2479 231 12 2cσ(j 2cσ(j NUM iajs-2479 231 13 ) ) PUNCT iajs-2479 231 14 dσ(j dσ(j NOUN iajs-2479 231 15 ) ) PUNCT iajs-2479 231 16 , , PUNCT iajs-2479 231 17 cσ(j cσ(j X iajs-2479 231 18 ) ) PUNCT iajs-2479 231 19 } } PUNCT iajs-2479 231 20 ) ) PUNCT iajs-2479 232 1 r r NOUN iajs-2479 232 2 = = PUNCT iajs-2479 232 3 ∑ ∑ PROPN iajs-2479 232 4 𝑟j 𝑟j NUM iajs-2479 232 5 j=1, j=1, NOUN iajs-2479 232 6 … … PUNCT iajs-2479 232 7 ,n ,n NOUN iajs-2479 232 8 . . PUNCT iajs-2479 233 1 then then ADV iajs-2479 233 2 for for ADP iajs-2479 233 3 problem problem NOUN iajs-2479 233 4 ( ( PUNCT iajs-2479 233 5 p1 p1 PROPN iajs-2479 233 6 ) ) PUNCT iajs-2479 233 7 , , PUNCT iajs-2479 233 8 the the DET iajs-2479 233 9 following follow VERB iajs-2479 233 10 algorithm algorithm NOUN iajs-2479 233 11 obtained obtain VERB iajs-2479 233 12 this this PRON iajs-2479 233 13 ( ( PUNCT iajs-2479 233 14 lb-1 lb-1 NUM iajs-2479 233 15 ) ) PUNCT iajs-2479 233 16 . . PUNCT iajs-2479 234 1 6.2.1 6.2.1 X iajs-2479 234 2 . . PUNCT iajs-2479 235 1 algorithm algorithm NOUN iajs-2479 235 2 ( ( PUNCT iajs-2479 235 3 lb-1 lb-1 PROPN iajs-2479 235 4 ) ) PUNCT iajs-2479 235 5 step(1 step(1 NOUN iajs-2479 235 6 ): ): PUNCT iajs-2479 235 7 order order NOUN iajs-2479 235 8 the the DET iajs-2479 235 9 jobs job NOUN iajs-2479 235 10 by by ADP iajs-2479 235 11 using use VERB iajs-2479 235 12 ( ( PUNCT iajs-2479 235 13 spt)rule spt)rule PROPN iajs-2479 235 14 . . PUNCT iajs-2479 236 1 step step NOUN iajs-2479 236 2 ( ( PUNCT iajs-2479 236 3 2 2 NUM iajs-2479 236 4 ): ): PUNCT iajs-2479 236 5 for for ADP iajs-2479 236 6 each each DET iajs-2479 236 7 job job NOUN iajs-2479 236 8 j j PROPN iajs-2479 236 9 compute compute VERB iajs-2479 236 10 the the DET iajs-2479 236 11 completion completion NOUN iajs-2479 236 12 time time NOUN iajs-2479 236 13 cj cj NOUN iajs-2479 236 14 , , PUNCT iajs-2479 236 15 2cσ(j 2cσ(j NUM iajs-2479 236 16 ) ) PUNCT iajs-2479 236 17 and and CCONJ iajs-2479 236 18 ∑ ∑ ADP iajs-2479 236 19 d d PROPN iajs-2479 236 20 j=1, j=1, NOUN iajs-2479 236 21 … … PUNCT iajs-2479 236 22 ,n ,n NOUN iajs-2479 236 23 . . PUNCT iajs-2479 237 1 step step NOUN iajs-2479 237 2 ( ( PUNCT iajs-2479 237 3 3 3 NUM iajs-2479 237 4 ): ): PUNCT iajs-2479 237 5 set set VERB iajs-2479 237 6 n n NOUN iajs-2479 237 7 = = PUNCT iajs-2479 237 8 number number NOUN iajs-2479 237 9 of of ADP iajs-2479 237 10 jobs job NOUN iajs-2479 237 11 and and CCONJ iajs-2479 237 12 r٭= r٭= PROPN iajs-2479 237 13 min min PROPN iajs-2479 237 14 rj rj PROPN iajs-2479 237 15 j=1, j=1, PROPN iajs-2479 237 16 … … PUNCT iajs-2479 237 17 ,n ,n SYM iajs-2479 237 18 . . PUNCT iajs-2479 238 1 step step NOUN iajs-2479 238 2 ( ( PUNCT iajs-2479 238 3 4 4 NUM iajs-2479 238 4 ): ): PUNCT iajs-2479 238 5 set set VERB iajs-2479 238 6 α α NOUN iajs-2479 238 7 = = SYM iajs-2479 238 8 ( ( PUNCT iajs-2479 238 9 max max PROPN iajs-2479 238 10 { { PUNCT iajs-2479 238 11 ∑ ∑ PROPN iajs-2479 238 12 d d PROPN iajs-2479 238 13 , , PUNCT iajs-2479 238 14 ∑ ∑ PROPN iajs-2479 238 15 max max PROPN iajs-2479 238 16 { { PUNCT iajs-2479 238 17 2cσ(j 2cσ(j NUM iajs-2479 238 18 ) ) PUNCT iajs-2479 238 19 dσ(j dσ(j NOUN iajs-2479 238 20 ) ) PUNCT iajs-2479 238 21 , , PUNCT iajs-2479 238 22 cσ(j cσ(j X iajs-2479 238 23 ) ) PUNCT iajs-2479 238 24 } } PUNCT iajs-2479 238 25 ) ) PUNCT iajs-2479 238 26 and and CCONJ iajs-2479 238 27 r= r= VERB iajs-2479 238 28 ∑ ∑ PUNCT iajs-2479 238 29 rj rj PROPN iajs-2479 238 30 j=1, j=1, PROPN iajs-2479 238 31 … … PUNCT iajs-2479 238 32 ,n ,n SYM iajs-2479 238 33 . . PUNCT iajs-2479 239 1 step step NOUN iajs-2479 239 2 ( ( PUNCT iajs-2479 239 3 5 5 NUM iajs-2479 239 4 ): ): PUNCT iajs-2479 239 5 find find VERB iajs-2479 239 6 ( ( PUNCT iajs-2479 239 7 lb-1)= lb-1)= PROPN iajs-2479 239 8 nr٭+𝛂 nr٭+𝛂 PROPN iajs-2479 239 9 – – PUNCT iajs-2479 239 10 r. r. NOUN iajs-2479 239 11 step step NOUN iajs-2479 239 12 ( ( PUNCT iajs-2479 239 13 6 6 NUM iajs-2479 239 14 ): ): PUNCT iajs-2479 239 15 stop stop NOUN iajs-2479 239 16 . . PUNCT iajs-2479 239 17   PUNCT iajs-2479 240 1 for for ADP iajs-2479 240 2 ( ( PUNCT iajs-2479 240 3 p2 p2 NOUN iajs-2479 240 4 ) ) PUNCT iajs-2479 240 5 we we PRON iajs-2479 240 6 get get VERB iajs-2479 240 7 a a DET iajs-2479 240 8 ( ( PUNCT iajs-2479 240 9 lb-2 lb-2 NOUN iajs-2479 240 10 ) ) PUNCT iajs-2479 240 11 for for ADP iajs-2479 240 12 p2 p2 NOUN iajs-2479 240 13 by by ADP iajs-2479 240 14 applying apply VERB iajs-2479 240 15 ( ( PUNCT iajs-2479 240 16 moore moore PROPN iajs-2479 240 17 algorithm algorithm PROPN iajs-2479 240 18 ) ) PUNCT iajs-2479 240 19 . . PUNCT iajs-2479 241 1   PROPN iajs-2479 242 1 for for ADP iajs-2479 242 2 ( ( PUNCT iajs-2479 242 3 p3 p3 PROPN iajs-2479 242 4 ) ) PUNCT iajs-2479 242 5 we we PRON iajs-2479 242 6 get get VERB iajs-2479 242 7 a a DET iajs-2479 242 8 ( ( PUNCT iajs-2479 242 9 lb-3 lb-3 NOUN iajs-2479 242 10 ) ) PUNCT iajs-2479 242 11 for for ADP iajs-2479 242 12 p3 p3 PROPN iajs-2479 242 13 , , PUNCT iajs-2479 242 14 firstly firstly ADV iajs-2479 242 15 we we PRON iajs-2479 242 16 calculate calculate VERB iajs-2479 242 17 a a DET iajs-2479 242 18 minimum minimum ADJ iajs-2479 242 19 maximum maximum ADJ iajs-2479 242 20 cost cost NOUN iajs-2479 242 21 of of ADP iajs-2479 242 22 the the DET iajs-2479 242 23 late late ADJ iajs-2479 242 24 work work NOUN iajs-2479 242 25 vmax vmax PROPN iajs-2479 242 26 by by ADP iajs-2479 242 27 applying apply VERB iajs-2479 242 28 ( ( PUNCT iajs-2479 242 29 lawler lawler PROPN iajs-2479 242 30 algorithm algorithm PROPN iajs-2479 242 31 ) ) PUNCT iajs-2479 242 32 , , PUNCT iajs-2479 242 33 since since SCONJ iajs-2479 242 34 vmax vmax PROPN iajs-2479 242 35 ≤ ≤ PROPN iajs-2479 242 36 ∑ ∑ PUNCT iajs-2479 242 37 𝑉 𝑉 PROPN iajs-2479 242 38 , , PUNCT iajs-2479 242 39 then then ADV iajs-2479 242 40 vmax vmax PROPN iajs-2479 242 41 is be AUX iajs-2479 242 42 ( ( PUNCT iajs-2479 242 43 lb lb NOUN iajs-2479 242 44 ) ) PUNCT iajs-2479 242 45 of of ADP iajs-2479 242 46 the the DET iajs-2479 242 47 problem problem NOUN iajs-2479 242 48 ( ( PUNCT iajs-2479 242 49 p3 p3 NOUN iajs-2479 242 50 ) ) PUNCT iajs-2479 242 51 i.e.(lb-3 i.e.(lb-3 PROPN iajs-2479 242 52 ) ) PUNCT iajs-2479 242 53 . . PUNCT iajs-2479 243 1 then then ADV iajs-2479 243 2 we we PRON iajs-2479 243 3 find find VERB iajs-2479 243 4 ( ( PUNCT iajs-2479 243 5 lb lb NOUN iajs-2479 243 6 ) ) PUNCT iajs-2479 243 7 of of ADP iajs-2479 243 8 problem problem NOUN iajs-2479 243 9 ( ( PUNCT iajs-2479 243 10 p p NOUN iajs-2479 243 11 ) ) PUNCT iajs-2479 243 12 , , PUNCT iajs-2479 243 13 where where SCONJ iajs-2479 243 14 : : PUNCT iajs-2479 243 15 ( ( PUNCT iajs-2479 243 16 lb lb X iajs-2479 243 17 ) ) PUNCT iajs-2479 243 18 = = SYM iajs-2479 243 19 ( ( PUNCT iajs-2479 243 20 lb-1 lb-1 NUM iajs-2479 243 21 ) ) PUNCT iajs-2479 243 22 + + CCONJ iajs-2479 243 23 ( ( PUNCT iajs-2479 243 24 lb-2 lb-2 NOUN iajs-2479 243 25 ) ) PUNCT iajs-2479 243 26 + + CCONJ iajs-2479 243 27 ( ( PUNCT iajs-2479 243 28 lb-3 lb-3 NUM iajs-2479 243 29 ) ) PUNCT iajs-2479 243 30 … … PUNCT iajs-2479 243 31 … … PUNCT iajs-2479 243 32 …… …… NOUN iajs-2479 243 33 …… …… NOUN iajs-2479 243 34 from from ADP iajs-2479 243 35 theorem theorem ADJ iajs-2479 243 36 ( ( PUNCT iajs-2479 243 37 1 1 NUM iajs-2479 243 38 ) ) PUNCT iajs-2479 243 39 . . PUNCT iajs-2479 244 1 both both PRON iajs-2479 244 2 of of ADP iajs-2479 244 3 the the DET iajs-2479 244 4 ( ( PUNCT iajs-2479 244 5 ub ub PROPN iajs-2479 244 6 ) ) PUNCT iajs-2479 244 7 , , PUNCT iajs-2479 244 8 ( ( PUNCT iajs-2479 244 9 ilb ilb PROPN iajs-2479 244 10 ) ) PUNCT iajs-2479 244 11 represent represent VERB iajs-2479 244 12 two two NUM iajs-2479 244 13 values value NOUN iajs-2479 244 14 a a DET iajs-2479 244 15 root root NOUN iajs-2479 244 16 node node NOUN iajs-2479 244 17 in in ADP iajs-2479 244 18 a a DET iajs-2479 244 19 search search NOUN iajs-2479 244 20 tree tree NOUN iajs-2479 244 21 . . PUNCT iajs-2479 245 1 the the DET iajs-2479 245 2 ( ( PUNCT iajs-2479 245 3 b.a.b b.a.b NOUN iajs-2479 245 4 ) ) PUNCT iajs-2479 245 5 method method NOUN iajs-2479 245 6 include include VERB iajs-2479 245 7 of of ADP iajs-2479 245 8 essential essential ADJ iajs-2479 245 9 procedures procedure NOUN iajs-2479 245 10 the the DET iajs-2479 245 11 following follow VERB iajs-2479 245 12 [ [ X iajs-2479 245 13 24 24 NUM iajs-2479 245 14 ] ] PUNCT iajs-2479 245 15 : : PUNCT iajs-2479 245 16   X iajs-2479 246 1 branching branch VERB iajs-2479 246 2 is be AUX iajs-2479 246 3 the the DET iajs-2479 246 4 procedure procedure NOUN iajs-2479 246 5 of of ADP iajs-2479 246 6 dividing divide VERB iajs-2479 246 7 mother mother NOUN iajs-2479 246 8 ( ( PUNCT iajs-2479 246 9 original original ADJ iajs-2479 246 10 ) ) PUNCT iajs-2479 246 11 problem problem NOUN iajs-2479 246 12 into into ADP iajs-2479 246 13 two two NUM iajs-2479 246 14 or or CCONJ iajs-2479 246 15 more more ADJ iajs-2479 246 16 sub sub NOUN iajs-2479 246 17 - - NOUN iajs-2479 246 18 problems problem NOUN iajs-2479 246 19 . . PUNCT iajs-2479 247 1 in in ADP iajs-2479 247 2 the the DET iajs-2479 247 3 search search NOUN iajs-2479 247 4 tree tree NOUN iajs-2479 247 5 , , PUNCT iajs-2479 247 6 the the DET iajs-2479 247 7 sub sub NOUN iajs-2479 247 8 problems problem NOUN iajs-2479 247 9 are be AUX iajs-2479 247 10 expressed express VERB iajs-2479 247 11 by by ADP iajs-2479 247 12 nodes node NOUN iajs-2479 247 13 . . PUNCT iajs-2479 248 1 the the DET iajs-2479 248 2 branching branch VERB iajs-2479 248 3 rule rule NOUN iajs-2479 248 4 specified specify VERB iajs-2479 248 5 by by ADP iajs-2479 248 6 use use NOUN iajs-2479 248 7 forward forward ADV iajs-2479 248 8 branching branch VERB iajs-2479 248 9 means mean VERB iajs-2479 248 10 the the DET iajs-2479 248 11 jobs job NOUN iajs-2479 248 12 are be AUX iajs-2479 248 13 sequenced sequence VERB iajs-2479 248 14 one one NUM iajs-2479 248 15 by by ADP iajs-2479 248 16 one one NUM iajs-2479 248 17 from from ADP iajs-2479 248 18 the the DET iajs-2479 248 19 beginning beginning NOUN iajs-2479 248 20 . . PUNCT iajs-2479 249 1 or or CCONJ iajs-2479 249 2 backward backward ADV iajs-2479 249 3 branching branch VERB iajs-2479 249 4 i.e. i.e. X iajs-2479 249 5 ( ( PUNCT iajs-2479 249 6 the the DET iajs-2479 249 7 jobs job NOUN iajs-2479 249 8 are be AUX iajs-2479 249 9 sequenced sequence VERB iajs-2479 249 10 one one NUM iajs-2479 249 11 by by ADP iajs-2479 249 12 one one NUM iajs-2479 249 13 from from ADP iajs-2479 249 14 the the DET iajs-2479 249 15 end end NOUN iajs-2479 249 16 ) ) PUNCT iajs-2479 249 17 . . PUNCT iajs-2479 250 1   NOUN iajs-2479 251 1 bounding bound VERB iajs-2479 251 2 is be AUX iajs-2479 251 3 procedure procedure NOUN iajs-2479 251 4 the the PRON iajs-2479 251 5 of of ADP iajs-2479 251 6 computing compute VERB iajs-2479 251 7 a a DET iajs-2479 251 8 lower lower ADV iajs-2479 251 9 bound bind VERB iajs-2479 251 10 on on ADP iajs-2479 251 11 the the DET iajs-2479 251 12 optimal optimal ADJ iajs-2479 251 13 solution solution NOUN iajs-2479 251 14 of of ADP iajs-2479 251 15 a a DET iajs-2479 251 16 sub sub NOUN iajs-2479 251 17 problems problem NOUN iajs-2479 251 18 ( ( PUNCT iajs-2479 251 19 nodes node NOUN iajs-2479 251 20 ) ) PUNCT iajs-2479 251 21 . . PUNCT iajs-2479 252 1   NOUN iajs-2479 252 2 search search NOUN iajs-2479 252 3 strategy strategy NOUN iajs-2479 252 4 is be AUX iajs-2479 252 5 a a DET iajs-2479 252 6 procedure procedure NOUN iajs-2479 252 7 reflect reflect VERB iajs-2479 252 8 the the DET iajs-2479 252 9 method method NOUN iajs-2479 252 10 of of ADP iajs-2479 252 11 choosing choose VERB iajs-2479 252 12 a a DET iajs-2479 252 13 node node NOUN iajs-2479 252 14 in in ADP iajs-2479 252 15 the the DET iajs-2479 252 16 search search NOUN iajs-2479 252 17 tree tree NOUN iajs-2479 252 18 to to ADP iajs-2479 252 19 branching branch VERB iajs-2479 252 20 from from ADP iajs-2479 252 21 it it PRON iajs-2479 252 22 , , PUNCT iajs-2479 252 23 usually usually ADV iajs-2479 252 24 the the DET iajs-2479 252 25 branch branch NOUN iajs-2479 252 26 be be AUX iajs-2479 252 27 from from ADP iajs-2479 252 28 a a DET iajs-2479 252 29 node node NOUN iajs-2479 252 30 with with ADP iajs-2479 252 31 the the DET iajs-2479 252 32 smallest small ADJ iajs-2479 252 33 ( ( PUNCT iajs-2479 252 34 lb lb X iajs-2479 252 35 ) ) PUNCT iajs-2479 252 36 in in ADP iajs-2479 252 37 the the DET iajs-2479 252 38 search search NOUN iajs-2479 252 39 tree tree NOUN iajs-2479 252 40 , , PUNCT iajs-2479 252 41 with with ADP iajs-2479 252 42 commitment commitment NOUN iajs-2479 252 43 to to ADP iajs-2479 252 44 the the DET iajs-2479 252 45 following following NOUN iajs-2479 252 46 [ [ X iajs-2479 252 47 30 30 NUM iajs-2479 252 48 ] ] PUNCT iajs-2479 252 49 . . PUNCT iajs-2479 253 1 o o X iajs-2479 253 2 if if SCONJ iajs-2479 253 3 ( ( PUNCT iajs-2479 253 4 lb lb X iajs-2479 253 5 ) ) PUNCT iajs-2479 253 6 ≥ ≥ NOUN iajs-2479 253 7 ( ( PUNCT iajs-2479 253 8 ub ub PROPN iajs-2479 253 9 ) ) PUNCT iajs-2479 253 10 , , PUNCT iajs-2479 253 11 then then ADV iajs-2479 253 12 this this DET iajs-2479 253 13 sub sub NOUN iajs-2479 253 14 problem problem NOUN iajs-2479 253 15 can can AUX iajs-2479 253 16 not not PART iajs-2479 253 17 yield yield VERB iajs-2479 253 18 a a DET iajs-2479 253 19 better well ADJ iajs-2479 253 20 solution solution NOUN iajs-2479 253 21 for for ADP iajs-2479 253 22 problem problem NOUN iajs-2479 253 23 . . PUNCT iajs-2479 254 1 thus thus ADV iajs-2479 254 2 , , PUNCT iajs-2479 254 3 we we PRON iajs-2479 254 4 need need AUX iajs-2479 254 5 not not PART iajs-2479 254 6 continue continue VERB iajs-2479 254 7 to to PART iajs-2479 254 8 branch branch VERB iajs-2479 254 9 from from ADP iajs-2479 254 10 the the DET iajs-2479 254 11 corresponding corresponding ADJ iajs-2479 254 12 node node NOUN iajs-2479 254 13 in in ADP iajs-2479 254 14 the the DET iajs-2479 254 15 branching branch VERB iajs-2479 254 16 tree tree NOUN iajs-2479 254 17 . . PUNCT iajs-2479 255 1 o o X iajs-2479 256 1 if if SCONJ iajs-2479 256 2 ( ( PUNCT iajs-2479 256 3 lb lb X iajs-2479 256 4 ) ) PUNCT iajs-2479 256 5 < < X iajs-2479 256 6 ( ( PUNCT iajs-2479 256 7 ub ub PROPN iajs-2479 256 8 ) ) PUNCT iajs-2479 256 9 , , PUNCT iajs-2479 256 10 then then ADV iajs-2479 256 11 ( ( PUNCT iajs-2479 256 12 ub ub AUX iajs-2479 256 13 ) ) PUNCT iajs-2479 256 14 is be AUX iajs-2479 256 15 reset reset ADJ iajs-2479 256 16 to to PART iajs-2479 256 17 take take VERB iajs-2479 256 18 ( ( PUNCT iajs-2479 256 19 lb lb NOUN iajs-2479 256 20 ) ) PUNCT iajs-2479 256 21 value value NOUN iajs-2479 256 22 , , PUNCT iajs-2479 256 23 ( ( PUNCT iajs-2479 256 24 i.e. i.e. X iajs-2479 256 25 replace replace NOUN iajs-2479 256 26 ( ( PUNCT iajs-2479 256 27 ub ub ADJ iajs-2479 256 28 ) ) PUNCT iajs-2479 256 29 by by ADP iajs-2479 256 30 ( ( PUNCT iajs-2479 256 31 lb lb NOUN iajs-2479 256 32 ) ) PUNCT iajs-2479 256 33 ) ) PUNCT iajs-2479 256 34 . . PUNCT iajs-2479 257 1 this this DET iajs-2479 257 2 procedure procedure NOUN iajs-2479 257 3 is be AUX iajs-2479 257 4 repeated repeat VERB iajs-2479 257 5 until until SCONJ iajs-2479 257 6 all all DET iajs-2479 257 7 nodes node NOUN iajs-2479 257 8 ( ( PUNCT iajs-2479 257 9 sub sub NOUN iajs-2479 257 10 - - NOUN iajs-2479 257 11 sets set NOUN iajs-2479 257 12 ) ) PUNCT iajs-2479 257 13 have have AUX iajs-2479 257 14 been be AUX iajs-2479 257 15 test test VERB iajs-2479 257 16 . . PUNCT iajs-2479 258 1 the the PRON iajs-2479 258 2 at at ADP iajs-2479 258 3 first first ADJ iajs-2479 258 4 noteworthy noteworthy ADJ iajs-2479 258 5 feature feature NOUN iajs-2479 258 6 of of ADP iajs-2479 258 7 ( ( PUNCT iajs-2479 258 8 b&b b&b PROPN iajs-2479 258 9 ) ) PUNCT iajs-2479 258 10 is be AUX iajs-2479 258 11 the the DET iajs-2479 258 12 use use NOUN iajs-2479 258 13 of of ADP iajs-2479 258 14 " " PUNCT iajs-2479 258 15 dominancerules dominancerule NOUN iajs-2479 258 16 " " PUNCT iajs-2479 258 17 ( ( PUNCT iajs-2479 258 18 dr dr PROPN iajs-2479 258 19 ) ) PUNCT iajs-2479 258 20 that that PRON iajs-2479 258 21 try try VERB iajs-2479 258 22 to to PART iajs-2479 258 23 exclude exclude VERB iajs-2479 258 24 nodes node NOUN iajs-2479 258 25 prior prior ADV iajs-2479 258 26 to to ADP iajs-2479 258 27 calculating calculate VERB iajs-2479 258 28 ( ( PUNCT iajs-2479 258 29 lb lb NOUN iajs-2479 258 30 ) ) PUNCT iajs-2479 258 31 to to ADP iajs-2479 258 32 it it PRON iajs-2479 258 33 [ [ X iajs-2479 258 34 2 2 NUM iajs-2479 258 35 ] ] PUNCT iajs-2479 258 36 . . PUNCT iajs-2479 259 1 these these PRON iajs-2479 259 2 ( ( PUNCT iajs-2479 259 3 dr dr NOUN iajs-2479 259 4 ) ) PUNCT iajs-2479 259 5 are be AUX iajs-2479 259 6 computationally computationally ADV iajs-2479 259 7     SPACE iajs-2479 259 8 148 148 NUM iajs-2479 259 9     SPACE iajs-2479 259 10 ibn ibn PROPN iajs-2479 259 11 al al PROPN iajs-2479 259 12 - - PUNCT iajs-2479 259 13 haitham haitham PROPN iajs-2479 259 14 jour jour X iajs-2479 259 15 . . PROPN iajs-2479 260 1 for for ADP iajs-2479 260 2 pure pure ADJ iajs-2479 260 3 & & CCONJ iajs-2479 260 4 appl appl PROPN iajs-2479 260 5 . . PUNCT iajs-2479 261 1 sci sci PROPN iajs-2479 261 2 . . PROPN iajs-2479 262 1 33 33 NUM iajs-2479 262 2 ( ( PUNCT iajs-2479 262 3 3 3 NUM iajs-2479 262 4 ) ) PUNCT iajs-2479 262 5 2020 2020 NUM iajs-2479 263 1 useful useful ADJ iajs-2479 263 2 as as SCONJ iajs-2479 263 3 they they PRON iajs-2479 263 4 reduce reduce VERB iajs-2479 263 5 storage storage NOUN iajs-2479 263 6 requirements requirement NOUN iajs-2479 263 7 on on ADP iajs-2479 263 8 the the DET iajs-2479 263 9 computer computer NOUN iajs-2479 263 10 as as ADV iajs-2479 263 11 well well ADV iajs-2479 263 12 as as ADP iajs-2479 263 13 reducing reduce VERB iajs-2479 263 14 computation computation NOUN iajs-2479 263 15 time time NOUN iajs-2479 263 16 . . PUNCT iajs-2479 264 1 7 7 X iajs-2479 264 2 . . NUM iajs-2479 264 3 dominancerules dominancerule NOUN iajs-2479 264 4 ( ( PUNCT iajs-2479 264 5 dr dr NOUN iajs-2479 264 6 ) ) PUNCT iajs-2479 264 7 dominance dominance NOUN iajs-2479 264 8 rules rule NOUN iajs-2479 264 9 ( ( PUNCT iajs-2479 264 10 dr dr PROPN iajs-2479 264 11 ) ) PUNCT iajs-2479 264 12 usually usually ADV iajs-2479 264 13 specify specify VERB iajs-2479 264 14 whether whether SCONJ iajs-2479 264 15 a a DET iajs-2479 264 16 node node NOUN iajs-2479 264 17 can can AUX iajs-2479 264 18 be be AUX iajs-2479 264 19 discarded discard VERB iajs-2479 264 20 in in ADP iajs-2479 264 21 search search NOUN iajs-2479 264 22 tree tree NOUN iajs-2479 264 23 before before SCONJ iajs-2479 264 24 its its PRON iajs-2479 264 25 lower low ADJ iajs-2479 264 26 bound bind VERB iajs-2479 264 27 ( ( PUNCT iajs-2479 264 28 lb lb NOUN iajs-2479 264 29 ) ) PUNCT iajs-2479 264 30 is be AUX iajs-2479 264 31 calculated calculate VERB iajs-2479 264 32 , , PUNCT iajs-2479 264 33 so so CCONJ iajs-2479 264 34 it it PRON iajs-2479 264 35 helps help VERB iajs-2479 264 36 reduce reduce VERB iajs-2479 264 37 search search NOUN iajs-2479 264 38 space space NOUN iajs-2479 264 39 . . PUNCT iajs-2479 265 1 clearly clearly ADV iajs-2479 265 2 ( ( PUNCT iajs-2479 265 3 dr dr NOUN iajs-2479 265 4 ) ) PUNCT iajs-2479 265 5 are be AUX iajs-2479 265 6 particularly particularly ADV iajs-2479 265 7 useful useful ADJ iajs-2479 265 8 when when SCONJ iajs-2479 265 9 a a DET iajs-2479 265 10 node node NOUN iajs-2479 265 11 can can AUX iajs-2479 265 12 be be AUX iajs-2479 265 13 eliminated eliminate VERB iajs-2479 265 14 which which PRON iajs-2479 265 15 has have VERB iajs-2479 265 16 ( ( PUNCT iajs-2479 265 17 lb lb X iajs-2479 265 18 ) ) PUNCT iajs-2479 265 19 that that PRON iajs-2479 265 20 is be AUX iajs-2479 265 21 less less ADJ iajs-2479 265 22 than than ADP iajs-2479 265 23 the the DET iajs-2479 265 24 optimal optimal ADJ iajs-2479 265 25 solution solution NOUN iajs-2479 265 26 . . PUNCT iajs-2479 266 1 to to PART iajs-2479 266 2 introduce introduce VERB iajs-2479 266 3 the the DET iajs-2479 266 4 ( ( PUNCT iajs-2479 266 5 dr dr PROPN iajs-2479 266 6 ) ) PUNCT iajs-2479 266 7 for for ADP iajs-2479 266 8 our our PRON iajs-2479 266 9 problem problem NOUN iajs-2479 266 10 ( ( PUNCT iajs-2479 266 11 p p X iajs-2479 266 12 ) ) PUNCT iajs-2479 266 13 consider consider VERB iajs-2479 266 14 schedules schedule NOUN iajs-2479 266 15 s s PART iajs-2479 266 16 = = SYM iajs-2479 266 17 ( ( PUNCT iajs-2479 266 18 σ σ PROPN iajs-2479 266 19 , , PUNCT iajs-2479 266 20 i i PROPN iajs-2479 266 21 , , PUNCT iajs-2479 266 22 j j PROPN iajs-2479 266 23 , , PUNCT iajs-2479 266 24 σ σ PROPN iajs-2479 266 25 ' ' PUNCT iajs-2479 266 26 ) ) PUNCT iajs-2479 266 27 and and CCONJ iajs-2479 266 28 s s X iajs-2479 266 29 ' ' PUNCT iajs-2479 266 30 = = SYM iajs-2479 266 31 ( ( PUNCT iajs-2479 266 32 σ σ PROPN iajs-2479 266 33 , , PUNCT iajs-2479 266 34 j j PROPN iajs-2479 266 35 , , PUNCT iajs-2479 266 36 i i PROPN iajs-2479 266 37 , , PUNCT iajs-2479 266 38 σ σ PROPN iajs-2479 266 39 ' ' PUNCT iajs-2479 266 40 ) ) PUNCT iajs-2479 266 41 where where SCONJ iajs-2479 266 42 σ σ PROPN iajs-2479 266 43 , , PUNCT iajs-2479 266 44 σ σ PROPN iajs-2479 266 45 ' ' PUNCT iajs-2479 266 46 are be AUX iajs-2479 266 47 two two NUM iajs-2479 266 48 a a DET iajs-2479 266 49 partial partial ADJ iajs-2479 266 50 schedule schedule NOUN iajs-2479 266 51 of of ADP iajs-2479 266 52 the the DET iajs-2479 266 53 remaining remain VERB iajs-2479 266 54 n-2 n-2 NOUN iajs-2479 266 55 jobs job NOUN iajs-2479 266 56 . . PUNCT iajs-2479 267 1 let let VERB iajs-2479 267 2 t=∑ t=∑ NOUN iajs-2479 267 3 𝑝∈ 𝑝∈ NOUN iajs-2479 267 4 , , PUNCT iajs-2479 267 5 be be AUX iajs-2479 267 6 the the DET iajs-2479 267 7 completion completion NOUN iajs-2479 267 8 time time NOUN iajs-2479 267 9 of of ADP iajs-2479 267 10 σ σ PROPN iajs-2479 267 11 , , PUNCT iajs-2479 267 12 with with ADP iajs-2479 267 13 rj rj PROPN iajs-2479 267 14 = = SYM iajs-2479 267 15 r r PROPN iajs-2479 267 16 , , PUNCT iajs-2479 267 17 di≤ di≤ PROPN iajs-2479 267 18 dj dj NOUN iajs-2479 267 19 , , PUNCT iajs-2479 267 20 and and CCONJ iajs-2479 268 1 pi≤ pi≤ PROPN iajs-2479 268 2 pj pj PROPN iajs-2479 268 3 . . PROPN iajs-2479 268 4 define define PROPN iajs-2479 268 5 ( ( PUNCT iajs-2479 268 6 ci(t ci(t ADV iajs-2479 268 7 ) ) PUNCT iajs-2479 268 8 + + CCONJ iajs-2479 268 9 ti(t ti(t PRON iajs-2479 268 10 ) ) PUNCT iajs-2479 268 11 + + NUM iajs-2479 268 12 ei(t ei(t X iajs-2479 268 13 ) ) PUNCT iajs-2479 269 1 + + NUM iajs-2479 269 2 ui(t ui(t NOUN iajs-2479 269 3 ) ) PUNCT iajs-2479 270 1 + + CCONJ iajs-2479 270 2 vi(t vi(t X iajs-2479 270 3 ) ) PUNCT iajs-2479 270 4 an an DET iajs-2479 270 5 the the DET iajs-2479 270 6 sum sum NOUN iajs-2479 270 7 of of ADP iajs-2479 270 8 total total ADJ iajs-2479 270 9 completion completion NOUN iajs-2479 270 10 time time NOUN iajs-2479 270 11 , , PUNCT iajs-2479 270 12 tardiness tardiness NOUN iajs-2479 270 13 , , PUNCT iajs-2479 270 14 earliness earliness NOUN iajs-2479 270 15 , , PUNCT iajs-2479 270 16 number number NOUN iajs-2479 270 17 of of ADP iajs-2479 270 18 tardy tardy ADJ iajs-2479 270 19 jobs job NOUN iajs-2479 270 20 and and CCONJ iajs-2479 270 21 late late ADJ iajs-2479 270 22 work work NOUN iajs-2479 270 23 of of ADP iajs-2479 270 24 job job NOUN iajs-2479 270 25 i i PRON iajs-2479 270 26 ) ) PUNCT iajs-2479 270 27 if if SCONJ iajs-2479 270 28 scheduled schedule VERB iajs-2479 270 29 at at ADP iajs-2479 270 30 time time NOUN iajs-2479 270 31 t t PROPN iajs-2479 270 32 and and CCONJ iajs-2479 270 33 let let VERB iajs-2479 270 34 fij= fij= PROPN iajs-2479 270 35 ( ( PUNCT iajs-2479 270 36 cij(t cij(t PROPN iajs-2479 270 37 ) ) PUNCT iajs-2479 270 38 + + SYM iajs-2479 271 1 tij(t tij(t PROPN iajs-2479 271 2 ) ) PUNCT iajs-2479 272 1 + + CCONJ iajs-2479 272 2 eij(t eij(t PROPN iajs-2479 272 3 ) ) PUNCT iajs-2479 272 4 + + CCONJ iajs-2479 272 5 uij(t uij(t PROPN iajs-2479 272 6 ) ) PUNCT iajs-2479 272 7 + + CCONJ iajs-2479 272 8 vij(t vij(t PROPN iajs-2479 272 9 ) ) PUNCT iajs-2479 272 10 ) ) PUNCT iajs-2479 272 11 be be AUX iajs-2479 272 12 the the DET iajs-2479 272 13 sum sum NOUN iajs-2479 272 14 of of ADP iajs-2479 272 15 total total ADJ iajs-2479 272 16 completion completion NOUN iajs-2479 272 17 time time NOUN iajs-2479 272 18 , , PUNCT iajs-2479 272 19 tardiness tardiness NOUN iajs-2479 272 20 , , PUNCT iajs-2479 272 21 earliness earliness NOUN iajs-2479 272 22 , , PUNCT iajs-2479 272 23 number number NOUN iajs-2479 272 24 of of ADP iajs-2479 272 25 tardy tardy ADJ iajs-2479 272 26 jobs job NOUN iajs-2479 272 27 and and CCONJ iajs-2479 272 28 late late ADJ iajs-2479 272 29 work work NOUN iajs-2479 272 30 of of ADP iajs-2479 272 31 job job NOUN iajs-2479 272 32 i i PRON iajs-2479 272 33 and and CCONJ iajs-2479 272 34 j j PROPN iajs-2479 272 35 , , PUNCT iajs-2479 272 36 if if SCONJ iajs-2479 272 37 i i PRON iajs-2479 272 38 precedes precede VERB iajs-2479 272 39 j j PROPN iajs-2479 272 40 and and CCONJ iajs-2479 272 41 their their PRON iajs-2479 272 42 processing processing NOUN iajs-2479 272 43 starts start NOUN iajs-2479 272 44 at at ADP iajs-2479 272 45 time time NOUN iajs-2479 272 46 t. t. PROPN iajs-2479 272 47 the the DET iajs-2479 272 48 following follow VERB iajs-2479 272 49 interchange interchange NOUN iajs-2479 272 50 function function NOUN iajs-2479 272 51 δij(t δij(t PROPN iajs-2479 272 52 ) ) PUNCT iajs-2479 272 53 is be AUX iajs-2479 272 54 used use VERB iajs-2479 272 55 to to PART iajs-2479 272 56 specify specify VERB iajs-2479 272 57 the the DET iajs-2479 272 58 new new ADJ iajs-2479 272 59 dominance dominance NOUN iajs-2479 272 60 properties property NOUN iajs-2479 272 61 which which PRON iajs-2479 272 62 gives give VERB iajs-2479 272 63 the the DET iajs-2479 272 64 cost cost NOUN iajs-2479 272 65 of of ADP iajs-2479 272 66 interchanging interchange VERB iajs-2479 272 67 adjacent adjacent ADJ iajs-2479 272 68 jobs job NOUN iajs-2479 272 69 i i PRON iajs-2479 272 70 and and CCONJ iajs-2479 272 71 j j PROPN iajs-2479 272 72 whose whose DET iajs-2479 272 73 processing processing NOUN iajs-2479 272 74 start start NOUN iajs-2479 272 75 at at ADP iajs-2479 272 76 time time NOUN iajs-2479 272 77 t. t. PROPN iajs-2479 272 78 δij(t δij(t PROPN iajs-2479 272 79 ) ) PUNCT iajs-2479 272 80 = = SYM iajs-2479 272 81 fij(t fij(t PROPN iajs-2479 272 82 ) ) PUNCT iajs-2479 272 83 – – PUNCT iajs-2479 272 84 fji(t fji(t NOUN iajs-2479 272 85 ) ) PUNCT iajs-2479 272 86 . . PUNCT iajs-2479 273 1 note note VERB iajs-2479 273 2 that that SCONJ iajs-2479 273 3 this this DET iajs-2479 273 4 cost cost NOUN iajs-2479 273 5 δij(t δij(t PROPN iajs-2479 273 6 ) ) PUNCT iajs-2479 273 7 does do AUX iajs-2479 273 8 not not PART iajs-2479 273 9 depend depend VERB iajs-2479 273 10 on on ADP iajs-2479 273 11 how how SCONJ iajs-2479 273 12 the the DET iajs-2479 273 13 jobs job NOUN iajs-2479 273 14 are be AUX iajs-2479 273 15 arranged arrange VERB iajs-2479 273 16 in in ADP iajs-2479 273 17 σ σ PROPN iajs-2479 273 18 and and CCONJ iajs-2479 273 19 σ σ PROPN iajs-2479 273 20 ' ' PUNCT iajs-2479 273 21 but but CCONJ iajs-2479 273 22 depends depend VERB iajs-2479 273 23 on on ADP iajs-2479 273 24 start start NOUN iajs-2479 273 25 time time NOUN iajs-2479 273 26 t t PROPN iajs-2479 273 27 of of ADP iajs-2479 273 28 the the DET iajs-2479 273 29 pair pair NOUN iajs-2479 273 30 , , PUNCT iajs-2479 273 31 and and CCONJ iajs-2479 273 32 : : PUNCT iajs-2479 273 33   NOUN iajs-2479 273 34 if if SCONJ iajs-2479 273 35 δij(t δij(t PROPN iajs-2479 273 36 ) ) PUNCT iajs-2479 273 37 < < X iajs-2479 273 38 0 0 PUNCT iajs-2479 274 1 then then ADV iajs-2479 274 2 i i PRON iajs-2479 274 3 precede precede VERB iajs-2479 274 4 j j PROPN iajs-2479 274 5 at at ADP iajs-2479 274 6 time time NOUN iajs-2479 274 7 t. t. PROPN iajs-2479 274 8   NOUN iajs-2479 275 1 if if SCONJ iajs-2479 275 2 δij(t δij(t PROPN iajs-2479 275 3 ) ) PUNCT iajs-2479 275 4 > > X iajs-2479 275 5 0 0 PUNCT iajs-2479 276 1 then then ADV iajs-2479 276 2 j j PROPN iajs-2479 276 3 precede precede VERB iajs-2479 276 4 i i PRON iajs-2479 276 5 at at ADP iajs-2479 276 6 time time NOUN iajs-2479 276 7 t. t. PROPN iajs-2479 276 8   NOUN iajs-2479 277 1 if if SCONJ iajs-2479 277 2 δij(t δij(t PROPN iajs-2479 277 3 ) ) PUNCT iajs-2479 278 1 = = SYM iajs-2479 278 2 0 0 PUNCT iajs-2479 279 1 then then ADV iajs-2479 279 2 it it PRON iajs-2479 279 3 is be AUX iajs-2479 279 4 indifferent indifferent ADJ iajs-2479 279 5 to to PART iajs-2479 279 6 schedule schedule VERB iajs-2479 279 7 i i PRON iajs-2479 279 8 or or CCONJ iajs-2479 279 9 j j PROPN iajs-2479 279 10 first first ADJ iajs-2479 279 11 . . PUNCT iajs-2479 280 1 first first ADV iajs-2479 280 2 : : PUNCT iajs-2479 280 3 if if SCONJ iajs-2479 280 4 r r NOUN iajs-2479 280 5 ≤ ≤ X iajs-2479 280 6 t t NOUN iajs-2479 280 7 , , PUNCT iajs-2479 280 8 we we PRON iajs-2479 280 9 divide divide VERB iajs-2479 280 10 the the DET iajs-2479 280 11 situation situation NOUN iajs-2479 280 12 into into ADP iajs-2479 280 13 the the DET iajs-2479 280 14 following following ADJ iajs-2479 280 15 cases case NOUN iajs-2479 280 16 : : PUNCT iajs-2479 280 17 case case NOUN iajs-2479 280 18 1 1 NUM iajs-2479 280 19 . . PUNCT iajs-2479 281 1 if if SCONJ iajs-2479 281 2 di di NOUN iajs-2479 281 3 ≤ ≤ X iajs-2479 281 4 t t PROPN iajs-2479 282 1 + + NOUN iajs-2479 282 2 pi pi NOUN iajs-2479 282 3 , , PUNCT iajs-2479 282 4 dj dj ADJ iajs-2479 282 5 ≤ ≤ NUM iajs-2479 282 6 t t PROPN iajs-2479 283 1 + + PROPN iajs-2479 283 2 pj pj PROPN iajs-2479 283 3 ( ( PUNCT iajs-2479 283 4 i.e. i.e. X iajs-2479 283 5 both both CCONJ iajs-2479 283 6 the the DET iajs-2479 283 7 jobs job NOUN iajs-2479 283 8 i i PRON iajs-2479 283 9 , , PUNCT iajs-2479 283 10 j j PROPN iajs-2479 283 11 are be AUX iajs-2479 283 12 always always ADV iajs-2479 283 13 tardy tardy ADJ iajs-2479 283 14 ) ) PUNCT iajs-2479 283 15 . . PUNCT iajs-2479 284 1 proof proof NOUN iajs-2479 284 2 . . PUNCT iajs-2479 285 1 to to PART iajs-2479 285 2 show show VERB iajs-2479 285 3 that that PRON iajs-2479 285 4 s s AUX iajs-2479 285 5 dominates dominate VERB iajs-2479 285 6 s s NOUN iajs-2479 285 7 ' ' PUNCT iajs-2479 285 8 , , PUNCT iajs-2479 285 9 it it PRON iajs-2479 285 10 suffices suffice VERB iajs-2479 285 11 to to PART iajs-2479 285 12 show show VERB iajs-2479 285 13 that that SCONJ iajs-2479 285 14 ( ( PUNCT iajs-2479 285 15 δij= δij= PROPN iajs-2479 285 16 fij fij PROPN iajs-2479 285 17 ( ( PUNCT iajs-2479 285 18 s)fji s)fji PROPN iajs-2479 285 19 ( ( PUNCT iajs-2479 285 20 s s NOUN iajs-2479 285 21 ' ' PUNCT iajs-2479 285 22 ) ) PUNCT iajs-2479 285 23 ≤ ≤ NOUN iajs-2479 285 24 0 0 NUM iajs-2479 285 25 ) ) PUNCT iajs-2479 285 26 and and CCONJ iajs-2479 285 27 vice vice ADV iajs-2479 285 28 versa versa ADV iajs-2479 285 29 . . PUNCT iajs-2479 286 1 since since SCONJ iajs-2479 286 2 the the DET iajs-2479 286 3 jobs job NOUN iajs-2479 286 4 i i PRON iajs-2479 286 5 and and CCONJ iajs-2479 286 6 j j PROPN iajs-2479 286 7 are be AUX iajs-2479 286 8 both both ADV iajs-2479 286 9 tardy tardy ADJ iajs-2479 286 10 , , PUNCT iajs-2479 286 11 then then ADV iajs-2479 286 12 ei ei X iajs-2479 286 13 = = SYM iajs-2479 286 14 ej=0 ej=0 ADJ iajs-2479 286 15 , , PUNCT iajs-2479 286 16 vi vi NOUN iajs-2479 286 17 = = SYM iajs-2479 286 18 pi pi NOUN iajs-2479 286 19 , , PUNCT iajs-2479 286 20 vj vj PROPN iajs-2479 286 21 = = PROPN iajs-2479 286 22 pj pj PROPN iajs-2479 286 23 , , PUNCT iajs-2479 286 24 and and CCONJ iajs-2479 286 25 ui ui PROPN iajs-2479 286 26 = = NOUN iajs-2479 286 27 uj=1 uj=1 PROPN iajs-2479 286 28 . . PUNCT iajs-2479 287 1 now now ADV iajs-2479 287 2 , , PUNCT iajs-2479 287 3 let let VERB iajs-2479 287 4   NOUN iajs-2479 287 5 fij(s)= fij(s)= NOUN iajs-2479 287 6 [ [ PUNCT iajs-2479 287 7 ( ( PUNCT iajs-2479 287 8 t t NOUN iajs-2479 287 9 + + NOUN iajs-2479 287 10 pi pi NOUN iajs-2479 287 11 ) ) PUNCT iajs-2479 288 1 + + CCONJ iajs-2479 288 2 ( ( PUNCT iajs-2479 288 3 t t NOUN iajs-2479 288 4 + + NOUN iajs-2479 288 5 pi pi NOUN iajs-2479 288 6 – – PUNCT iajs-2479 288 7 di di NOUN iajs-2479 288 8 ) ) PUNCT iajs-2479 289 1 +0 +0 ADP iajs-2479 289 2 + + NOUN iajs-2479 289 3 1 1 NUM iajs-2479 289 4 + + NOUN iajs-2479 289 5 pi pi NOUN iajs-2479 289 6 + + ADJ iajs-2479 289 7 ( ( PUNCT iajs-2479 289 8 t t NOUN iajs-2479 289 9 + + NOUN iajs-2479 289 10 pi pi PROPN iajs-2479 289 11 + + PROPN iajs-2479 289 12 pj pj X iajs-2479 289 13 ) ) PUNCT iajs-2479 289 14 + + CCONJ iajs-2479 289 15 ( ( PUNCT iajs-2479 289 16 t t NOUN iajs-2479 289 17 + + NOUN iajs-2479 289 18 pi pi NOUN iajs-2479 289 19 + + PROPN iajs-2479 289 20 pj pj PROPN iajs-2479 289 21 – – PUNCT iajs-2479 289 22 dj dj NOUN iajs-2479 289 23 ) ) PUNCT iajs-2479 290 1 +0 +0 ADP iajs-2479 290 2 +1 +1 PROPN iajs-2479 291 1 + + NOUN iajs-2479 291 2 pj pj PROPN iajs-2479 291 3 ]= ]= NUM iajs-2479 291 4 4 4 NUM iajs-2479 291 5 t t NOUN iajs-2479 291 6 +5pi +5pi PUNCT iajs-2479 291 7 +3pj +3pj PUNCT iajs-2479 291 8 – – PUNCT iajs-2479 291 9 di di NOUN iajs-2479 291 10 – – PUNCT iajs-2479 291 11 dj dj NOUN iajs-2479 291 12 +2 +2 PRON iajs-2479 291 13 … … PUNCT iajs-2479 291 14 .. .. PUNCT iajs-2479 291 15 ( ( PUNCT iajs-2479 291 16 a a X iajs-2479 291 17 ) ) PUNCT iajs-2479 291 18   NOUN iajs-2479 292 1 f'ji= f'ji= PROPN iajs-2479 293 1 [ [ X iajs-2479 293 2 ( ( PUNCT iajs-2479 293 3 t t PROPN iajs-2479 293 4 + + PROPN iajs-2479 293 5 pj pj PROPN iajs-2479 293 6 ) ) PUNCT iajs-2479 294 1 + + CCONJ iajs-2479 294 2 ( ( PUNCT iajs-2479 294 3 t t PROPN iajs-2479 294 4 + + PROPN iajs-2479 294 5 pj pj PROPN iajs-2479 294 6 – – PUNCT iajs-2479 294 7 dj dj NOUN iajs-2479 294 8 ) ) PUNCT iajs-2479 295 1 +0 +0 ADP iajs-2479 295 2 +1 +1 PROPN iajs-2479 296 1 + + NOUN iajs-2479 296 2 pj pj PROPN iajs-2479 296 3 + + CCONJ iajs-2479 296 4 ( ( PUNCT iajs-2479 296 5 t t PROPN iajs-2479 296 6 + + PROPN iajs-2479 296 7 pj pj PROPN iajs-2479 296 8 + + PROPN iajs-2479 296 9 pi pi NOUN iajs-2479 296 10 ) ) PUNCT iajs-2479 297 1 + + CCONJ iajs-2479 297 2 ( ( PUNCT iajs-2479 297 3 t t PROPN iajs-2479 297 4 + + PROPN iajs-2479 297 5 pj pj PROPN iajs-2479 297 6 + + PROPN iajs-2479 297 7 pi pi NOUN iajs-2479 297 8 -di -di NOUN iajs-2479 297 9 ) ) PUNCT iajs-2479 298 1 +0 +0 ADP iajs-2479 298 2 +1 +1 PROPN iajs-2479 299 1 + + NOUN iajs-2479 299 2 pi pi NOUN iajs-2479 299 3 ]= ]= NUM iajs-2479 299 4 4 4 NUM iajs-2479 299 5 t t NOUN iajs-2479 299 6 +3pi +3pi X iajs-2479 299 7 +5pj +5pj X iajs-2479 299 8 – – PUNCT iajs-2479 299 9 dj dj NOUN iajs-2479 299 10 – – PUNCT iajs-2479 299 11 di di NOUN iajs-2479 299 12 +2 +2 NOUN iajs-2479 299 13 … … PUNCT iajs-2479 299 14 .. .. PUNCT iajs-2479 299 15 ( ( PUNCT iajs-2479 299 16 b b NOUN iajs-2479 299 17 ) ) PUNCT iajs-2479 299 18 . . PUNCT iajs-2479 300 1 δij= δij= PROPN iajs-2479 300 2 ( ( PUNCT iajs-2479 300 3 a a X iajs-2479 300 4 ) ) PUNCT iajs-2479 300 5 ( ( PUNCT iajs-2479 300 6 b)= b)= X iajs-2479 300 7 2pi 2pi PROPN iajs-2479 301 1 -2pj -2pj PROPN iajs-2479 302 1 ≤0 ≤0 PROPN iajs-2479 302 2 , , PUNCT iajs-2479 302 3 then then ADV iajs-2479 302 4 job job NOUN iajs-2479 302 5 i i PRON iajs-2479 302 6 precede precede VERB iajs-2479 302 7 j j NOUN iajs-2479 302 8 case case NOUN iajs-2479 302 9 2 2 X iajs-2479 302 10 . . X iajs-2479 303 1 if if SCONJ iajs-2479 303 2 di di NOUN iajs-2479 303 3 ≤ ≤ X iajs-2479 303 4 t t PROPN iajs-2479 304 1 + + NOUN iajs-2479 304 2 pi pi NOUN iajs-2479 304 3 , , PUNCT iajs-2479 304 4 t t PROPN iajs-2479 305 1 + + PROPN iajs-2479 305 2 pj pj PROPN iajs-2479 305 3 ≤ ≤ NOUN iajs-2479 305 4 dj dj NOUN iajs-2479 305 5 ≤ ≤ NUM iajs-2479 305 6 t t NOUN iajs-2479 306 1 + + NOUN iajs-2479 306 2 pi pi PROPN iajs-2479 306 3 + + PROPN iajs-2479 306 4 pj pj PROPN iajs-2479 306 5 ( ( PUNCT iajs-2479 306 6 i.e. i.e. X iajs-2479 306 7 the the DET iajs-2479 306 8 job job NOUN iajs-2479 306 9 i i PRON iajs-2479 306 10 , , PUNCT iajs-2479 306 11 is be AUX iajs-2479 306 12 always always ADV iajs-2479 306 13 tardy tardy ADJ iajs-2479 306 14 and and CCONJ iajs-2479 306 15 the the DET iajs-2479 306 16 job job NOUN iajs-2479 306 17 j j PROPN iajs-2479 306 18 , , PUNCT iajs-2479 306 19 is be AUX iajs-2479 306 20 tardy tardy ADJ iajs-2479 306 21 if if SCONJ iajs-2479 306 22 not not PART iajs-2479 306 23 scheduled schedule VERB iajs-2479 306 24 first first ADV iajs-2479 306 25 ) ) PUNCT iajs-2479 306 26 . . PUNCT iajs-2479 307 1 proof proof NOUN iajs-2479 307 2 . . PUNCT iajs-2479 308 1 since since SCONJ iajs-2479 308 2 the the DET iajs-2479 308 3 job job NOUN iajs-2479 308 4 i i PRON iajs-2479 308 5 , , PUNCT iajs-2479 308 6 is be AUX iajs-2479 308 7 always always ADV iajs-2479 308 8 tardy tardy ADJ iajs-2479 308 9 then then ADV iajs-2479 308 10 ei=0 ei=0 PROPN iajs-2479 308 11 , , PUNCT iajs-2479 308 12 ui=1 ui=1 ADV iajs-2479 308 13 , , PUNCT iajs-2479 308 14 and and CCONJ iajs-2479 308 15 if if SCONJ iajs-2479 308 16 job job NOUN iajs-2479 308 17 j j PROPN iajs-2479 308 18 scheduled schedule VERB iajs-2479 308 19 first first ADV iajs-2479 308 20 then then ADV iajs-2479 308 21 tj=0 tj=0 ADJ iajs-2479 308 22 , , PUNCT iajs-2479 308 23 and and CCONJ iajs-2479 308 24 vj={0 vj={0 NUM iajs-2479 308 25 , , PUNCT iajs-2479 308 26 cj cj PROPN iajs-2479 308 27 – – PUNCT iajs-2479 308 28 dj dj NOUN iajs-2479 308 29 } } PUNCT iajs-2479 308 30 ( ( PUNCT iajs-2479 308 31 i.e. i.e. X iajs-2479 308 32 j j PROPN iajs-2479 308 33 , , PUNCT iajs-2479 308 34 is be AUX iajs-2479 308 35 early early ADJ iajs-2479 308 36 or or CCONJ iajs-2479 308 37 partial partial ADJ iajs-2479 308 38 early early ADJ iajs-2479 308 39 ) ) PUNCT iajs-2479 308 40 . . PUNCT iajs-2479 309 1   X iajs-2479 310 1 fij= fij= PROPN iajs-2479 310 2 [ [ PUNCT iajs-2479 310 3 ( ( PUNCT iajs-2479 310 4 t t NOUN iajs-2479 310 5 + + NOUN iajs-2479 310 6 pi pi NOUN iajs-2479 310 7 ) ) PUNCT iajs-2479 311 1 + + CCONJ iajs-2479 311 2 ( ( PUNCT iajs-2479 311 3 t t NOUN iajs-2479 311 4 + + NOUN iajs-2479 311 5 pi pi NOUN iajs-2479 311 6 – – PUNCT iajs-2479 311 7 di di NOUN iajs-2479 311 8 ) ) PUNCT iajs-2479 312 1 +0 +0 ADP iajs-2479 312 2 + + NOUN iajs-2479 312 3 1 1 NUM iajs-2479 312 4 + + NOUN iajs-2479 312 5 pi pi NOUN iajs-2479 312 6 + + ADJ iajs-2479 312 7 ( ( PUNCT iajs-2479 312 8 t t NOUN iajs-2479 312 9 + + NOUN iajs-2479 312 10 pi pi PROPN iajs-2479 312 11 + + PROPN iajs-2479 312 12 pj pj X iajs-2479 312 13 ) ) PUNCT iajs-2479 312 14 + + CCONJ iajs-2479 312 15 ( ( PUNCT iajs-2479 312 16 t t NOUN iajs-2479 312 17 + + NOUN iajs-2479 312 18 pi pi NOUN iajs-2479 312 19 + + PROPN iajs-2479 312 20 pj pj PROPN iajs-2479 312 21 -dj -dj PROPN iajs-2479 312 22 ) ) PUNCT iajs-2479 313 1 +0 +0 ADP iajs-2479 313 2 +1 +1 PROPN iajs-2479 314 1 + + NOUN iajs-2479 314 2 pj pj PROPN iajs-2479 314 3 ]= ]= NUM iajs-2479 314 4 4 4 NUM iajs-2479 314 5 t t NOUN iajs-2479 314 6 +5pi +5pi PUNCT iajs-2479 314 7 +3pj +3pj PUNCT iajs-2479 314 8 – – PUNCT iajs-2479 314 9 di di NOUN iajs-2479 314 10 – – PUNCT iajs-2479 314 11 dj dj NOUN iajs-2479 314 12 +2 +2 PRON iajs-2479 314 13 … … PUNCT iajs-2479 314 14 .. .. PUNCT iajs-2479 314 15 ( ( PUNCT iajs-2479 314 16 a a NOUN iajs-2479 314 17 ) ) PUNCT iajs-2479 314 18 . . PUNCT iajs-2479 315 1   X iajs-2479 315 2 f'ji= f'ji= PROPN iajs-2479 316 1 [ [ X iajs-2479 316 2 ( ( PUNCT iajs-2479 316 3 t t PROPN iajs-2479 316 4 + + PROPN iajs-2479 316 5 pj pj PROPN iajs-2479 316 6 ) ) PUNCT iajs-2479 317 1 +0 +0 ADP iajs-2479 317 2 + + CCONJ iajs-2479 317 3 ( ( PUNCT iajs-2479 317 4 dj dj NOUN iajs-2479 317 5 – – PUNCT iajs-2479 317 6 t t PROPN iajs-2479 317 7 – – PUNCT iajs-2479 317 8 pj pj PROPN iajs-2479 317 9 ) ) PUNCT iajs-2479 318 1 +0 +0 ADP iajs-2479 318 2 +0 +0 ADP iajs-2479 318 3 + + PROPN iajs-2479 318 4 ( ( PUNCT iajs-2479 318 5 t t PROPN iajs-2479 318 6 + + PROPN iajs-2479 318 7 pj pj PROPN iajs-2479 318 8 + + PROPN iajs-2479 318 9 pi pi NOUN iajs-2479 318 10 ) ) PUNCT iajs-2479 318 11 + + CCONJ iajs-2479 318 12 ( ( PUNCT iajs-2479 318 13 t t PROPN iajs-2479 318 14 + + PROPN iajs-2479 318 15 pj pj PROPN iajs-2479 318 16 + + PROPN iajs-2479 318 17 pi pi NOUN iajs-2479 318 18 -di -di NOUN iajs-2479 318 19 ) ) PUNCT iajs-2479 319 1 +0 +0 ADP iajs-2479 319 2 +1 +1 PROPN iajs-2479 320 1 + + NOUN iajs-2479 320 2 pi pi NOUN iajs-2479 320 3 ]= ]= NUM iajs-2479 320 4 2 2 NUM iajs-2479 320 5 t t NOUN iajs-2479 320 6 +3pi +3pi X iajs-2479 321 1 +2pj +2pj PUNCT iajs-2479 321 2 + + PUNCT iajs-2479 321 3 dj dj X iajs-2479 321 4 – – PUNCT iajs-2479 321 5 di di X iajs-2479 321 6 +1 +1 NOUN iajs-2479 321 7 … … PUNCT iajs-2479 321 8 . . PUNCT iajs-2479 322 1 ( ( PUNCT iajs-2479 322 2 b b NOUN iajs-2479 322 3 ) ) PUNCT iajs-2479 322 4 . . PUNCT iajs-2479 323 1 ( ( PUNCT iajs-2479 323 2 when when SCONJ iajs-2479 323 3 vj=0 vj=0 NUM iajs-2479 323 4 ) ) PUNCT iajs-2479 323 5 . . PUNCT iajs-2479 324 1   X iajs-2479 324 2 f'ji= f'ji= PROPN iajs-2479 325 1 [ [ X iajs-2479 325 2 ( ( PUNCT iajs-2479 325 3 t t PROPN iajs-2479 325 4 + + PROPN iajs-2479 325 5 pj pj PROPN iajs-2479 325 6 ) ) PUNCT iajs-2479 326 1 +0 +0 ADP iajs-2479 326 2 + + CCONJ iajs-2479 326 3 ( ( PUNCT iajs-2479 326 4 dj dj X iajs-2479 326 5 – – PUNCT iajs-2479 326 6 t t PROPN iajs-2479 326 7 – – PUNCT iajs-2479 326 8 pj pj PROPN iajs-2479 326 9 ) ) PUNCT iajs-2479 327 1 +0 +0 ADP iajs-2479 327 2 + + PROPN iajs-2479 327 3 ( ( PUNCT iajs-2479 327 4 t t PROPN iajs-2479 327 5 + + PROPN iajs-2479 327 6 pj pj PROPN iajs-2479 327 7 -dj -dj PROPN iajs-2479 327 8 ) ) PUNCT iajs-2479 327 9 + + PROPN iajs-2479 327 10 ( ( PUNCT iajs-2479 327 11 t t PROPN iajs-2479 327 12 + + PROPN iajs-2479 327 13 pj pj PROPN iajs-2479 327 14 + + PROPN iajs-2479 327 15 pi pi NOUN iajs-2479 327 16 ) ) PUNCT iajs-2479 327 17 + + CCONJ iajs-2479 327 18 ( ( PUNCT iajs-2479 327 19 t t PROPN iajs-2479 327 20 + + PROPN iajs-2479 327 21 pj pj PROPN iajs-2479 327 22 + + PROPN iajs-2479 327 23 pi pi NOUN iajs-2479 327 24 -di -di NOUN iajs-2479 327 25 ) ) PUNCT iajs-2479 328 1 +0 +0 ADP iajs-2479 328 2 +1 +1 PROPN iajs-2479 329 1 + + NOUN iajs-2479 329 2 pi pi NOUN iajs-2479 329 3 ]= ]= NUM iajs-2479 329 4 3 3 NUM iajs-2479 329 5 t t NOUN iajs-2479 329 6 +3pi +3pi PROPN iajs-2479 329 7 +3pj +3pj PUNCT iajs-2479 329 8 – – PUNCT iajs-2479 329 9 di di X iajs-2479 329 10 +1 +1 NOUN iajs-2479 329 11 … … PUNCT iajs-2479 329 12 . . PUNCT iajs-2479 330 1 ( ( PUNCT iajs-2479 330 2 c c NOUN iajs-2479 330 3 ) ) PUNCT iajs-2479 330 4 . . PUNCT iajs-2479 331 1 ( ( PUNCT iajs-2479 331 2 when when SCONJ iajs-2479 331 3 vj vj NOUN iajs-2479 331 4 = = NOUN iajs-2479 331 5 cj cj NOUN iajs-2479 331 6 -dj -dj NOUN iajs-2479 331 7 ) ) PUNCT iajs-2479 331 8 . . PUNCT iajs-2479 331 9     SPACE iajs-2479 332 1 149 149 NUM iajs-2479 332 2     SPACE iajs-2479 332 3 ibn ibn PROPN iajs-2479 332 4 al al PROPN iajs-2479 332 5 - - PUNCT iajs-2479 332 6 haitham haitham PROPN iajs-2479 332 7 jour jour X iajs-2479 332 8 . . PROPN iajs-2479 332 9 for for ADP iajs-2479 332 10 pure pure ADJ iajs-2479 332 11 & & CCONJ iajs-2479 332 12 appl appl PROPN iajs-2479 332 13 . . PUNCT iajs-2479 333 1 sci sci PROPN iajs-2479 333 2 . . PROPN iajs-2479 334 1 33 33 NUM iajs-2479 334 2 ( ( PUNCT iajs-2479 334 3 3 3 NUM iajs-2479 334 4 ) ) PUNCT iajs-2479 334 5 2020 2020 NUM iajs-2479 334 6 1 1 NUM iajs-2479 334 7 . . PUNCT iajs-2479 335 1 δij=(a δij=(a NOUN iajs-2479 335 2 ) ) PUNCT iajs-2479 335 3 – – PUNCT iajs-2479 335 4 ( ( PUNCT iajs-2479 335 5 b)= b)= X iajs-2479 335 6 2 2 NUM iajs-2479 335 7 t t NOUN iajs-2479 335 8 +2pi +2pi PUNCT iajs-2479 336 1 + + CCONJ iajs-2479 336 2 pj pj PROPN iajs-2479 336 3 – – PUNCT iajs-2479 336 4 2dj 2dj NOUN iajs-2479 336 5 +1 +1 X iajs-2479 336 6 > > X iajs-2479 336 7 0 0 PUNCT iajs-2479 336 8 , , PUNCT iajs-2479 336 9 then then ADV iajs-2479 336 10 job job NOUN iajs-2479 336 11 j j PROPN iajs-2479 336 12 precede precede VERB iajs-2479 336 13 i. i. PROPN iajs-2479 336 14 2 2 NUM iajs-2479 336 15 . . PUNCT iajs-2479 336 16 δij=(a δij=(a NOUN iajs-2479 336 17 ) ) PUNCT iajs-2479 336 18 – – PUNCT iajs-2479 336 19 ( ( PUNCT iajs-2479 336 20 c)= c)= PROPN iajs-2479 336 21 t t PROPN iajs-2479 336 22 +2pi +2pi PUNCT iajs-2479 336 23 – – PUNCT iajs-2479 336 24 dj dj X iajs-2479 336 25 +1 +1 NOUN iajs-2479 336 26 > > X iajs-2479 336 27 0 0 PUNCT iajs-2479 336 28 , , PUNCT iajs-2479 336 29 then then ADV iajs-2479 336 30 job job NOUN iajs-2479 336 31 j j PROPN iajs-2479 336 32 precede precede PROPN iajs-2479 336 33 i. i. NOUN iajs-2479 336 34 case case NOUN iajs-2479 336 35 3 3 X iajs-2479 336 36 . . PUNCT iajs-2479 337 1 if if SCONJ iajs-2479 337 2 di di NOUN iajs-2479 337 3 ≤ ≤ X iajs-2479 337 4 t t PROPN iajs-2479 338 1 + + NOUN iajs-2479 338 2 pi pi NOUN iajs-2479 338 3 , , PUNCT iajs-2479 338 4 t t PROPN iajs-2479 339 1 + + PROPN iajs-2479 339 2 pi pi NOUN iajs-2479 339 3 + + ADJ iajs-2479 339 4 pj pj PROPN iajs-2479 339 5 ≤ ≤ ADJ iajs-2479 339 6 dj dj NOUN iajs-2479 339 7 ( ( PUNCT iajs-2479 339 8 i.e. i.e. X iajs-2479 339 9 the the DET iajs-2479 339 10 job job NOUN iajs-2479 339 11 i i PRON iajs-2479 339 12 , , PUNCT iajs-2479 339 13 is be AUX iajs-2479 339 14 always always ADV iajs-2479 339 15 tardy tardy ADJ iajs-2479 339 16 and and CCONJ iajs-2479 339 17 the the DET iajs-2479 339 18 job job NOUN iajs-2479 339 19 j j PROPN iajs-2479 339 20 , , PUNCT iajs-2479 339 21 is be AUX iajs-2479 339 22 always always ADV iajs-2479 339 23 early early ADJ iajs-2479 339 24 ) ) PUNCT iajs-2479 339 25 . . PUNCT iajs-2479 340 1 proof proof NOUN iajs-2479 340 2 . . PUNCT iajs-2479 341 1 since since SCONJ iajs-2479 341 2 the the DET iajs-2479 341 3 job job NOUN iajs-2479 341 4 i i PRON iajs-2479 341 5 , , PUNCT iajs-2479 341 6 is be AUX iajs-2479 341 7 always always ADV iajs-2479 341 8 tardy tardy ADJ iajs-2479 341 9 then then ADV iajs-2479 341 10 ei=0 ei=0 PROPN iajs-2479 341 11 , , PUNCT iajs-2479 341 12 ui=1 ui=1 ADV iajs-2479 341 13 , , PUNCT iajs-2479 341 14 and and CCONJ iajs-2479 341 15 if if SCONJ iajs-2479 341 16 job job NOUN iajs-2479 341 17 j j PROPN iajs-2479 341 18 is be AUX iajs-2479 341 19 always always ADV iajs-2479 341 20 early early ADJ iajs-2479 341 21 , , PUNCT iajs-2479 341 22 then then ADV iajs-2479 341 23 tj=0 tj=0 ADJ iajs-2479 341 24 , , PUNCT iajs-2479 341 25 and and CCONJ iajs-2479 341 26 vj={0 vj={0 NUM iajs-2479 341 27 , , PUNCT iajs-2479 341 28 cj cj PROPN iajs-2479 341 29 – – PUNCT iajs-2479 341 30 dj dj NOUN iajs-2479 341 31 } } PUNCT iajs-2479 341 32 ( ( PUNCT iajs-2479 341 33 i.e. i.e. X iajs-2479 341 34 j j PROPN iajs-2479 341 35 , , PUNCT iajs-2479 341 36 is be AUX iajs-2479 341 37 early early ADJ iajs-2479 341 38 or or CCONJ iajs-2479 341 39 partial partial ADJ iajs-2479 341 40 early early ADV iajs-2479 341 41 ) ) PUNCT iajs-2479 341 42 . . PUNCT iajs-2479 342 1   INTJ iajs-2479 342 2 ( ( PUNCT iajs-2479 342 3 when when SCONJ iajs-2479 342 4 vj=0 vj=0 NUM iajs-2479 342 5 ) ) PUNCT iajs-2479 342 6 . . PUNCT iajs-2479 343 1   X iajs-2479 344 1 fij= fij= PROPN iajs-2479 344 2 [ [ PUNCT iajs-2479 344 3 ( ( PUNCT iajs-2479 344 4 t t NOUN iajs-2479 344 5 + + NOUN iajs-2479 344 6 pi pi NOUN iajs-2479 344 7 ) ) PUNCT iajs-2479 345 1 + + CCONJ iajs-2479 345 2 ( ( PUNCT iajs-2479 345 3 t t NOUN iajs-2479 345 4 + + NOUN iajs-2479 345 5 pi pi NOUN iajs-2479 345 6 – – PUNCT iajs-2479 345 7 di di NOUN iajs-2479 345 8 ) ) PUNCT iajs-2479 346 1 +0 +0 ADP iajs-2479 346 2 + + NOUN iajs-2479 346 3 1 1 NUM iajs-2479 346 4 + + NOUN iajs-2479 346 5 pi pi NOUN iajs-2479 346 6 + + ADJ iajs-2479 346 7 ( ( PUNCT iajs-2479 346 8 t t NOUN iajs-2479 346 9 + + NOUN iajs-2479 346 10 pi pi PROPN iajs-2479 346 11 + + PROPN iajs-2479 346 12 pj pj X iajs-2479 346 13 ) ) PUNCT iajs-2479 347 1 +0 +0 ADP iajs-2479 347 2 + + CCONJ iajs-2479 347 3 ( ( PUNCT iajs-2479 347 4 dj dj NOUN iajs-2479 347 5 – – PUNCT iajs-2479 347 6 t t NOUN iajs-2479 347 7 – – PUNCT iajs-2479 347 8 pi pi NOUN iajs-2479 347 9 – – PUNCT iajs-2479 347 10 pj pj PROPN iajs-2479 347 11 ) ) PUNCT iajs-2479 348 1 +0 +0 ADP iajs-2479 348 2 +0 +0 ADP iajs-2479 348 3 ]= ]= NUM iajs-2479 348 4 2 2 NUM iajs-2479 348 5 t t NOUN iajs-2479 348 6 +3pi +3pi PROPN iajs-2479 348 7 – – PUNCT iajs-2479 348 8 di di NOUN iajs-2479 348 9 + + NOUN iajs-2479 348 10 dj dj ADJ iajs-2479 348 11 +1 +1 PROPN iajs-2479 348 12 … … PUNCT iajs-2479 348 13 .. .. PUNCT iajs-2479 348 14 ( ( PUNCT iajs-2479 348 15 a a NOUN iajs-2479 348 16 ) ) PUNCT iajs-2479 348 17 . . PUNCT iajs-2479 349 1   X iajs-2479 349 2 f'ji= f'ji= PROPN iajs-2479 350 1 [ [ X iajs-2479 350 2 ( ( PUNCT iajs-2479 350 3 t t PROPN iajs-2479 350 4 + + PROPN iajs-2479 350 5 pj pj PROPN iajs-2479 350 6 ) ) PUNCT iajs-2479 351 1 +0 +0 ADP iajs-2479 351 2 + + CCONJ iajs-2479 351 3 ( ( PUNCT iajs-2479 351 4 dj dj NOUN iajs-2479 351 5 – – PUNCT iajs-2479 351 6 t t PROPN iajs-2479 351 7 – – PUNCT iajs-2479 351 8 pj pj PROPN iajs-2479 351 9 ) ) PUNCT iajs-2479 352 1 +0 +0 ADP iajs-2479 352 2 +0 +0 ADP iajs-2479 352 3 + + PROPN iajs-2479 352 4 ( ( PUNCT iajs-2479 352 5 t t PROPN iajs-2479 352 6 + + PROPN iajs-2479 352 7 pj pj PROPN iajs-2479 352 8 + + PROPN iajs-2479 352 9 pi pi NOUN iajs-2479 352 10 ) ) PUNCT iajs-2479 352 11 + + CCONJ iajs-2479 352 12 ( ( PUNCT iajs-2479 352 13 t t PROPN iajs-2479 352 14 + + PROPN iajs-2479 352 15 pj pj PROPN iajs-2479 352 16 + + PROPN iajs-2479 352 17 pi pi NOUN iajs-2479 352 18 – – PUNCT iajs-2479 352 19 di di NOUN iajs-2479 352 20 ) ) PUNCT iajs-2479 352 21 +0 +0 ADP iajs-2479 352 22 +1 +1 PROPN iajs-2479 353 1 + + NOUN iajs-2479 353 2 pi pi NOUN iajs-2479 353 3 ]= ]= NUM iajs-2479 353 4 2 2 NUM iajs-2479 353 5 t t NOUN iajs-2479 353 6 +3pi +3pi X iajs-2479 354 1 +2pj +2pj PUNCT iajs-2479 354 2 + + PUNCT iajs-2479 354 3 dj dj X iajs-2479 354 4 – – PUNCT iajs-2479 354 5 di di X iajs-2479 354 6 +1 +1 NOUN iajs-2479 354 7 … … PUNCT iajs-2479 354 8 . . PUNCT iajs-2479 355 1 ( ( PUNCT iajs-2479 355 2 b b NOUN iajs-2479 355 3 ) ) PUNCT iajs-2479 355 4 . . PUNCT iajs-2479 356 1 δij=(a δij=(a NOUN iajs-2479 356 2 ) ) PUNCT iajs-2479 356 3 – – PUNCT iajs-2479 356 4 ( ( PUNCT iajs-2479 356 5 b)= b)= NOUN iajs-2479 356 6 – – PUNCT iajs-2479 356 7 2pj 2pj NOUN iajs-2479 356 8 < < X iajs-2479 356 9 0 0 NUM iajs-2479 356 10 , , PUNCT iajs-2479 356 11 then then ADV iajs-2479 356 12 job job NOUN iajs-2479 356 13 i i PRON iajs-2479 356 14 precede precede VERB iajs-2479 356 15 j j PROPN iajs-2479 356 16   INTJ iajs-2479 356 17 when when SCONJ iajs-2479 356 18 ( ( PUNCT iajs-2479 356 19 when when SCONJ iajs-2479 356 20 vj= vj= PROPN iajs-2479 356 21 cj cj PROPN iajs-2479 356 22 – – PUNCT iajs-2479 356 23 dj dj NOUN iajs-2479 356 24 ) ) PUNCT iajs-2479 356 25 . . PUNCT iajs-2479 357 1   X iajs-2479 358 1 fij= fij= PROPN iajs-2479 358 2 [ [ PUNCT iajs-2479 358 3 ( ( PUNCT iajs-2479 358 4 t t NOUN iajs-2479 358 5 + + NOUN iajs-2479 358 6 pi pi NOUN iajs-2479 358 7 ) ) PUNCT iajs-2479 359 1 + + CCONJ iajs-2479 359 2 ( ( PUNCT iajs-2479 359 3 t t NOUN iajs-2479 359 4 + + NOUN iajs-2479 359 5 pi pi NOUN iajs-2479 359 6 – – PUNCT iajs-2479 359 7 di di NOUN iajs-2479 359 8 ) ) PUNCT iajs-2479 360 1 +0 +0 ADP iajs-2479 360 2 + + NOUN iajs-2479 360 3 1 1 NUM iajs-2479 360 4 + + NOUN iajs-2479 360 5 pi pi NOUN iajs-2479 360 6 + + ADJ iajs-2479 360 7 ( ( PUNCT iajs-2479 360 8 t t NOUN iajs-2479 360 9 + + NOUN iajs-2479 360 10 pi pi PROPN iajs-2479 360 11 + + PROPN iajs-2479 360 12 pj pj X iajs-2479 360 13 ) ) PUNCT iajs-2479 361 1 +0 +0 ADP iajs-2479 361 2 + + CCONJ iajs-2479 361 3 ( ( PUNCT iajs-2479 361 4 dj dj NOUN iajs-2479 361 5 – – PUNCT iajs-2479 361 6 t t NOUN iajs-2479 361 7 – – PUNCT iajs-2479 361 8 pi pi NOUN iajs-2479 361 9 – – PUNCT iajs-2479 361 10 pj pj PROPN iajs-2479 361 11 ) ) PUNCT iajs-2479 362 1 +0 +0 ADP iajs-2479 362 2 + + NOUN iajs-2479 362 3 t t NOUN iajs-2479 362 4 + + NUM iajs-2479 362 5 pi pi PROPN iajs-2479 362 6 + + PROPN iajs-2479 362 7 pj pj PROPN iajs-2479 362 8 – – PUNCT iajs-2479 362 9 dj]= dj]= VERB iajs-2479 362 10 3 3 NUM iajs-2479 362 11 t t NOUN iajs-2479 362 12 +4pi +4pi PROPN iajs-2479 362 13 + + CCONJ iajs-2479 362 14 pj pj PROPN iajs-2479 362 15 – – PUNCT iajs-2479 362 16 di di NOUN iajs-2479 362 17 +1 +1 NOUN iajs-2479 362 18 … … PUNCT iajs-2479 362 19 .(c .(c NOUN iajs-2479 362 20 ) ) PUNCT iajs-2479 362 21 . . PUNCT iajs-2479 363 1   X iajs-2479 363 2 f'ji= f'ji= PROPN iajs-2479 364 1 [ [ X iajs-2479 364 2 ( ( PUNCT iajs-2479 364 3 t t PROPN iajs-2479 364 4 + + PROPN iajs-2479 364 5 pj pj PROPN iajs-2479 364 6 ) ) PUNCT iajs-2479 365 1 +0 +0 ADP iajs-2479 365 2 + + CCONJ iajs-2479 365 3 ( ( PUNCT iajs-2479 365 4 dj dj NOUN iajs-2479 365 5 – – PUNCT iajs-2479 365 6 t t PROPN iajs-2479 365 7 – – PUNCT iajs-2479 365 8 pj pj PROPN iajs-2479 365 9 ) ) PUNCT iajs-2479 366 1 +0 +0 ADP iajs-2479 366 2 + + PROPN iajs-2479 366 3 ( ( PUNCT iajs-2479 366 4 t t PROPN iajs-2479 366 5 + + CCONJ iajs-2479 366 6 pj pj PROPN iajs-2479 366 7 – – PUNCT iajs-2479 366 8 dj dj NOUN iajs-2479 366 9 ) ) PUNCT iajs-2479 366 10 + + PROPN iajs-2479 366 11 ( ( PUNCT iajs-2479 366 12 t t PROPN iajs-2479 366 13 + + PROPN iajs-2479 366 14 pj pj PROPN iajs-2479 366 15 + + PROPN iajs-2479 366 16 pi pi NOUN iajs-2479 366 17 ) ) PUNCT iajs-2479 366 18 + + CCONJ iajs-2479 366 19 ( ( PUNCT iajs-2479 366 20 t t PROPN iajs-2479 366 21 + + PROPN iajs-2479 366 22 pj pj PROPN iajs-2479 366 23 + + PROPN iajs-2479 366 24 pi pi NOUN iajs-2479 366 25 – – PUNCT iajs-2479 366 26 di di NOUN iajs-2479 366 27 ) ) PUNCT iajs-2479 366 28 +0 +0 ADP iajs-2479 366 29 +1 +1 PROPN iajs-2479 367 1 + + NOUN iajs-2479 367 2 pi pi NOUN iajs-2479 367 3 ] ] X iajs-2479 367 4 = = PUNCT iajs-2479 367 5 3 3 NUM iajs-2479 367 6 t t NOUN iajs-2479 368 1 + + CCONJ iajs-2479 368 2 3pi 3pi NOUN iajs-2479 368 3 +3pj +3pj PUNCT iajs-2479 368 4 – – PUNCT iajs-2479 368 5 di di X iajs-2479 368 6 +1 +1 PROPN iajs-2479 368 7 … … PUNCT iajs-2479 368 8 .. .. PUNCT iajs-2479 368 9 ( ( PUNCT iajs-2479 368 10 e e NOUN iajs-2479 368 11 ) ) PUNCT iajs-2479 368 12 . . PUNCT iajs-2479 369 1 δij=(c δij=(c NUM iajs-2479 369 2 ) ) PUNCT iajs-2479 369 3 – – PUNCT iajs-2479 369 4 ( ( PUNCT iajs-2479 369 5 e)= e)= ADJ iajs-2479 369 6 pi pi NOUN iajs-2479 369 7 – – PUNCT iajs-2479 369 8 2pj 2pj ADJ iajs-2479 369 9 ≤0 ≤0 PROPN iajs-2479 369 10 , , PUNCT iajs-2479 369 11 then then ADV iajs-2479 369 12 job job NOUN iajs-2479 369 13 i i PRON iajs-2479 369 14 precede precede VERB iajs-2479 369 15 j j NOUN iajs-2479 369 16 case case NOUN iajs-2479 369 17 4 4 X iajs-2479 369 18 . . PUNCT iajs-2479 370 1 if if SCONJ iajs-2479 370 2 t t PROPN iajs-2479 370 3 + + NOUN iajs-2479 370 4 pi pi NOUN iajs-2479 370 5 ≤ ≤ NUM iajs-2479 370 6 di di NOUN iajs-2479 370 7 ≤ ≤ NOUN iajs-2479 370 8 dj dj NOUN iajs-2479 370 9 ≤ ≤ NUM iajs-2479 370 10 t t PROPN iajs-2479 370 11 + + PROPN iajs-2479 370 12 pj pj PROPN iajs-2479 370 13 ( ( PUNCT iajs-2479 370 14 i.e. i.e. X iajs-2479 370 15 the the DET iajs-2479 370 16 job job NOUN iajs-2479 370 17 j j PROPN iajs-2479 370 18 , , PUNCT iajs-2479 370 19 is be AUX iajs-2479 370 20 always always ADV iajs-2479 370 21 tardy tardy ADJ iajs-2479 370 22 and and CCONJ iajs-2479 370 23 the the DET iajs-2479 370 24 job job NOUN iajs-2479 370 25 i i PRON iajs-2479 370 26 , , PUNCT iajs-2479 370 27 is be AUX iajs-2479 370 28 tardy tardy ADJ iajs-2479 370 29 if if SCONJ iajs-2479 370 30 not not PART iajs-2479 370 31 scheduled schedule VERB iajs-2479 370 32 first first ADV iajs-2479 370 33 ) ) PUNCT iajs-2479 370 34 . . PUNCT iajs-2479 371 1 proof proof NOUN iajs-2479 371 2 . . PUNCT iajs-2479 372 1 since since SCONJ iajs-2479 372 2 the the DET iajs-2479 372 3 job job NOUN iajs-2479 372 4 j j PROPN iajs-2479 372 5 , , PUNCT iajs-2479 372 6 is be AUX iajs-2479 372 7 always always ADV iajs-2479 372 8 tardy tardy ADJ iajs-2479 372 9 then then ADV iajs-2479 372 10 ej=0 ej=0 ADJ iajs-2479 372 11 , , PUNCT iajs-2479 372 12 uj=1 uj=1 NOUN iajs-2479 372 13 , , PUNCT iajs-2479 372 14 and and CCONJ iajs-2479 372 15 if if SCONJ iajs-2479 372 16 job job NOUN iajs-2479 372 17 i i PRON iajs-2479 372 18 , , PUNCT iajs-2479 372 19 scheduled schedule VERB iajs-2479 372 20 first first ADV iajs-2479 372 21 then then ADV iajs-2479 372 22 ti=0 ti=0 ADJ iajs-2479 372 23 , , PUNCT iajs-2479 372 24 and and CCONJ iajs-2479 372 25 vi={0 vi={0 PROPN iajs-2479 372 26 , , PUNCT iajs-2479 372 27 ci ci PROPN iajs-2479 372 28 – – PUNCT iajs-2479 372 29 di di NOUN iajs-2479 372 30 } } PUNCT iajs-2479 372 31 ( ( PUNCT iajs-2479 372 32 i.e. i.e. X iajs-2479 372 33 i i PRON iajs-2479 372 34 , , PUNCT iajs-2479 372 35 is be AUX iajs-2479 372 36 early early ADJ iajs-2479 372 37 or or CCONJ iajs-2479 372 38 partial partial ADJ iajs-2479 372 39 early early ADV iajs-2479 372 40 ) ) PUNCT iajs-2479 372 41 . . PUNCT iajs-2479 373 1   NOUN iajs-2479 373 2 ( ( PUNCT iajs-2479 373 3 when when SCONJ iajs-2479 373 4 vi=0 vi=0 VERB iajs-2479 373 5 ) ) PUNCT iajs-2479 373 6 . . PUNCT iajs-2479 374 1 fij= fij= PUNCT iajs-2479 375 1 [ [ X iajs-2479 375 2 ( ( PUNCT iajs-2479 375 3 t t NOUN iajs-2479 375 4 + + NOUN iajs-2479 375 5 pi pi NOUN iajs-2479 375 6 ) ) PUNCT iajs-2479 376 1 +0 +0 ADP iajs-2479 376 2 + + CCONJ iajs-2479 376 3 ( ( PUNCT iajs-2479 376 4 di di INTJ iajs-2479 376 5 – – PUNCT iajs-2479 376 6 t t NOUN iajs-2479 376 7 – – PUNCT iajs-2479 376 8 pi pi NOUN iajs-2479 376 9 ) ) PUNCT iajs-2479 377 1 +0 +0 ADP iajs-2479 377 2 +0 +0 ADP iajs-2479 377 3 + + PROPN iajs-2479 377 4 ( ( PUNCT iajs-2479 377 5 t t NOUN iajs-2479 377 6 + + NOUN iajs-2479 377 7 pi pi PROPN iajs-2479 377 8 + + PROPN iajs-2479 377 9 pj pj X iajs-2479 377 10 ) ) PUNCT iajs-2479 377 11 + + CCONJ iajs-2479 377 12 ( ( PUNCT iajs-2479 377 13 t t NOUN iajs-2479 377 14 + + NOUN iajs-2479 377 15 pi pi NOUN iajs-2479 377 16 + + PROPN iajs-2479 377 17 pj pj PROPN iajs-2479 377 18 – – PUNCT iajs-2479 377 19 dj dj NOUN iajs-2479 377 20 ) ) PUNCT iajs-2479 377 21 +0 +0 ADP iajs-2479 377 22 +1 +1 PROPN iajs-2479 378 1 + + NOUN iajs-2479 378 2 pj pj NOUN iajs-2479 378 3 ]= ]= NUM iajs-2479 378 4 2 2 NUM iajs-2479 378 5 t t NOUN iajs-2479 378 6 +2pi +2pi SYM iajs-2479 378 7 +3pj +3pj PUNCT iajs-2479 378 8 – – PUNCT iajs-2479 378 9 dj dj NOUN iajs-2479 379 1 + + NOUN iajs-2479 379 2 di di X iajs-2479 379 3 +1 +1 NOUN iajs-2479 379 4 … … PUNCT iajs-2479 379 5 .. .. PUNCT iajs-2479 379 6 ( ( PUNCT iajs-2479 379 7 a a NOUN iajs-2479 379 8 ) ) PUNCT iajs-2479 379 9 . . PUNCT iajs-2479 380 1   X iajs-2479 380 2 f'ji= f'ji= PROPN iajs-2479 381 1 [ [ X iajs-2479 381 2 ( ( PUNCT iajs-2479 381 3 t t PROPN iajs-2479 381 4 + + PROPN iajs-2479 381 5 pj pj PROPN iajs-2479 381 6 ) ) PUNCT iajs-2479 382 1 + + CCONJ iajs-2479 382 2 ( ( PUNCT iajs-2479 382 3 t t PROPN iajs-2479 382 4 + + PROPN iajs-2479 382 5 pj pj PROPN iajs-2479 382 6 – – PUNCT iajs-2479 382 7 dj dj NOUN iajs-2479 382 8 ) ) PUNCT iajs-2479 383 1 +0 +0 ADP iajs-2479 383 2 +1 +1 PROPN iajs-2479 384 1 + + NOUN iajs-2479 384 2 pj pj PROPN iajs-2479 384 3 + + CCONJ iajs-2479 384 4 ( ( PUNCT iajs-2479 384 5 t t PROPN iajs-2479 384 6 + + PROPN iajs-2479 384 7 pj pj PROPN iajs-2479 384 8 + + PROPN iajs-2479 384 9 pi pi NOUN iajs-2479 384 10 ) ) PUNCT iajs-2479 385 1 + + CCONJ iajs-2479 385 2 ( ( PUNCT iajs-2479 385 3 t t PROPN iajs-2479 385 4 + + PROPN iajs-2479 385 5 pj pj PROPN iajs-2479 385 6 + + PROPN iajs-2479 385 7 pi pi NOUN iajs-2479 385 8 – – PUNCT iajs-2479 385 9 di di NOUN iajs-2479 385 10 ) ) PUNCT iajs-2479 385 11 +0 +0 ADP iajs-2479 385 12 +1 +1 PROPN iajs-2479 386 1 + + NOUN iajs-2479 386 2 pi pi NOUN iajs-2479 386 3 ]= ]= NUM iajs-2479 386 4 4 4 NUM iajs-2479 386 5 t t NOUN iajs-2479 386 6 +3pi +3pi X iajs-2479 386 7 +5pj +5pj X iajs-2479 386 8 – – PUNCT iajs-2479 386 9 dj dj NOUN iajs-2479 386 10 – – PUNCT iajs-2479 386 11 di di NOUN iajs-2479 386 12 +2 +2 NOUN iajs-2479 386 13 … … PUNCT iajs-2479 386 14 .. .. PUNCT iajs-2479 386 15 ( ( PUNCT iajs-2479 386 16 b b NOUN iajs-2479 386 17 ) ) PUNCT iajs-2479 386 18 . . PUNCT iajs-2479 387 1 δij=(a δij=(a NOUN iajs-2479 387 2 ) ) PUNCT iajs-2479 387 3 – – PUNCT iajs-2479 387 4 ( ( PUNCT iajs-2479 387 5 b)= b)= NOUN iajs-2479 387 6 – – PUNCT iajs-2479 387 7 2 2 NUM iajs-2479 387 8 t t NOUN iajs-2479 387 9 – – PUNCT iajs-2479 387 10 pi pi NOUN iajs-2479 387 11 – – PUNCT iajs-2479 387 12 2pj 2pj NOUN iajs-2479 387 13 +2di +2di PUNCT iajs-2479 387 14 – – PUNCT iajs-2479 387 15 1 1 NUM iajs-2479 387 16 ≤ ≤ NUM iajs-2479 387 17 0 0 NUM iajs-2479 387 18 , , PUNCT iajs-2479 387 19 then then ADV iajs-2479 387 20 job job NOUN iajs-2479 387 21 i i PRON iajs-2479 387 22 precede precede VERB iajs-2479 387 23 j j PROPN iajs-2479 387 24   NOUN iajs-2479 387 25 ( ( PUNCT iajs-2479 387 26 when when SCONJ iajs-2479 387 27 vi= vi= PROPN iajs-2479 387 28 ci ci PROPN iajs-2479 387 29 – – PUNCT iajs-2479 387 30 di di NOUN iajs-2479 387 31 ) ) PUNCT iajs-2479 387 32 . . PUNCT iajs-2479 388 1 fij= fij= PUNCT iajs-2479 389 1 [ [ X iajs-2479 389 2 ( ( PUNCT iajs-2479 389 3 t t NOUN iajs-2479 389 4 + + NOUN iajs-2479 389 5 pi pi NOUN iajs-2479 389 6 ) ) PUNCT iajs-2479 390 1 +0 +0 ADP iajs-2479 390 2 + + CCONJ iajs-2479 390 3 ( ( PUNCT iajs-2479 390 4 di di INTJ iajs-2479 390 5 – – PUNCT iajs-2479 390 6 t t NOUN iajs-2479 390 7 – – PUNCT iajs-2479 390 8 pi pi NOUN iajs-2479 390 9 ) ) PUNCT iajs-2479 390 10 +0 +0 ADP iajs-2479 390 11 + + PROPN iajs-2479 390 12 ( ( PUNCT iajs-2479 390 13 t t NOUN iajs-2479 390 14 + + NOUN iajs-2479 390 15 pi pi NOUN iajs-2479 390 16 – – PUNCT iajs-2479 390 17 di di NOUN iajs-2479 390 18 ) ) PUNCT iajs-2479 390 19 + + PROPN iajs-2479 390 20 ( ( PUNCT iajs-2479 390 21 t t NOUN iajs-2479 390 22 + + NOUN iajs-2479 390 23 pi pi PROPN iajs-2479 390 24 + + PROPN iajs-2479 390 25 pj pj X iajs-2479 390 26 ) ) PUNCT iajs-2479 390 27 + + CCONJ iajs-2479 390 28 ( ( PUNCT iajs-2479 390 29 t t NOUN iajs-2479 390 30 + + NOUN iajs-2479 390 31 pi pi NOUN iajs-2479 390 32 + + PROPN iajs-2479 390 33 pj pj PROPN iajs-2479 390 34 – – PUNCT iajs-2479 390 35 dj dj NOUN iajs-2479 390 36 ) ) PUNCT iajs-2479 390 37 +0 +0 ADP iajs-2479 390 38 +1 +1 PROPN iajs-2479 391 1 + + NOUN iajs-2479 391 2 pj pj X iajs-2479 391 3 ] ] X iajs-2479 391 4 = = PUNCT iajs-2479 391 5 3 3 NUM iajs-2479 391 6 t t NOUN iajs-2479 391 7 +3pi +3pi PROPN iajs-2479 391 8 +3pj +3pj PUNCT iajs-2479 391 9 – – PUNCT iajs-2479 391 10 dj dj X iajs-2479 391 11 +1 +1 PROPN iajs-2479 391 12 … … PUNCT iajs-2479 391 13 . . PUNCT iajs-2479 392 1 ( ( PUNCT iajs-2479 392 2 c c NOUN iajs-2479 392 3 ) ) PUNCT iajs-2479 392 4 . . PUNCT iajs-2479 393 1   X iajs-2479 393 2 f'ji= f'ji= PROPN iajs-2479 394 1 [ [ X iajs-2479 394 2 ( ( PUNCT iajs-2479 394 3 t t PROPN iajs-2479 394 4 + + PROPN iajs-2479 394 5 pj pj PROPN iajs-2479 394 6 ) ) PUNCT iajs-2479 395 1 + + CCONJ iajs-2479 395 2 ( ( PUNCT iajs-2479 395 3 t t PROPN iajs-2479 395 4 + + PROPN iajs-2479 395 5 pj pj PROPN iajs-2479 395 6 – – PUNCT iajs-2479 395 7 dj dj NOUN iajs-2479 395 8 ) ) PUNCT iajs-2479 396 1 +0 +0 ADP iajs-2479 396 2 +1 +1 PROPN iajs-2479 397 1 + + NOUN iajs-2479 397 2 pj pj PROPN iajs-2479 397 3 + + CCONJ iajs-2479 397 4 ( ( PUNCT iajs-2479 397 5 t t PROPN iajs-2479 397 6 + + PROPN iajs-2479 397 7 pj pj PROPN iajs-2479 397 8 + + PROPN iajs-2479 397 9 pi pi NOUN iajs-2479 397 10 ) ) PUNCT iajs-2479 398 1 + + CCONJ iajs-2479 398 2 ( ( PUNCT iajs-2479 398 3 t t PROPN iajs-2479 398 4 + + PROPN iajs-2479 398 5 pj pj PROPN iajs-2479 398 6 + + PROPN iajs-2479 398 7 pi pi NOUN iajs-2479 398 8 – – PUNCT iajs-2479 398 9 di di NOUN iajs-2479 398 10 ) ) PUNCT iajs-2479 398 11 +0 +0 ADP iajs-2479 398 12 +1 +1 PROPN iajs-2479 399 1 + + NOUN iajs-2479 399 2 pi pi NOUN iajs-2479 399 3 ]= ]= NUM iajs-2479 399 4 4 4 NUM iajs-2479 399 5 t t NOUN iajs-2479 399 6 +3pi +3pi X iajs-2479 399 7 +5pj +5pj X iajs-2479 399 8 – – PUNCT iajs-2479 399 9 dj dj NOUN iajs-2479 399 10 – – PUNCT iajs-2479 399 11 di di NOUN iajs-2479 399 12 +2 +2 NOUN iajs-2479 399 13 … … PUNCT iajs-2479 399 14 .. .. PUNCT iajs-2479 399 15 ( ( PUNCT iajs-2479 399 16 e e NOUN iajs-2479 399 17 ) ) PUNCT iajs-2479 399 18 . . PUNCT iajs-2479 400 1 δij=(c δij=(c NUM iajs-2479 400 2 ) ) PUNCT iajs-2479 400 3 – – PUNCT iajs-2479 401 1 ( ( PUNCT iajs-2479 401 2 e)= e)= ADJ iajs-2479 401 3 – – PUNCT iajs-2479 401 4 t t NOUN iajs-2479 401 5 – – PUNCT iajs-2479 401 6 2pj 2pj NOUN iajs-2479 402 1 + + NOUN iajs-2479 402 2 di di NOUN iajs-2479 402 3 – – PUNCT iajs-2479 402 4 1 1 NUM iajs-2479 402 5 ≤ ≤ NUM iajs-2479 402 6 0 0 NUM iajs-2479 402 7 , , PUNCT iajs-2479 402 8 then then ADV iajs-2479 402 9 job job NOUN iajs-2479 402 10 i i PRON iajs-2479 402 11 precede precede VERB iajs-2479 402 12 j j NOUN iajs-2479 402 13 case case NOUN iajs-2479 402 14 5 5 X iajs-2479 402 15 . . PUNCT iajs-2479 403 1 if if SCONJ iajs-2479 403 2 t t PROPN iajs-2479 403 3 + + NOUN iajs-2479 403 4 pi pi NOUN iajs-2479 403 5 ≤ ≤ NUM iajs-2479 403 6 di di NOUN iajs-2479 403 7 , , PUNCT iajs-2479 403 8 t t PROPN iajs-2479 403 9 + + PROPN iajs-2479 403 10 pj pj PROPN iajs-2479 403 11 ≤ ≤ NOUN iajs-2479 403 12 dj dj NOUN iajs-2479 403 13 ≤ ≤ NUM iajs-2479 403 14 t t NOUN iajs-2479 404 1 + + NOUN iajs-2479 404 2 pi pi PROPN iajs-2479 404 3 + + PROPN iajs-2479 404 4 pj pj PROPN iajs-2479 404 5 ( ( PUNCT iajs-2479 404 6 i.e. i.e. X iajs-2479 404 7 each each PRON iajs-2479 404 8 of of ADP iajs-2479 404 9 the the DET iajs-2479 404 10 two two NUM iajs-2479 404 11 jobs job NOUN iajs-2479 404 12 i i PRON iajs-2479 404 13 and and CCONJ iajs-2479 404 14 j j PROPN iajs-2479 404 15 are be AUX iajs-2479 404 16 tardy tardy ADJ iajs-2479 404 17 if if SCONJ iajs-2479 404 18 not not PART iajs-2479 404 19 scheduled schedule VERB iajs-2479 404 20 first first ADV iajs-2479 404 21 ) ) PUNCT iajs-2479 404 22 . . PUNCT iajs-2479 405 1 proof proof NOUN iajs-2479 405 2 : : PUNCT iajs-2479 405 3   PRON iajs-2479 405 4 ( ( PUNCT iajs-2479 405 5 when when SCONJ iajs-2479 405 6 vi=0 vi=0 VERB iajs-2479 405 7 ) ) PUNCT iajs-2479 405 8 . . PUNCT iajs-2479 406 1 fij= fij= PUNCT iajs-2479 407 1 [ [ X iajs-2479 407 2 ( ( PUNCT iajs-2479 407 3 t t NOUN iajs-2479 407 4 + + NOUN iajs-2479 407 5 pi pi NOUN iajs-2479 407 6 ) ) PUNCT iajs-2479 408 1 +0 +0 ADP iajs-2479 408 2 + + CCONJ iajs-2479 408 3 ( ( PUNCT iajs-2479 408 4 di di INTJ iajs-2479 408 5 – – PUNCT iajs-2479 408 6 t t NOUN iajs-2479 408 7 – – PUNCT iajs-2479 408 8 pi pi NOUN iajs-2479 408 9 ) ) PUNCT iajs-2479 409 1 +0 +0 ADP iajs-2479 409 2 +0 +0 ADP iajs-2479 409 3 + + PROPN iajs-2479 409 4 ( ( PUNCT iajs-2479 409 5 t t NOUN iajs-2479 409 6 + + NOUN iajs-2479 409 7 pi pi PROPN iajs-2479 409 8 + + PROPN iajs-2479 409 9 pj pj X iajs-2479 409 10 ) ) PUNCT iajs-2479 409 11 + + CCONJ iajs-2479 409 12 ( ( PUNCT iajs-2479 409 13 t t NOUN iajs-2479 409 14 + + NOUN iajs-2479 409 15 pi pi NOUN iajs-2479 409 16 + + PROPN iajs-2479 409 17 pj pj PROPN iajs-2479 409 18 – – PUNCT iajs-2479 409 19 dj dj NOUN iajs-2479 409 20 ) ) PUNCT iajs-2479 409 21 +0 +0 ADP iajs-2479 409 22 +1 +1 PROPN iajs-2479 410 1 + + NOUN iajs-2479 410 2 pj pj NOUN iajs-2479 410 3 ]= ]= NUM iajs-2479 410 4 2 2 NUM iajs-2479 410 5 t t NOUN iajs-2479 410 6 +2pi +2pi SYM iajs-2479 410 7 +3pj +3pj PUNCT iajs-2479 410 8 – – PUNCT iajs-2479 410 9 dj dj NOUN iajs-2479 411 1 + + NOUN iajs-2479 411 2 di di X iajs-2479 411 3 +1 +1 NOUN iajs-2479 411 4 … … PUNCT iajs-2479 411 5 .. .. PUNCT iajs-2479 411 6 ( ( PUNCT iajs-2479 411 7 a a NOUN iajs-2479 411 8 ) ) PUNCT iajs-2479 411 9 . . PUNCT iajs-2479 412 1   NOUN iajs-2479 412 2 ( ( PUNCT iajs-2479 412 3 when when SCONJ iajs-2479 412 4 vj=0 vj=0 NUM iajs-2479 412 5 ) ) PUNCT iajs-2479 412 6 . . PUNCT iajs-2479 413 1 f'ji= f'ji= PROPN iajs-2479 414 1 [ [ X iajs-2479 414 2 ( ( PUNCT iajs-2479 414 3 t t PROPN iajs-2479 414 4 + + PROPN iajs-2479 414 5 pj pj PROPN iajs-2479 414 6 ) ) PUNCT iajs-2479 415 1 +0 +0 ADP iajs-2479 415 2 + + CCONJ iajs-2479 415 3 ( ( PUNCT iajs-2479 415 4 dj dj NOUN iajs-2479 415 5 – – PUNCT iajs-2479 415 6 t t PROPN iajs-2479 415 7 – – PUNCT iajs-2479 415 8 pj pj PROPN iajs-2479 415 9 ) ) PUNCT iajs-2479 416 1 +0 +0 ADP iajs-2479 416 2 +0 +0 ADP iajs-2479 416 3 + + PROPN iajs-2479 416 4 ( ( PUNCT iajs-2479 416 5 t t PROPN iajs-2479 416 6 + + PROPN iajs-2479 416 7 pj pj PROPN iajs-2479 416 8 + + PROPN iajs-2479 416 9 pi pi NOUN iajs-2479 416 10 ) ) PUNCT iajs-2479 416 11 + + CCONJ iajs-2479 416 12 ( ( PUNCT iajs-2479 416 13 t t PROPN iajs-2479 416 14 + + PROPN iajs-2479 416 15 pj pj PROPN iajs-2479 416 16 + + PROPN iajs-2479 416 17 pi pi NOUN iajs-2479 416 18 – – PUNCT iajs-2479 416 19 di di NOUN iajs-2479 416 20 ) ) PUNCT iajs-2479 416 21 +0 +0 ADP iajs-2479 416 22 +1 +1 PROPN iajs-2479 417 1 + + NOUN iajs-2479 417 2 pi pi NOUN iajs-2479 417 3 ]= ]= NUM iajs-2479 417 4 2 2 NUM iajs-2479 417 5 t t NOUN iajs-2479 417 6 +3pi +3pi X iajs-2479 418 1 +2pj +2pj PUNCT iajs-2479 418 2 + + PUNCT iajs-2479 418 3 dj dj X iajs-2479 418 4 – – PUNCT iajs-2479 418 5 di di X iajs-2479 418 6 +1 +1 NOUN iajs-2479 418 7 … … PUNCT iajs-2479 418 8 . . PUNCT iajs-2479 419 1 ( ( PUNCT iajs-2479 419 2 b b NOUN iajs-2479 419 3 ) ) PUNCT iajs-2479 419 4 . . PUNCT iajs-2479 420 1 δij=(a δij=(a NOUN iajs-2479 420 2 ) ) PUNCT iajs-2479 420 3 – – PUNCT iajs-2479 420 4 ( ( PUNCT iajs-2479 420 5 b)= b)= NOUN iajs-2479 420 6 – – PUNCT iajs-2479 420 7 pi pi NOUN iajs-2479 421 1 + + PROPN iajs-2479 421 2 pj pj PROPN iajs-2479 421 3 +2di +2di PUNCT iajs-2479 421 4 – – PUNCT iajs-2479 421 5 2dj 2dj NOUN iajs-2479 421 6 > > PUNCT iajs-2479 421 7 0 0 NUM iajs-2479 421 8 , , PUNCT iajs-2479 421 9 then then ADV iajs-2479 421 10 job job NOUN iajs-2479 421 11 j j PROPN iajs-2479 421 12 precede precede VERB iajs-2479 421 13 i. i. NOUN iajs-2479 421 14   NOUN iajs-2479 422 1 ( ( PUNCT iajs-2479 422 2 when when SCONJ iajs-2479 422 3 vi= vi= PROPN iajs-2479 422 4 ci ci PROPN iajs-2479 422 5 – – PUNCT iajs-2479 422 6 di di NOUN iajs-2479 422 7 ) ) PUNCT iajs-2479 422 8 . . PUNCT iajs-2479 423 1 fij= fij= PUNCT iajs-2479 424 1 [ [ X iajs-2479 424 2 ( ( PUNCT iajs-2479 424 3 t t NOUN iajs-2479 424 4 + + NOUN iajs-2479 424 5 pi pi NOUN iajs-2479 424 6 ) ) PUNCT iajs-2479 425 1 +0 +0 ADP iajs-2479 425 2 + + CCONJ iajs-2479 425 3 ( ( PUNCT iajs-2479 425 4 di di INTJ iajs-2479 425 5 – – PUNCT iajs-2479 425 6 t t NOUN iajs-2479 425 7 – – PUNCT iajs-2479 425 8 pi pi NOUN iajs-2479 425 9 ) ) PUNCT iajs-2479 425 10 +0 +0 ADP iajs-2479 425 11 + + PROPN iajs-2479 425 12 ( ( PUNCT iajs-2479 425 13 t t NOUN iajs-2479 425 14 + + NOUN iajs-2479 425 15 pi pi NOUN iajs-2479 425 16 – – PUNCT iajs-2479 425 17 di di NOUN iajs-2479 425 18 ) ) PUNCT iajs-2479 425 19 + + PROPN iajs-2479 425 20 ( ( PUNCT iajs-2479 425 21 t t NOUN iajs-2479 425 22 + + NOUN iajs-2479 425 23 pi pi PROPN iajs-2479 425 24 + + PROPN iajs-2479 425 25 pj pj X iajs-2479 425 26 ) ) PUNCT iajs-2479 425 27 + + CCONJ iajs-2479 425 28 ( ( PUNCT iajs-2479 425 29 t t NOUN iajs-2479 425 30 + + NOUN iajs-2479 425 31 pi pi NOUN iajs-2479 425 32 + + PROPN iajs-2479 425 33 pj pj PROPN iajs-2479 425 34 – – PUNCT iajs-2479 425 35 dj dj NOUN iajs-2479 425 36 ) ) PUNCT iajs-2479 425 37 +0 +0 ADP iajs-2479 425 38 +1 +1 PROPN iajs-2479 426 1 + + NOUN iajs-2479 426 2 pj pj X iajs-2479 426 3 ] ] X iajs-2479 426 4 = = PUNCT iajs-2479 426 5 3 3 NUM iajs-2479 426 6 t t NOUN iajs-2479 426 7 +3pi +3pi PROPN iajs-2479 426 8 +3pj +3pj PUNCT iajs-2479 426 9 – – PUNCT iajs-2479 426 10 dj dj X iajs-2479 426 11 +1 +1 PROPN iajs-2479 426 12 … … PUNCT iajs-2479 426 13 . . PUNCT iajs-2479 427 1 ( ( PUNCT iajs-2479 427 2 c c NOUN iajs-2479 427 3 ) ) PUNCT iajs-2479 427 4 . . PUNCT iajs-2479 427 5     SPACE iajs-2479 428 1 150 150 NUM iajs-2479 428 2     SPACE iajs-2479 428 3 ibn ibn PROPN iajs-2479 428 4 al al PROPN iajs-2479 428 5 - - PUNCT iajs-2479 428 6 haitham haitham PROPN iajs-2479 428 7 jour jour X iajs-2479 428 8 . . PROPN iajs-2479 428 9 for for ADP iajs-2479 428 10 pure pure ADJ iajs-2479 428 11 & & CCONJ iajs-2479 428 12 appl appl PROPN iajs-2479 428 13 . . PUNCT iajs-2479 429 1 sci sci PROPN iajs-2479 429 2 . . PROPN iajs-2479 430 1 33 33 NUM iajs-2479 430 2 ( ( PUNCT iajs-2479 430 3 3 3 NUM iajs-2479 430 4 ) ) PUNCT iajs-2479 430 5 2020 2020 NUM iajs-2479 430 6   NOUN iajs-2479 430 7 ( ( PUNCT iajs-2479 430 8 when when SCONJ iajs-2479 430 9 vj= vj= PROPN iajs-2479 430 10 cj cj PROPN iajs-2479 430 11 – – PUNCT iajs-2479 430 12 dj dj NOUN iajs-2479 430 13 ) ) PUNCT iajs-2479 430 14 . . PUNCT iajs-2479 431 1 f'ji= f'ji= PROPN iajs-2479 432 1 [ [ X iajs-2479 432 2 ( ( PUNCT iajs-2479 432 3 t t PROPN iajs-2479 432 4 + + PROPN iajs-2479 432 5 pj pj PROPN iajs-2479 432 6 ) ) PUNCT iajs-2479 433 1 +0 +0 ADP iajs-2479 433 2 + + CCONJ iajs-2479 433 3 ( ( PUNCT iajs-2479 433 4 dj dj NOUN iajs-2479 433 5 – – PUNCT iajs-2479 433 6 t t PROPN iajs-2479 433 7 – – PUNCT iajs-2479 433 8 pj pj PROPN iajs-2479 433 9 ) ) PUNCT iajs-2479 434 1 +0 +0 ADP iajs-2479 434 2 + + PROPN iajs-2479 434 3 ( ( PUNCT iajs-2479 434 4 t t PROPN iajs-2479 434 5 + + CCONJ iajs-2479 434 6 pj pj PROPN iajs-2479 434 7 – – PUNCT iajs-2479 434 8 dj dj NOUN iajs-2479 434 9 ) ) PUNCT iajs-2479 434 10 + + PROPN iajs-2479 434 11 ( ( PUNCT iajs-2479 434 12 t t PROPN iajs-2479 434 13 + + PROPN iajs-2479 434 14 pj pj PROPN iajs-2479 434 15 + + PROPN iajs-2479 434 16 pi pi NOUN iajs-2479 434 17 ) ) PUNCT iajs-2479 434 18 + + CCONJ iajs-2479 434 19 ( ( PUNCT iajs-2479 434 20 t t PROPN iajs-2479 434 21 + + PROPN iajs-2479 434 22 pj pj PROPN iajs-2479 434 23 + + PROPN iajs-2479 434 24 pi pi NOUN iajs-2479 434 25 – – PUNCT iajs-2479 434 26 di di NOUN iajs-2479 434 27 ) ) PUNCT iajs-2479 435 1 + + NOUN iajs-2479 435 2 o o X iajs-2479 435 3 +1 +1 X iajs-2479 435 4 + + NOUN iajs-2479 435 5 pi pi NOUN iajs-2479 435 6 ] ] X iajs-2479 435 7 = = PUNCT iajs-2479 435 8 3 3 NUM iajs-2479 435 9 t t NOUN iajs-2479 435 10 + + CCONJ iajs-2479 435 11 3pi 3pi NOUN iajs-2479 435 12 +3pj +3pj PUNCT iajs-2479 435 13 – – PUNCT iajs-2479 435 14 di di X iajs-2479 435 15 +1 +1 PROPN iajs-2479 435 16 … … PUNCT iajs-2479 435 17 .. .. PUNCT iajs-2479 435 18 ( ( PUNCT iajs-2479 435 19 e e NOUN iajs-2479 435 20 ) ) PUNCT iajs-2479 435 21 . . PUNCT iajs-2479 436 1 δij=(c δij=(c NUM iajs-2479 436 2 ) ) PUNCT iajs-2479 436 3 – – PUNCT iajs-2479 436 4 ( ( PUNCT iajs-2479 436 5 e)= e)= ADJ iajs-2479 436 6 – – PUNCT iajs-2479 436 7 dj dj NOUN iajs-2479 436 8 + + CCONJ iajs-2479 436 9 di di X iajs-2479 436 10 ≤ ≤ NOUN iajs-2479 436 11 0 0 NUM iajs-2479 436 12 , , PUNCT iajs-2479 436 13 then then ADV iajs-2479 436 14 job job NOUN iajs-2479 436 15 i i PRON iajs-2479 436 16 precede precede VERB iajs-2479 436 17 j. j. PROPN iajs-2479 436 18   PRON iajs-2479 436 19 ( ( PUNCT iajs-2479 436 20 when when SCONJ iajs-2479 436 21 vi=0 vi=0 VERB iajs-2479 436 22 ) ) PUNCT iajs-2479 436 23 . . PUNCT iajs-2479 437 1 fij= fij= PUNCT iajs-2479 438 1 [ [ X iajs-2479 438 2 ( ( PUNCT iajs-2479 438 3 t t NOUN iajs-2479 438 4 + + NOUN iajs-2479 438 5 pi pi NOUN iajs-2479 438 6 ) ) PUNCT iajs-2479 439 1 +0 +0 ADP iajs-2479 439 2 + + CCONJ iajs-2479 439 3 ( ( PUNCT iajs-2479 439 4 di di INTJ iajs-2479 439 5 – – PUNCT iajs-2479 439 6 t t NOUN iajs-2479 439 7 – – PUNCT iajs-2479 439 8 pi pi NOUN iajs-2479 439 9 ) ) PUNCT iajs-2479 440 1 +0 +0 ADP iajs-2479 440 2 +0 +0 ADP iajs-2479 440 3 + + PROPN iajs-2479 440 4 ( ( PUNCT iajs-2479 440 5 t t NOUN iajs-2479 440 6 + + NOUN iajs-2479 440 7 pi pi PROPN iajs-2479 440 8 + + PROPN iajs-2479 440 9 pj pj X iajs-2479 440 10 ) ) PUNCT iajs-2479 440 11 + + CCONJ iajs-2479 440 12 ( ( PUNCT iajs-2479 440 13 t t NOUN iajs-2479 440 14 + + NOUN iajs-2479 440 15 pi pi NOUN iajs-2479 440 16 + + PROPN iajs-2479 440 17 pj pj PROPN iajs-2479 440 18 – – PUNCT iajs-2479 440 19 dj dj NOUN iajs-2479 440 20 ) ) PUNCT iajs-2479 440 21 +0 +0 ADP iajs-2479 440 22 +1 +1 PROPN iajs-2479 441 1 + + NOUN iajs-2479 441 2 pj pj NOUN iajs-2479 441 3 ]= ]= NUM iajs-2479 441 4 2 2 NUM iajs-2479 441 5 t t NOUN iajs-2479 441 6 +2pi +2pi SYM iajs-2479 441 7 +3pj +3pj PUNCT iajs-2479 441 8 – – PUNCT iajs-2479 441 9 dj dj NOUN iajs-2479 442 1 + + NOUN iajs-2479 442 2 di di X iajs-2479 442 3 +1 +1 NOUN iajs-2479 442 4 … … PUNCT iajs-2479 442 5 .. .. PUNCT iajs-2479 442 6 ( ( PUNCT iajs-2479 442 7 a a DET iajs-2479 442 8 ' ' NOUN iajs-2479 442 9 ) ) PUNCT iajs-2479 442 10 . . PUNCT iajs-2479 443 1   NOUN iajs-2479 443 2 ( ( PUNCT iajs-2479 443 3 when when SCONJ iajs-2479 443 4 vj= vj= PROPN iajs-2479 443 5 cj cj PROPN iajs-2479 443 6 – – PUNCT iajs-2479 443 7 dj dj NOUN iajs-2479 443 8 ) ) PUNCT iajs-2479 443 9 . . PUNCT iajs-2479 444 1 f'ji= f'ji= PROPN iajs-2479 445 1 [ [ X iajs-2479 445 2 ( ( PUNCT iajs-2479 445 3 t t PROPN iajs-2479 445 4 + + PROPN iajs-2479 445 5 pj pj PROPN iajs-2479 445 6 ) ) PUNCT iajs-2479 446 1 +0 +0 ADP iajs-2479 446 2 + + CCONJ iajs-2479 446 3 ( ( PUNCT iajs-2479 446 4 dj dj NOUN iajs-2479 446 5 – – PUNCT iajs-2479 446 6 t t PROPN iajs-2479 446 7 – – PUNCT iajs-2479 446 8 pj pj PROPN iajs-2479 446 9 ) ) PUNCT iajs-2479 447 1 +0 +0 ADP iajs-2479 447 2 + + PROPN iajs-2479 447 3 ( ( PUNCT iajs-2479 447 4 t t PROPN iajs-2479 447 5 + + CCONJ iajs-2479 447 6 pj pj PROPN iajs-2479 447 7 – – PUNCT iajs-2479 447 8 dj dj NOUN iajs-2479 447 9 ) ) PUNCT iajs-2479 447 10 + + PROPN iajs-2479 447 11 ( ( PUNCT iajs-2479 447 12 t t PROPN iajs-2479 447 13 + + PROPN iajs-2479 447 14 pj pj PROPN iajs-2479 447 15 + + PROPN iajs-2479 447 16 pi pi NOUN iajs-2479 447 17 ) ) PUNCT iajs-2479 447 18 + + CCONJ iajs-2479 447 19 ( ( PUNCT iajs-2479 447 20 t t PROPN iajs-2479 447 21 + + PROPN iajs-2479 447 22 pj pj PROPN iajs-2479 447 23 + + PROPN iajs-2479 447 24 pi pi NOUN iajs-2479 447 25 – – PUNCT iajs-2479 447 26 di di NOUN iajs-2479 447 27 ) ) PUNCT iajs-2479 447 28 +0 +0 ADP iajs-2479 447 29 +1 +1 PROPN iajs-2479 448 1 + + NOUN iajs-2479 448 2 pi pi NOUN iajs-2479 448 3 ] ] X iajs-2479 448 4 = = PUNCT iajs-2479 448 5 3 3 NUM iajs-2479 448 6 t t NOUN iajs-2479 449 1 + + CCONJ iajs-2479 449 2 3pi 3pi NOUN iajs-2479 449 3 +3pj +3pj PUNCT iajs-2479 449 4 – – PUNCT iajs-2479 449 5 di di X iajs-2479 449 6 +1 +1 PROPN iajs-2479 449 7 … … PUNCT iajs-2479 449 8 .. .. PUNCT iajs-2479 449 9 ( ( PUNCT iajs-2479 449 10 e e NOUN iajs-2479 449 11 ' ' NUM iajs-2479 449 12 ) ) PUNCT iajs-2479 449 13 . . PUNCT iajs-2479 450 1 δij=(a δij=(a NOUN iajs-2479 450 2 ' ' PUNCT iajs-2479 450 3 ) ) PUNCT iajs-2479 450 4 – – PUNCT iajs-2479 450 5 ( ( PUNCT iajs-2479 450 6 e')= e')= PROPN iajs-2479 450 7 – – PUNCT iajs-2479 450 8 t t PROPN iajs-2479 450 9 – – PUNCT iajs-2479 450 10 pi pi NOUN iajs-2479 450 11 +2di +2di PUNCT iajs-2479 450 12 – – PUNCT iajs-2479 450 13 dj dj X iajs-2479 450 14 > > X iajs-2479 450 15 0 0 NUM iajs-2479 450 16 , , PUNCT iajs-2479 450 17 then then ADV iajs-2479 450 18 job job NOUN iajs-2479 450 19 j j PROPN iajs-2479 450 20 precede precede VERB iajs-2479 450 21 i. i. NOUN iajs-2479 450 22   NOUN iajs-2479 451 1 ( ( PUNCT iajs-2479 451 2 when when SCONJ iajs-2479 451 3 vi= vi= PROPN iajs-2479 451 4 ci ci PROPN iajs-2479 451 5 – – PUNCT iajs-2479 451 6 di di NOUN iajs-2479 451 7 ) ) PUNCT iajs-2479 451 8 . . PUNCT iajs-2479 452 1 fij= fij= PUNCT iajs-2479 453 1 [ [ X iajs-2479 453 2 ( ( PUNCT iajs-2479 453 3 t t NOUN iajs-2479 453 4 + + NOUN iajs-2479 453 5 pi pi NOUN iajs-2479 453 6 ) ) PUNCT iajs-2479 454 1 +0 +0 ADP iajs-2479 454 2 + + CCONJ iajs-2479 454 3 ( ( PUNCT iajs-2479 454 4 di di INTJ iajs-2479 454 5 – – PUNCT iajs-2479 454 6 t t NOUN iajs-2479 454 7 – – PUNCT iajs-2479 454 8 pi pi NOUN iajs-2479 454 9 ) ) PUNCT iajs-2479 454 10 +0 +0 ADP iajs-2479 454 11 + + PROPN iajs-2479 454 12 ( ( PUNCT iajs-2479 454 13 t t NOUN iajs-2479 454 14 + + NOUN iajs-2479 454 15 pi pi NOUN iajs-2479 454 16 – – PUNCT iajs-2479 454 17 di di NOUN iajs-2479 454 18 ) ) PUNCT iajs-2479 454 19 + + PROPN iajs-2479 454 20 ( ( PUNCT iajs-2479 454 21 t t NOUN iajs-2479 454 22 + + NOUN iajs-2479 454 23 pi pi PROPN iajs-2479 454 24 + + PROPN iajs-2479 454 25 pj pj X iajs-2479 454 26 ) ) PUNCT iajs-2479 454 27 + + CCONJ iajs-2479 454 28 ( ( PUNCT iajs-2479 454 29 t t NOUN iajs-2479 454 30 + + NOUN iajs-2479 454 31 pi pi NOUN iajs-2479 454 32 + + PROPN iajs-2479 454 33 pj pj PROPN iajs-2479 454 34 – – PUNCT iajs-2479 454 35 dj dj NOUN iajs-2479 454 36 ) ) PUNCT iajs-2479 454 37 +0 +0 ADP iajs-2479 454 38 +1 +1 PROPN iajs-2479 455 1 + + NOUN iajs-2479 455 2 pj pj X iajs-2479 455 3 ] ] X iajs-2479 455 4 = = PUNCT iajs-2479 455 5 3 3 NUM iajs-2479 455 6 t t NOUN iajs-2479 455 7 +3pi +3pi PROPN iajs-2479 455 8 +3pj +3pj PUNCT iajs-2479 455 9 – – PUNCT iajs-2479 455 10 dj dj X iajs-2479 455 11 +1 +1 PROPN iajs-2479 455 12 … … PUNCT iajs-2479 455 13 . . PUNCT iajs-2479 456 1 ( ( PUNCT iajs-2479 456 2 c c NOUN iajs-2479 456 3 ' ' PUNCT iajs-2479 456 4 ) ) PUNCT iajs-2479 456 5 . . PUNCT iajs-2479 457 1   NOUN iajs-2479 457 2 ( ( PUNCT iajs-2479 457 3 when when SCONJ iajs-2479 457 4 vj=0 vj=0 NUM iajs-2479 457 5 ) ) PUNCT iajs-2479 457 6 . . PUNCT iajs-2479 458 1 f'ji= f'ji= PROPN iajs-2479 459 1 [ [ X iajs-2479 459 2 ( ( PUNCT iajs-2479 459 3 t t PROPN iajs-2479 459 4 + + PROPN iajs-2479 459 5 pj pj PROPN iajs-2479 459 6 ) ) PUNCT iajs-2479 460 1 +0 +0 ADP iajs-2479 460 2 + + CCONJ iajs-2479 460 3 ( ( PUNCT iajs-2479 460 4 dj dj NOUN iajs-2479 460 5 – – PUNCT iajs-2479 460 6 t t PROPN iajs-2479 460 7 – – PUNCT iajs-2479 460 8 pj pj PROPN iajs-2479 460 9 ) ) PUNCT iajs-2479 461 1 +0 +0 ADP iajs-2479 461 2 +0 +0 ADP iajs-2479 461 3 + + PROPN iajs-2479 461 4 ( ( PUNCT iajs-2479 461 5 t t PROPN iajs-2479 461 6 + + PROPN iajs-2479 461 7 pj pj PROPN iajs-2479 461 8 + + PROPN iajs-2479 461 9 pi pi NOUN iajs-2479 461 10 ) ) PUNCT iajs-2479 461 11 + + CCONJ iajs-2479 461 12 ( ( PUNCT iajs-2479 461 13 t t PROPN iajs-2479 461 14 + + PROPN iajs-2479 461 15 pj pj PROPN iajs-2479 461 16 + + PROPN iajs-2479 461 17 pi pi NOUN iajs-2479 461 18 – – PUNCT iajs-2479 461 19 di di NOUN iajs-2479 461 20 ) ) PUNCT iajs-2479 461 21 +0 +0 ADP iajs-2479 461 22 +1 +1 PROPN iajs-2479 462 1 + + NOUN iajs-2479 462 2 pi pi NOUN iajs-2479 462 3 ]= ]= NUM iajs-2479 462 4 2 2 NUM iajs-2479 462 5 t t NOUN iajs-2479 462 6 +3pi +3pi X iajs-2479 463 1 +2pj +2pj PUNCT iajs-2479 463 2 + + PUNCT iajs-2479 463 3 dj dj X iajs-2479 463 4 – – PUNCT iajs-2479 463 5 di di X iajs-2479 463 6 +1 +1 NOUN iajs-2479 463 7 … … PUNCT iajs-2479 463 8 . . PUNCT iajs-2479 464 1 ( ( PUNCT iajs-2479 464 2 b b NOUN iajs-2479 464 3 ) ) PUNCT iajs-2479 464 4 . . PUNCT iajs-2479 465 1 δij=(c δij=(c NUM iajs-2479 465 2 ' ' PUNCT iajs-2479 465 3 ) ) PUNCT iajs-2479 465 4 – – PUNCT iajs-2479 465 5 ( ( PUNCT iajs-2479 465 6 b')= b')= NOUN iajs-2479 465 7 t t PROPN iajs-2479 465 8 + + NOUN iajs-2479 465 9 pj pj PROPN iajs-2479 465 10 + + PROPN iajs-2479 465 11 di di X iajs-2479 465 12 – – PUNCT iajs-2479 465 13 2dj 2dj NOUN iajs-2479 465 14 ≤ ≤ NOUN iajs-2479 465 15 0 0 NUM iajs-2479 465 16 , , PUNCT iajs-2479 465 17 then then ADV iajs-2479 465 18 job job NOUN iajs-2479 465 19 i i PRON iajs-2479 465 20 precede precede VERB iajs-2479 465 21 j. j. PROPN iajs-2479 465 22 case case PROPN iajs-2479 465 23 6 6 NUM iajs-2479 465 24 . . PUNCT iajs-2479 466 1 if if SCONJ iajs-2479 466 2 t t PROPN iajs-2479 466 3 + + NOUN iajs-2479 466 4 pi pi NOUN iajs-2479 466 5 ≤ ≤ NUM iajs-2479 466 6 di di NOUN iajs-2479 466 7 ≤ ≤ PROPN iajs-2479 466 8 t t NOUN iajs-2479 466 9 + + NOUN iajs-2479 466 10 pi pi NOUN iajs-2479 466 11 + + ADJ iajs-2479 466 12 pj pj PROPN iajs-2479 466 13 ≤ ≤ ADJ iajs-2479 466 14 dj dj NOUN iajs-2479 466 15 ( ( PUNCT iajs-2479 466 16 i.e. i.e. X iajs-2479 466 17 the the DET iajs-2479 466 18 job job NOUN iajs-2479 467 1 i i PRON iajs-2479 467 2 , , PUNCT iajs-2479 467 3 is be AUX iajs-2479 467 4 tardy tardy ADJ iajs-2479 467 5 if if SCONJ iajs-2479 467 6 not not PART iajs-2479 467 7 scheduled schedule VERB iajs-2479 467 8 first first ADV iajs-2479 467 9 , , PUNCT iajs-2479 467 10 and and CCONJ iajs-2479 467 11 j j NOUN iajs-2479 467 12 , , PUNCT iajs-2479 467 13 is be AUX iajs-2479 467 14 always always ADV iajs-2479 467 15 early early ADJ iajs-2479 467 16 ) ) PUNCT iajs-2479 467 17 . . PUNCT iajs-2479 468 1 proof proof NOUN iajs-2479 468 2 . . PUNCT iajs-2479 469 1   X iajs-2479 469 2 ( ( PUNCT iajs-2479 469 3 when when SCONJ iajs-2479 469 4 vi vi ADJ iajs-2479 469 5 , , PUNCT iajs-2479 469 6 vj=0 vj=0 NUM iajs-2479 469 7 ) ) PUNCT iajs-2479 469 8 . . PUNCT iajs-2479 470 1 fij= fij= PUNCT iajs-2479 471 1 [ [ X iajs-2479 471 2 ( ( PUNCT iajs-2479 471 3 t t NOUN iajs-2479 471 4 + + NOUN iajs-2479 471 5 pi pi NOUN iajs-2479 471 6 ) ) PUNCT iajs-2479 472 1 +0 +0 ADP iajs-2479 472 2 + + CCONJ iajs-2479 472 3 ( ( PUNCT iajs-2479 472 4 di di INTJ iajs-2479 472 5 – – PUNCT iajs-2479 472 6 t t NOUN iajs-2479 472 7 – – PUNCT iajs-2479 472 8 pi pi NOUN iajs-2479 472 9 ) ) PUNCT iajs-2479 473 1 +0 +0 ADP iajs-2479 473 2 +0 +0 ADP iajs-2479 473 3 + + PROPN iajs-2479 473 4 ( ( PUNCT iajs-2479 473 5 t t NOUN iajs-2479 473 6 + + NOUN iajs-2479 473 7 pi pi PROPN iajs-2479 473 8 + + PROPN iajs-2479 473 9 pj pj X iajs-2479 473 10 ) ) PUNCT iajs-2479 474 1 +0 +0 ADP iajs-2479 474 2 + + CCONJ iajs-2479 474 3 ( ( PUNCT iajs-2479 474 4 dj dj NOUN iajs-2479 474 5 – – PUNCT iajs-2479 474 6 t t NOUN iajs-2479 474 7 – – PUNCT iajs-2479 474 8 pi pi NOUN iajs-2479 474 9 – – PUNCT iajs-2479 474 10 pj pj PROPN iajs-2479 474 11 ) ) PUNCT iajs-2479 475 1 +0 +0 ADP iajs-2479 475 2 +0 +0 ADP iajs-2479 475 3 ]= ]= NUM iajs-2479 475 4 di di NOUN iajs-2479 475 5 + + X iajs-2479 475 6 dj dj NOUN iajs-2479 475 7 … … PUNCT iajs-2479 475 8 .. .. PUNCT iajs-2479 475 9 ( ( PUNCT iajs-2479 475 10 a a NOUN iajs-2479 475 11 ) ) PUNCT iajs-2479 475 12 . . PUNCT iajs-2479 476 1   NOUN iajs-2479 476 2 ( ( PUNCT iajs-2479 476 3 when when SCONJ iajs-2479 476 4 vj=0 vj=0 NUM iajs-2479 476 5 ) ) PUNCT iajs-2479 476 6 . . PUNCT iajs-2479 477 1 f'ji= f'ji= PROPN iajs-2479 478 1 [ [ X iajs-2479 478 2 ( ( PUNCT iajs-2479 478 3 t t PROPN iajs-2479 478 4 + + PROPN iajs-2479 478 5 pj pj PROPN iajs-2479 478 6 ) ) PUNCT iajs-2479 479 1 +0 +0 ADP iajs-2479 479 2 + + CCONJ iajs-2479 479 3 ( ( PUNCT iajs-2479 479 4 dj dj NOUN iajs-2479 479 5 – – PUNCT iajs-2479 479 6 t t PROPN iajs-2479 479 7 – – PUNCT iajs-2479 479 8 pj pj PROPN iajs-2479 479 9 ) ) PUNCT iajs-2479 480 1 +0 +0 ADP iajs-2479 480 2 +0 +0 ADP iajs-2479 480 3 + + PROPN iajs-2479 480 4 ( ( PUNCT iajs-2479 480 5 t t PROPN iajs-2479 480 6 + + PROPN iajs-2479 480 7 pj pj PROPN iajs-2479 480 8 + + PROPN iajs-2479 480 9 pi pi NOUN iajs-2479 480 10 ) ) PUNCT iajs-2479 480 11 + + CCONJ iajs-2479 480 12 ( ( PUNCT iajs-2479 480 13 t t PROPN iajs-2479 480 14 + + PROPN iajs-2479 480 15 pj pj PROPN iajs-2479 480 16 + + PROPN iajs-2479 480 17 pi pi NOUN iajs-2479 480 18 – – PUNCT iajs-2479 480 19 di di NOUN iajs-2479 480 20 ) ) PUNCT iajs-2479 480 21 +0 +0 ADP iajs-2479 480 22 +1 +1 PROPN iajs-2479 481 1 + + NOUN iajs-2479 481 2 pi pi NOUN iajs-2479 481 3 ]= ]= NUM iajs-2479 481 4 2 2 NUM iajs-2479 481 5 t t NOUN iajs-2479 481 6 +3pi +3pi X iajs-2479 482 1 +2pj +2pj PUNCT iajs-2479 482 2 + + PUNCT iajs-2479 482 3 dj dj X iajs-2479 482 4 – – PUNCT iajs-2479 482 5 di di X iajs-2479 482 6 +1 +1 NOUN iajs-2479 482 7 … … PUNCT iajs-2479 482 8 . . PUNCT iajs-2479 483 1 ( ( PUNCT iajs-2479 483 2 b b NOUN iajs-2479 483 3 ) ) PUNCT iajs-2479 483 4 . . PUNCT iajs-2479 484 1 δij=(a δij=(a NOUN iajs-2479 484 2 ) ) PUNCT iajs-2479 484 3 – – PUNCT iajs-2479 484 4 ( ( PUNCT iajs-2479 484 5 b)= b)= NOUN iajs-2479 484 6 – – PUNCT iajs-2479 484 7 2 2 NUM iajs-2479 484 8 t t NOUN iajs-2479 484 9 – – PUNCT iajs-2479 484 10 3pi 3pi ADJ iajs-2479 484 11 – – PUNCT iajs-2479 484 12 2pj 2pj ADJ iajs-2479 484 13 +2di +2di PUNCT iajs-2479 484 14 – – PUNCT iajs-2479 484 15 1 1 NUM iajs-2479 484 16 ≤ ≤ NUM iajs-2479 484 17 0 0 NUM iajs-2479 484 18 , , PUNCT iajs-2479 484 19 then then ADV iajs-2479 484 20 job job NOUN iajs-2479 484 21 i i PRON iajs-2479 484 22 precede precede VERB iajs-2479 484 23 j. j. PROPN iajs-2479 484 24   PROPN iajs-2479 484 25 ( ( PUNCT iajs-2479 484 26 when when SCONJ iajs-2479 484 27 vi= vi= PROPN iajs-2479 484 28 ci ci PROPN iajs-2479 484 29 – – PUNCT iajs-2479 484 30 di di NOUN iajs-2479 484 31 , , PUNCT iajs-2479 484 32 and and CCONJ iajs-2479 484 33 vj vj INTJ iajs-2479 484 34 = = PUNCT iajs-2479 484 35 cj cj PROPN iajs-2479 484 36 – – PUNCT iajs-2479 484 37 dj dj NOUN iajs-2479 484 38 ) ) PUNCT iajs-2479 484 39 . . PUNCT iajs-2479 485 1 fij= fij= PUNCT iajs-2479 486 1 [ [ X iajs-2479 486 2 ( ( PUNCT iajs-2479 486 3 t t NOUN iajs-2479 486 4 + + NOUN iajs-2479 486 5 pi pi NOUN iajs-2479 486 6 ) ) PUNCT iajs-2479 487 1 +0 +0 ADP iajs-2479 487 2 + + CCONJ iajs-2479 487 3 ( ( PUNCT iajs-2479 487 4 di di INTJ iajs-2479 487 5 – – PUNCT iajs-2479 487 6 t t NOUN iajs-2479 487 7 – – PUNCT iajs-2479 487 8 pi pi NOUN iajs-2479 487 9 ) ) PUNCT iajs-2479 487 10 +0 +0 ADP iajs-2479 487 11 + + PROPN iajs-2479 487 12 ( ( PUNCT iajs-2479 487 13 t t NOUN iajs-2479 487 14 + + NOUN iajs-2479 487 15 pi pi NOUN iajs-2479 487 16 – – PUNCT iajs-2479 487 17 di di NOUN iajs-2479 487 18 ) ) PUNCT iajs-2479 487 19 + + PROPN iajs-2479 487 20 ( ( PUNCT iajs-2479 487 21 t t NOUN iajs-2479 487 22 + + NOUN iajs-2479 487 23 pi pi PROPN iajs-2479 487 24 + + PROPN iajs-2479 487 25 pj pj X iajs-2479 487 26 ) ) PUNCT iajs-2479 488 1 +0 +0 ADP iajs-2479 488 2 + + CCONJ iajs-2479 488 3 ( ( PUNCT iajs-2479 488 4 dj dj NOUN iajs-2479 488 5 – – PUNCT iajs-2479 488 6 t t NOUN iajs-2479 488 7 – – PUNCT iajs-2479 488 8 pi pi NOUN iajs-2479 488 9 – – PUNCT iajs-2479 488 10 pj pj PROPN iajs-2479 488 11 ) ) PUNCT iajs-2479 489 1 +0 +0 ADP iajs-2479 489 2 + + NOUN iajs-2479 489 3 t t NOUN iajs-2479 489 4 + + NUM iajs-2479 489 5 pi pi PROPN iajs-2479 489 6 + + PROPN iajs-2479 489 7 pj pj PROPN iajs-2479 489 8 – – PUNCT iajs-2479 489 9 dj dj X iajs-2479 489 10 ] ] X iajs-2479 489 11 = = SYM iajs-2479 489 12 2 2 NUM iajs-2479 489 13 t t NOUN iajs-2479 489 14 +2pi +2pi PUNCT iajs-2479 489 15 + + PROPN iajs-2479 489 16 pj pj PROPN iajs-2479 489 17 … … SYM iajs-2479 489 18 .. .. PUNCT iajs-2479 489 19 (c (c NUM iajs-2479 489 20 ) ) PUNCT iajs-2479 489 21 . . PUNCT iajs-2479 490 1   INTJ iajs-2479 490 2 ( ( PUNCT iajs-2479 490 3 when when SCONJ iajs-2479 490 4 vj vj PROPN iajs-2479 490 5 = = PROPN iajs-2479 490 6 cj cj PROPN iajs-2479 490 7 – – PUNCT iajs-2479 490 8 dj dj NOUN iajs-2479 490 9 ) ) PUNCT iajs-2479 490 10 . . PUNCT iajs-2479 491 1 f'ji= f'ji= PROPN iajs-2479 492 1 [ [ X iajs-2479 492 2 ( ( PUNCT iajs-2479 492 3 t t PROPN iajs-2479 492 4 + + PROPN iajs-2479 492 5 pj pj PROPN iajs-2479 492 6 ) ) PUNCT iajs-2479 493 1 +0 +0 ADP iajs-2479 493 2 + + CCONJ iajs-2479 493 3 ( ( PUNCT iajs-2479 493 4 dj dj NOUN iajs-2479 493 5 – – PUNCT iajs-2479 493 6 t t PROPN iajs-2479 493 7 – – PUNCT iajs-2479 493 8 pj pj PROPN iajs-2479 493 9 ) ) PUNCT iajs-2479 494 1 +0 +0 ADP iajs-2479 494 2 + + PROPN iajs-2479 494 3 ( ( PUNCT iajs-2479 494 4 t t PROPN iajs-2479 494 5 + + CCONJ iajs-2479 494 6 pj pj PROPN iajs-2479 494 7 – – PUNCT iajs-2479 494 8 dj dj NOUN iajs-2479 494 9 ) ) PUNCT iajs-2479 494 10 + + PROPN iajs-2479 494 11 ( ( PUNCT iajs-2479 494 12 t t PROPN iajs-2479 494 13 + + PROPN iajs-2479 494 14 pj pj PROPN iajs-2479 494 15 + + PROPN iajs-2479 494 16 pi pi NOUN iajs-2479 494 17 ) ) PUNCT iajs-2479 494 18 + + CCONJ iajs-2479 494 19 ( ( PUNCT iajs-2479 494 20 t t PROPN iajs-2479 494 21 + + PROPN iajs-2479 494 22 pj pj PROPN iajs-2479 494 23 + + PROPN iajs-2479 494 24 pi pi NOUN iajs-2479 494 25 – – PUNCT iajs-2479 494 26 di di NOUN iajs-2479 494 27 ) ) PUNCT iajs-2479 494 28 +0 +0 ADP iajs-2479 494 29 +1 +1 PROPN iajs-2479 495 1 + + NOUN iajs-2479 495 2 pi pi NOUN iajs-2479 495 3 ] ] X iajs-2479 495 4 = = PUNCT iajs-2479 495 5 3 3 NUM iajs-2479 495 6 t t NOUN iajs-2479 496 1 + + CCONJ iajs-2479 496 2 3pi 3pi NOUN iajs-2479 496 3 +3pj +3pj PUNCT iajs-2479 496 4 – – PUNCT iajs-2479 496 5 di di X iajs-2479 496 6 +1 +1 PROPN iajs-2479 496 7 … … PUNCT iajs-2479 496 8 .. .. PUNCT iajs-2479 496 9 ( ( PUNCT iajs-2479 496 10 e e NOUN iajs-2479 496 11 ) ) PUNCT iajs-2479 496 12 . . PUNCT iajs-2479 497 1 δij=(c δij=(c NUM iajs-2479 497 2 ) ) PUNCT iajs-2479 497 3 – – PUNCT iajs-2479 498 1 ( ( PUNCT iajs-2479 498 2 e)= e)= ADJ iajs-2479 498 3 – – PUNCT iajs-2479 498 4 t t NOUN iajs-2479 498 5 – – PUNCT iajs-2479 498 6 pi pi NOUN iajs-2479 498 7 – – PUNCT iajs-2479 498 8 2pj 2pj NOUN iajs-2479 498 9 + + SYM iajs-2479 498 10 di di NOUN iajs-2479 498 11 – – PUNCT iajs-2479 498 12 1 1 NUM iajs-2479 498 13 ≤ ≤ NUM iajs-2479 498 14 0 0 NUM iajs-2479 498 15 , , PUNCT iajs-2479 498 16 then then ADV iajs-2479 498 17 job job NOUN iajs-2479 499 1 i i PRON iajs-2479 499 2 precede precede VERB iajs-2479 499 3 j. j. PROPN iajs-2479 499 4 case case PROPN iajs-2479 499 5 7 7 X iajs-2479 499 6 . . PUNCT iajs-2479 500 1 if if SCONJ iajs-2479 500 2 t t PROPN iajs-2479 500 3 + + NOUN iajs-2479 500 4 pi pi NOUN iajs-2479 500 5 + + PROPN iajs-2479 500 6 pj pj PROPN iajs-2479 500 7 ≤ ≤ PROPN iajs-2479 500 8 di di NOUN iajs-2479 500 9 ≤ ≤ NOUN iajs-2479 500 10 dj dj NOUN iajs-2479 500 11 ( ( PUNCT iajs-2479 500 12 i.e. i.e. X iajs-2479 500 13 both both CCONJ iajs-2479 500 14 the the DET iajs-2479 500 15 jobs job NOUN iajs-2479 500 16 i i PRON iajs-2479 500 17 , , PUNCT iajs-2479 500 18 j j PROPN iajs-2479 500 19 are be AUX iajs-2479 500 20 always always ADV iajs-2479 500 21 early early ADJ iajs-2479 500 22 ) ) PUNCT iajs-2479 500 23 . . PUNCT iajs-2479 501 1 proof proof NOUN iajs-2479 501 2 . . PUNCT iajs-2479 502 1   INTJ iajs-2479 502 2 when when SCONJ iajs-2479 502 3 vi vi PROPN iajs-2479 502 4 , , PUNCT iajs-2479 502 5 vj vj X iajs-2479 502 6 = = PROPN iajs-2479 502 7 0 0 PROPN iajs-2479 502 8 . . PUNCT iajs-2479 502 9   PROPN iajs-2479 503 1 fij fij PROPN iajs-2479 503 2 = = PUNCT iajs-2479 504 1 [ [ X iajs-2479 504 2 ( ( PUNCT iajs-2479 504 3 t t NOUN iajs-2479 504 4 + + NOUN iajs-2479 504 5 pi pi NOUN iajs-2479 504 6 ) ) PUNCT iajs-2479 505 1 +0 +0 ADP iajs-2479 505 2 + + CCONJ iajs-2479 505 3 ( ( PUNCT iajs-2479 505 4 di di INTJ iajs-2479 505 5 – – PUNCT iajs-2479 505 6 t t NOUN iajs-2479 505 7 – – PUNCT iajs-2479 505 8 pi pi NOUN iajs-2479 505 9 ) ) PUNCT iajs-2479 506 1 +0 +0 ADP iajs-2479 506 2 +0 +0 ADP iajs-2479 506 3 + + PROPN iajs-2479 506 4 ( ( PUNCT iajs-2479 506 5 t t NOUN iajs-2479 506 6 + + NOUN iajs-2479 506 7 pi pi PROPN iajs-2479 506 8 + + PROPN iajs-2479 506 9 pj pj X iajs-2479 506 10 ) ) PUNCT iajs-2479 507 1 +0 +0 ADP iajs-2479 507 2 + + CCONJ iajs-2479 507 3 ( ( PUNCT iajs-2479 507 4 dj dj NOUN iajs-2479 507 5 – – PUNCT iajs-2479 507 6 t t NOUN iajs-2479 507 7 – – PUNCT iajs-2479 507 8 pi pi NOUN iajs-2479 507 9 – – PUNCT iajs-2479 507 10 pj pj PROPN iajs-2479 507 11 ) ) PUNCT iajs-2479 508 1 +0 +0 ADP iajs-2479 508 2 +0 +0 ADP iajs-2479 508 3 ]= ]= NUM iajs-2479 508 4 di di NOUN iajs-2479 508 5 + + X iajs-2479 508 6 dj dj NOUN iajs-2479 508 7 … … PUNCT iajs-2479 508 8 .. .. PUNCT iajs-2479 508 9 ( ( PUNCT iajs-2479 508 10 a a NOUN iajs-2479 508 11 ) ) PUNCT iajs-2479 508 12 . . PUNCT iajs-2479 509 1   X iajs-2479 509 2 f'ji f'ji NOUN iajs-2479 510 1 = = PUNCT iajs-2479 511 1 [ [ X iajs-2479 511 2 ( ( PUNCT iajs-2479 511 3 t t PROPN iajs-2479 511 4 + + PROPN iajs-2479 511 5 pj pj PROPN iajs-2479 511 6 ) ) PUNCT iajs-2479 512 1 +0 +0 ADP iajs-2479 512 2 + + CCONJ iajs-2479 512 3 ( ( PUNCT iajs-2479 512 4 dj dj NOUN iajs-2479 512 5 – – PUNCT iajs-2479 512 6 t t PROPN iajs-2479 512 7 – – PUNCT iajs-2479 512 8 pj pj PROPN iajs-2479 512 9 ) ) PUNCT iajs-2479 513 1 +0 +0 ADP iajs-2479 513 2 +0 +0 ADP iajs-2479 513 3 + + PROPN iajs-2479 513 4 ( ( PUNCT iajs-2479 513 5 t t PROPN iajs-2479 513 6 + + PROPN iajs-2479 513 7 pj pj PROPN iajs-2479 513 8 + + PROPN iajs-2479 513 9 pi pi NOUN iajs-2479 513 10 ) ) PUNCT iajs-2479 514 1 +0 +0 ADP iajs-2479 514 2 + + CCONJ iajs-2479 514 3 ( ( PUNCT iajs-2479 514 4 di di INTJ iajs-2479 514 5 – – PUNCT iajs-2479 514 6 t t PROPN iajs-2479 514 7 – – PUNCT iajs-2479 514 8 pj pj PROPN iajs-2479 514 9 – – PUNCT iajs-2479 514 10 pi)+0 pi)+0 VERB iajs-2479 514 11 +0 +0 ADP iajs-2479 514 12 ] ] X iajs-2479 514 13 = = SYM iajs-2479 514 14 dj dj X iajs-2479 514 15 + + CCONJ iajs-2479 514 16 di di NOUN iajs-2479 514 17 … … PUNCT iajs-2479 514 18 .(b .(b NUM iajs-2479 514 19 ) ) PUNCT iajs-2479 514 20 . . PUNCT iajs-2479 515 1 δij=(a δij=(a NOUN iajs-2479 515 2 ) ) PUNCT iajs-2479 515 3 – – PUNCT iajs-2479 515 4 ( ( PUNCT iajs-2479 515 5 b)=0 b)=0 ADV iajs-2479 515 6 , , PUNCT iajs-2479 515 7 then then ADV iajs-2479 515 8 it it PRON iajs-2479 515 9 is be AUX iajs-2479 515 10 indifferent indifferent ADJ iajs-2479 515 11 to to PART iajs-2479 515 12 schedule schedule VERB iajs-2479 515 13 i i PRON iajs-2479 515 14 or or CCONJ iajs-2479 515 15 j j PROPN iajs-2479 515 16 first first ADV iajs-2479 515 17 . . PUNCT iajs-2479 516 1   INTJ iajs-2479 517 1 when when SCONJ iajs-2479 517 2 vi= vi= PROPN iajs-2479 517 3 ci ci PROPN iajs-2479 517 4 – – PUNCT iajs-2479 517 5 di di NOUN iajs-2479 517 6 , , PUNCT iajs-2479 517 7 vj vj PROPN iajs-2479 517 8 = = PUNCT iajs-2479 517 9 cj cj PROPN iajs-2479 517 10 – – PUNCT iajs-2479 517 11 dj dj NOUN iajs-2479 517 12 . . PUNCT iajs-2479 517 13   PROPN iajs-2479 518 1 fij fij PROPN iajs-2479 518 2 = = PUNCT iajs-2479 519 1 [ [ X iajs-2479 519 2 ( ( PUNCT iajs-2479 519 3 t t NOUN iajs-2479 519 4 + + NOUN iajs-2479 519 5 pi pi NOUN iajs-2479 519 6 ) ) PUNCT iajs-2479 520 1 +0 +0 ADP iajs-2479 520 2 + + CCONJ iajs-2479 520 3 ( ( PUNCT iajs-2479 520 4 di di INTJ iajs-2479 520 5 – – PUNCT iajs-2479 520 6 t t NOUN iajs-2479 520 7 – – PUNCT iajs-2479 520 8 pi pi NOUN iajs-2479 520 9 ) ) PUNCT iajs-2479 520 10 +0 +0 ADP iajs-2479 520 11 + + PROPN iajs-2479 520 12 ( ( PUNCT iajs-2479 520 13 t t NOUN iajs-2479 520 14 + + NOUN iajs-2479 520 15 pi pi NOUN iajs-2479 520 16 – – PUNCT iajs-2479 520 17 di di NOUN iajs-2479 520 18 ) ) PUNCT iajs-2479 520 19 + + PROPN iajs-2479 520 20 ( ( PUNCT iajs-2479 520 21 t t NOUN iajs-2479 520 22 + + NOUN iajs-2479 520 23 pi pi PROPN iajs-2479 520 24 + + PROPN iajs-2479 520 25 pj pj X iajs-2479 520 26 ) ) PUNCT iajs-2479 521 1 +0 +0 ADP iajs-2479 521 2 + + CCONJ iajs-2479 521 3 ( ( PUNCT iajs-2479 521 4 dj dj NOUN iajs-2479 521 5 – – PUNCT iajs-2479 521 6 t t NOUN iajs-2479 521 7 – – PUNCT iajs-2479 521 8 pi pi NOUN iajs-2479 521 9 – – PUNCT iajs-2479 521 10 pj pj PROPN iajs-2479 521 11 ) ) PUNCT iajs-2479 522 1 +0 +0 ADP iajs-2479 522 2 + + PROPN iajs-2479 522 3 ( ( PUNCT iajs-2479 522 4 t t NOUN iajs-2479 522 5 + + NUM iajs-2479 522 6 pi pi PROPN iajs-2479 522 7 + + PROPN iajs-2479 522 8 pj pj PROPN iajs-2479 522 9 – – PUNCT iajs-2479 522 10 dj)]=2 dj)]=2 PROPN iajs-2479 522 11 t t NOUN iajs-2479 522 12 +2pi +2pi PUNCT iajs-2479 522 13 + + PROPN iajs-2479 522 14 pj pj PROPN iajs-2479 522 15 … … SYM iajs-2479 522 16 .. .. PUNCT iajs-2479 522 17 (c (c NUM iajs-2479 522 18 ) ) PUNCT iajs-2479 522 19 . . PUNCT iajs-2479 523 1   X iajs-2479 523 2 f'ji= f'ji= PROPN iajs-2479 524 1 [ [ X iajs-2479 524 2 ( ( PUNCT iajs-2479 524 3 t t PROPN iajs-2479 524 4 + + PROPN iajs-2479 524 5 pj pj PROPN iajs-2479 524 6 ) ) PUNCT iajs-2479 525 1 +0 +0 ADP iajs-2479 525 2 + + CCONJ iajs-2479 525 3 ( ( PUNCT iajs-2479 525 4 dj dj NOUN iajs-2479 525 5 – – PUNCT iajs-2479 525 6 t t PROPN iajs-2479 525 7 – – PUNCT iajs-2479 525 8 pj pj PROPN iajs-2479 525 9 ) ) PUNCT iajs-2479 526 1 +0 +0 ADP iajs-2479 526 2 + + PROPN iajs-2479 526 3 ( ( PUNCT iajs-2479 526 4 t t PROPN iajs-2479 526 5 + + PROPN iajs-2479 526 6 pj pj PROPN iajs-2479 526 7 – – PUNCT iajs-2479 526 8 dj dj NOUN iajs-2479 526 9 ) ) PUNCT iajs-2479 526 10 + + PROPN iajs-2479 526 11 ( ( PUNCT iajs-2479 526 12 t t PROPN iajs-2479 526 13 + + PROPN iajs-2479 526 14 pj pj PROPN iajs-2479 526 15 + + PROPN iajs-2479 526 16 pi pi NOUN iajs-2479 526 17 ) ) PUNCT iajs-2479 527 1 +0 +0 ADP iajs-2479 527 2 + + CCONJ iajs-2479 527 3 ( ( PUNCT iajs-2479 527 4 di di INTJ iajs-2479 527 5 – – PUNCT iajs-2479 527 6 t t PROPN iajs-2479 527 7 – – PUNCT iajs-2479 527 8 pj pj PROPN iajs-2479 527 9 – – PUNCT iajs-2479 527 10 pi pi NOUN iajs-2479 527 11 ) ) PUNCT iajs-2479 527 12 +0 +0 ADP iajs-2479 527 13 + + PROPN iajs-2479 527 14 ( ( PUNCT iajs-2479 527 15 t t PROPN iajs-2479 527 16 + + PROPN iajs-2479 527 17 pj pj PROPN iajs-2479 527 18 + + PROPN iajs-2479 527 19 pi pi NOUN iajs-2479 527 20 – – PUNCT iajs-2479 527 21 di)]= di)]= PROPN iajs-2479 527 22 2 2 NUM iajs-2479 527 23 t t NOUN iajs-2479 527 24 + + NOUN iajs-2479 527 25 pi pi NOUN iajs-2479 527 26 +2pj +2pj X iajs-2479 527 27 … … PUNCT iajs-2479 527 28 .(e .(e NUM iajs-2479 527 29 ) ) PUNCT iajs-2479 527 30 . . PUNCT iajs-2479 528 1 δij=(c δij=(c NUM iajs-2479 528 2 ) ) PUNCT iajs-2479 528 3 – – PUNCT iajs-2479 528 4 ( ( PUNCT iajs-2479 528 5 e)= e)= ADJ iajs-2479 528 6 pi pi NOUN iajs-2479 528 7 – – PUNCT iajs-2479 528 8 pj pj PROPN iajs-2479 528 9 ≤ ≤ PROPN iajs-2479 528 10 0 0 NUM iajs-2479 528 11 , , PUNCT iajs-2479 528 12 then then ADV iajs-2479 528 13 job job NOUN iajs-2479 528 14 i i PRON iajs-2479 528 15 precede precede VERB iajs-2479 528 16 j. j. PROPN iajs-2479 528 17   PROPN iajs-2479 528 18 when when SCONJ iajs-2479 528 19 vi= vi= PROPN iajs-2479 528 20 ci ci PROPN iajs-2479 528 21 – – PUNCT iajs-2479 528 22 di di NOUN iajs-2479 528 23 , , PUNCT iajs-2479 528 24 vj vj X iajs-2479 528 25 = = SYM iajs-2479 528 26 0 0 PROPN iajs-2479 528 27 . . PUNCT iajs-2479 528 28     SPACE iajs-2479 529 1 151 151 NUM iajs-2479 529 2     SPACE iajs-2479 529 3 ibn ibn PROPN iajs-2479 529 4 al al PROPN iajs-2479 529 5 - - PUNCT iajs-2479 529 6 haitham haitham PROPN iajs-2479 529 7 jour jour X iajs-2479 529 8 . . PROPN iajs-2479 529 9 for for ADP iajs-2479 529 10 pure pure ADJ iajs-2479 529 11 & & CCONJ iajs-2479 529 12 appl appl PROPN iajs-2479 529 13 . . PUNCT iajs-2479 530 1 sci sci PROPN iajs-2479 530 2 . . PROPN iajs-2479 531 1 33 33 NUM iajs-2479 531 2 ( ( PUNCT iajs-2479 531 3 3 3 NUM iajs-2479 531 4 ) ) PUNCT iajs-2479 531 5 2020 2020 NUM iajs-2479 531 6   NOUN iajs-2479 532 1 fij fij PROPN iajs-2479 532 2 = = PUNCT iajs-2479 533 1 [ [ X iajs-2479 533 2 ( ( PUNCT iajs-2479 533 3 t t NOUN iajs-2479 533 4 + + NOUN iajs-2479 533 5 pi pi NOUN iajs-2479 533 6 ) ) PUNCT iajs-2479 534 1 +0 +0 ADP iajs-2479 534 2 + + CCONJ iajs-2479 534 3 ( ( PUNCT iajs-2479 534 4 di di INTJ iajs-2479 534 5 – – PUNCT iajs-2479 534 6 t t NOUN iajs-2479 534 7 – – PUNCT iajs-2479 534 8 pi pi NOUN iajs-2479 534 9 ) ) PUNCT iajs-2479 534 10 +0 +0 ADP iajs-2479 534 11 + + PROPN iajs-2479 534 12 ( ( PUNCT iajs-2479 534 13 t t NOUN iajs-2479 534 14 + + NOUN iajs-2479 534 15 pi pi NOUN iajs-2479 534 16 – – PUNCT iajs-2479 534 17 di di NOUN iajs-2479 534 18 ) ) PUNCT iajs-2479 534 19 + + PROPN iajs-2479 534 20 ( ( PUNCT iajs-2479 534 21 t t NOUN iajs-2479 534 22 + + NOUN iajs-2479 534 23 pi pi PROPN iajs-2479 534 24 + + PROPN iajs-2479 534 25 pj pj X iajs-2479 534 26 ) ) PUNCT iajs-2479 535 1 +0 +0 ADP iajs-2479 535 2 + + CCONJ iajs-2479 535 3 ( ( PUNCT iajs-2479 535 4 dj dj NOUN iajs-2479 535 5 – – PUNCT iajs-2479 535 6 t t NOUN iajs-2479 535 7 – – PUNCT iajs-2479 535 8 pi pi NOUN iajs-2479 535 9 – – PUNCT iajs-2479 535 10 pj pj PROPN iajs-2479 535 11 ) ) PUNCT iajs-2479 536 1 +0 +0 ADP iajs-2479 536 2 +0 +0 ADP iajs-2479 536 3 ]= ]= NUM iajs-2479 536 4 t t NOUN iajs-2479 536 5 + + NUM iajs-2479 536 6 pi pi NOUN iajs-2479 536 7 + + NOUN iajs-2479 536 8 dj dj NOUN iajs-2479 536 9 … … PUNCT iajs-2479 536 10 .(n .(n NUM iajs-2479 536 11 ) ) PUNCT iajs-2479 536 12 . . PUNCT iajs-2479 537 1   X iajs-2479 537 2 f'ji= f'ji= PROPN iajs-2479 538 1 [ [ X iajs-2479 538 2 ( ( PUNCT iajs-2479 538 3 t t PROPN iajs-2479 538 4 + + PROPN iajs-2479 538 5 pj pj PROPN iajs-2479 538 6 ) ) PUNCT iajs-2479 539 1 +0 +0 ADP iajs-2479 539 2 + + CCONJ iajs-2479 539 3 ( ( PUNCT iajs-2479 539 4 dj dj NOUN iajs-2479 539 5 – – PUNCT iajs-2479 539 6 t t PROPN iajs-2479 539 7 – – PUNCT iajs-2479 539 8 pj pj PROPN iajs-2479 539 9 ) ) PUNCT iajs-2479 540 1 +0 +0 ADP iajs-2479 540 2 +0 +0 ADP iajs-2479 540 3 + + PROPN iajs-2479 540 4 [ [ X iajs-2479 540 5 ( ( PUNCT iajs-2479 540 6 t t PROPN iajs-2479 540 7 + + PROPN iajs-2479 540 8 pj pj PROPN iajs-2479 540 9 + + PROPN iajs-2479 540 10 pi pi NOUN iajs-2479 540 11 ) ) PUNCT iajs-2479 541 1 +0 +0 ADP iajs-2479 541 2 + + CCONJ iajs-2479 541 3 ( ( PUNCT iajs-2479 541 4 di di INTJ iajs-2479 541 5 – – PUNCT iajs-2479 541 6 t t PROPN iajs-2479 541 7 – – PUNCT iajs-2479 541 8 pj pj PROPN iajs-2479 541 9 – – PUNCT iajs-2479 541 10 pi pi NOUN iajs-2479 541 11 ) ) PUNCT iajs-2479 542 1 +0 +0 ADP iajs-2479 542 2 + + PROPN iajs-2479 542 3 ( ( PUNCT iajs-2479 542 4 t t PROPN iajs-2479 542 5 + + PROPN iajs-2479 542 6 pj pj PROPN iajs-2479 542 7 + + PROPN iajs-2479 542 8 pi pi NOUN iajs-2479 542 9 – – PUNCT iajs-2479 542 10 di di NOUN iajs-2479 542 11 ) ) PUNCT iajs-2479 542 12 = = PUNCT iajs-2479 542 13 t t PROPN iajs-2479 543 1 + + PROPN iajs-2479 543 2 pj pj PROPN iajs-2479 543 3 + + PROPN iajs-2479 543 4 pi pi NOUN iajs-2479 543 5 + + X iajs-2479 543 6 dj dj NOUN iajs-2479 543 7 … … PUNCT iajs-2479 543 8 .. .. PUNCT iajs-2479 543 9 ( ( PUNCT iajs-2479 543 10 m m NOUN iajs-2479 543 11 ) ) PUNCT iajs-2479 543 12 . . PUNCT iajs-2479 544 1 δij=(n δij=(n PROPN iajs-2479 544 2 ) ) PUNCT iajs-2479 544 3 – – PUNCT iajs-2479 544 4 ( ( PUNCT iajs-2479 544 5 m)= m)= NOUN iajs-2479 544 6 – – PUNCT iajs-2479 544 7 pj pj PROPN iajs-2479 544 8 ≤ ≤ PROPN iajs-2479 544 9 0 0 NUM iajs-2479 544 10 , , PUNCT iajs-2479 544 11 then then ADV iajs-2479 544 12 job job NOUN iajs-2479 544 13 i i PRON iajs-2479 544 14 precede precede VERB iajs-2479 544 15 j. j. PROPN iajs-2479 544 16 second second PROPN iajs-2479 544 17 : : PUNCT iajs-2479 544 18 if if SCONJ iajs-2479 544 19 r r NOUN iajs-2479 544 20 > > X iajs-2479 544 21 t t PROPN iajs-2479 544 22 , , PUNCT iajs-2479 544 23 then then ADV iajs-2479 544 24 in in ADP iajs-2479 544 25 the the DET iajs-2479 544 26 same same ADJ iajs-2479 544 27 way way NOUN iajs-2479 544 28 above above ADV iajs-2479 544 29 we we PRON iajs-2479 544 30 show show VERB iajs-2479 544 31 that that SCONJ iajs-2479 544 32 the the DET iajs-2479 544 33 theorem theorem NOUN iajs-2479 544 34 is be AUX iajs-2479 544 35 true true ADJ iajs-2479 544 36 ( ( PUNCT iajs-2479 544 37 integral integral ADJ iajs-2479 544 38 ) ) PUNCT iajs-2479 544 39 . . PUNCT iajs-2479 545 1 theorem theorem NOUN iajs-2479 545 2 2 2 NUM iajs-2479 545 3 for for ADP iajs-2479 545 4 the the DET iajs-2479 545 5 problem problem NOUN iajs-2479 545 6 ( ( PUNCT iajs-2479 545 7 p p NOUN iajs-2479 545 8 ) ) PUNCT iajs-2479 545 9 , , PUNCT iajs-2479 545 10 if if SCONJ iajs-2479 545 11 ri ri PROPN iajs-2479 545 12 = = SYM iajs-2479 545 13 r r NOUN iajs-2479 545 14 , , PUNCT iajs-2479 545 15 di di NOUN iajs-2479 545 16 = = SYM iajs-2479 545 17 d d PROPN iajs-2479 545 18 , , PUNCT iajs-2479 545 19 for for SCONJ iajs-2479 545 20 every every PRON iajs-2479 545 21 ( ( PUNCT iajs-2479 545 22 i i PRON iajs-2479 545 23 ϵn ϵn VERB iajs-2479 545 24 ) ) PUNCT iajs-2479 545 25 , , PUNCT iajs-2479 545 26 and and CCONJ iajs-2479 545 27 if if SCONJ iajs-2479 545 28 pi pi NOUN iajs-2479 545 29 ≤pj ≤pj VERB iajs-2479 545 30 and and CCONJ iajs-2479 545 31 dj dj X iajs-2479 545 32 = = ADJ iajs-2479 545 33 d d PROPN iajs-2479 545 34 , , PUNCT iajs-2479 545 35 where where SCONJ iajs-2479 545 36 jobs job NOUN iajs-2479 545 37 ( ( PUNCT iajs-2479 545 38 i i NOUN iajs-2479 545 39 ) ) PUNCT iajs-2479 545 40 , , PUNCT iajs-2479 545 41 and and CCONJ iajs-2479 545 42 ( ( PUNCT iajs-2479 545 43 j j NOUN iajs-2479 545 44 ) ) PUNCT iajs-2479 545 45 are be AUX iajs-2479 545 46 adjacent adjacent ADJ iajs-2479 545 47 jobs job NOUN iajs-2479 545 48 , , PUNCT iajs-2479 545 49 then then ADV iajs-2479 545 50 job job NOUN iajs-2479 545 51 ( ( PUNCT iajs-2479 545 52 i i NOUN iajs-2479 545 53 ) ) PUNCT iajs-2479 545 54 must must AUX iajs-2479 545 55 precede precede VERB iajs-2479 545 56 job job NOUN iajs-2479 545 57 ( ( PUNCT iajs-2479 545 58 j j NOUN iajs-2479 545 59 ) ) PUNCT iajs-2479 545 60 in in ADP iajs-2479 545 61 at at ADV iajs-2479 545 62 least least ADV iajs-2479 545 63 one one NUM iajs-2479 545 64 optimal optimal ADJ iajs-2479 545 65 sequence sequence NOUN iajs-2479 545 66 . . PUNCT iajs-2479 546 1 proof proof NOUN iajs-2479 546 2 . . PUNCT iajs-2479 547 1 using use VERB iajs-2479 547 2 the the DET iajs-2479 547 3 same same ADJ iajs-2479 547 4 previous previous ADJ iajs-2479 547 5 methodology methodology NOUN iajs-2479 547 6 the the DET iajs-2479 547 7 we we PRON iajs-2479 547 8 can can AUX iajs-2479 547 9 prove prove VERB iajs-2479 547 10 the the DET iajs-2479 547 11 validity validity NOUN iajs-2479 547 12 of of ADP iajs-2479 547 13 this this DET iajs-2479 547 14 theorem theorem NOUN iajs-2479 547 15 with with ADP iajs-2479 547 16 the the DET iajs-2479 547 17 following follow VERB iajs-2479 547 18 cases case NOUN iajs-2479 547 19 : : PUNCT iajs-2479 547 20 first first ADV iajs-2479 547 21 : : PUNCT iajs-2479 547 22 r r NOUN iajs-2479 547 23 ≤ ≤ PUNCT iajs-2479 547 24 t t PROPN iajs-2479 547 25 : : PUNCT iajs-2479 547 26 case case NOUN iajs-2479 547 27 1 1 NUM iajs-2479 547 28 : : PUNCT iajs-2479 547 29 if if SCONJ iajs-2479 547 30 d d PROPN iajs-2479 547 31 ≤ ≤ X iajs-2479 547 32 t t X iajs-2479 548 1 + + NOUN iajs-2479 548 2 pi pi NOUN iajs-2479 548 3 ≤ ≤ X iajs-2479 548 4 t t PROPN iajs-2479 549 1 + + PROPN iajs-2479 549 2 pj pj PROPN iajs-2479 549 3 ( ( PUNCT iajs-2479 549 4 i.e. i.e. X iajs-2479 549 5 both both CCONJ iajs-2479 549 6 the the DET iajs-2479 549 7 jobs job NOUN iajs-2479 549 8 i i PRON iajs-2479 549 9 , , PUNCT iajs-2479 549 10 j j PROPN iajs-2479 549 11 are be AUX iajs-2479 549 12 always always ADV iajs-2479 549 13 tardy tardy ADJ iajs-2479 549 14 ) ) PUNCT iajs-2479 549 15 . . PUNCT iajs-2479 550 1 proof proof NOUN iajs-2479 550 2 . . PUNCT iajs-2479 551 1 to to PART iajs-2479 551 2 show show VERB iajs-2479 551 3 that that PRON iajs-2479 551 4 s s AUX iajs-2479 551 5 dominates dominate VERB iajs-2479 551 6 s s NOUN iajs-2479 551 7 ' ' PUNCT iajs-2479 551 8 , , PUNCT iajs-2479 551 9 it it PRON iajs-2479 551 10 suffices suffice VERB iajs-2479 551 11 to to PART iajs-2479 551 12 show show VERB iajs-2479 551 13 that that SCONJ iajs-2479 551 14 ( ( PUNCT iajs-2479 551 15 δij= δij= PROPN iajs-2479 551 16 fij fij PROPN iajs-2479 551 17 ( ( PUNCT iajs-2479 551 18 s)fji s)fji PROPN iajs-2479 551 19 ( ( PUNCT iajs-2479 551 20 s s NOUN iajs-2479 551 21 ' ' PUNCT iajs-2479 551 22 ) ) PUNCT iajs-2479 551 23 ≤ ≤ NOUN iajs-2479 551 24 0 0 NUM iajs-2479 551 25 ) ) PUNCT iajs-2479 551 26 . . PUNCT iajs-2479 552 1 since since SCONJ iajs-2479 552 2 the the DET iajs-2479 552 3 jobs job NOUN iajs-2479 552 4 i i PRON iajs-2479 552 5 and and CCONJ iajs-2479 552 6 j j PROPN iajs-2479 552 7 are be AUX iajs-2479 552 8 both both ADV iajs-2479 552 9 tardy tardy ADJ iajs-2479 552 10 , , PUNCT iajs-2479 552 11 then then ADV iajs-2479 552 12 ei ei X iajs-2479 552 13 = = SYM iajs-2479 552 14 ej=0 ej=0 ADJ iajs-2479 552 15 , , PUNCT iajs-2479 552 16 vi vi NOUN iajs-2479 552 17 = = SYM iajs-2479 552 18 pi pi NOUN iajs-2479 552 19 , , PUNCT iajs-2479 552 20 vj vj PROPN iajs-2479 552 21 = = PROPN iajs-2479 552 22 pj pj PROPN iajs-2479 552 23 , , PUNCT iajs-2479 552 24 and and CCONJ iajs-2479 552 25 ui ui PROPN iajs-2479 552 26 = = NOUN iajs-2479 552 27 uj=1 uj=1 PROPN iajs-2479 552 28 . . PUNCT iajs-2479 553 1 now now ADV iajs-2479 553 2 , , PUNCT iajs-2479 553 3 let let VERB iajs-2479 553 4   NOUN iajs-2479 553 5 fij(s)= fij(s)= NOUN iajs-2479 553 6 [ [ PUNCT iajs-2479 553 7 ( ( PUNCT iajs-2479 553 8 t t NOUN iajs-2479 553 9 + + NOUN iajs-2479 553 10 pi pi NOUN iajs-2479 553 11 ) ) PUNCT iajs-2479 554 1 + + CCONJ iajs-2479 554 2 ( ( PUNCT iajs-2479 554 3 t t NOUN iajs-2479 554 4 + + NOUN iajs-2479 554 5 pi pi NOUN iajs-2479 554 6 – – PUNCT iajs-2479 554 7 d d NOUN iajs-2479 554 8 ) ) PUNCT iajs-2479 555 1 +0 +0 ADP iajs-2479 555 2 + + SYM iajs-2479 555 3 1 1 NUM iajs-2479 555 4 + + NOUN iajs-2479 555 5 pi pi NOUN iajs-2479 555 6 + + ADJ iajs-2479 555 7 ( ( PUNCT iajs-2479 555 8 t t NOUN iajs-2479 555 9 + + NOUN iajs-2479 555 10 pi pi PROPN iajs-2479 555 11 + + PROPN iajs-2479 555 12 pj pj X iajs-2479 555 13 ) ) PUNCT iajs-2479 555 14 + + CCONJ iajs-2479 555 15 ( ( PUNCT iajs-2479 555 16 t t NOUN iajs-2479 555 17 + + NOUN iajs-2479 555 18 pi pi NOUN iajs-2479 555 19 + + PROPN iajs-2479 555 20 pj pj PROPN iajs-2479 555 21 – – PUNCT iajs-2479 555 22 d d NOUN iajs-2479 555 23 ) ) PUNCT iajs-2479 556 1 +0 +0 ADP iajs-2479 556 2 +1 +1 PROPN iajs-2479 557 1 + + NOUN iajs-2479 557 2 pj pj PROPN iajs-2479 557 3 ]= ]= NUM iajs-2479 557 4 4 4 NUM iajs-2479 557 5 t t NOUN iajs-2479 557 6 +5pi +5pi PUNCT iajs-2479 557 7 +3pj +3pj PUNCT iajs-2479 557 8 – – PUNCT iajs-2479 557 9 2d 2d NOUN iajs-2479 557 10 +2 +2 PROPN iajs-2479 557 11 … … PUNCT iajs-2479 557 12 .. .. PUNCT iajs-2479 557 13 ( ( PUNCT iajs-2479 557 14 a a X iajs-2479 557 15 ) ) PUNCT iajs-2479 557 16   NOUN iajs-2479 558 1 f'ji= f'ji= PROPN iajs-2479 559 1 [ [ X iajs-2479 559 2 ( ( PUNCT iajs-2479 559 3 t t PROPN iajs-2479 559 4 + + PROPN iajs-2479 559 5 pj pj PROPN iajs-2479 559 6 ) ) PUNCT iajs-2479 560 1 + + CCONJ iajs-2479 560 2 ( ( PUNCT iajs-2479 560 3 t t PROPN iajs-2479 560 4 + + PROPN iajs-2479 560 5 pj pj PROPN iajs-2479 560 6 – – PUNCT iajs-2479 560 7 d d NOUN iajs-2479 560 8 ) ) PUNCT iajs-2479 561 1 +0 +0 ADP iajs-2479 561 2 +1 +1 PROPN iajs-2479 562 1 + + NOUN iajs-2479 562 2 pj pj PROPN iajs-2479 562 3 + + CCONJ iajs-2479 562 4 ( ( PUNCT iajs-2479 562 5 t t PROPN iajs-2479 562 6 + + PROPN iajs-2479 562 7 pj pj PROPN iajs-2479 562 8 + + PROPN iajs-2479 562 9 pi pi NOUN iajs-2479 562 10 ) ) PUNCT iajs-2479 563 1 + + CCONJ iajs-2479 563 2 ( ( PUNCT iajs-2479 563 3 t t PROPN iajs-2479 563 4 + + PROPN iajs-2479 563 5 pj pj PROPN iajs-2479 563 6 + + PROPN iajs-2479 563 7 pi pi NOUN iajs-2479 563 8 – – PUNCT iajs-2479 563 9 d d NOUN iajs-2479 563 10 ) ) PUNCT iajs-2479 564 1 +0 +0 ADP iajs-2479 564 2 +1 +1 PROPN iajs-2479 565 1 + + NOUN iajs-2479 565 2 pi pi NOUN iajs-2479 565 3 ]= ]= NUM iajs-2479 565 4 4 4 NUM iajs-2479 565 5 t t NOUN iajs-2479 565 6 +3pi +3pi PROPN iajs-2479 565 7 +5pj +5pj PROPN iajs-2479 565 8 – – PUNCT iajs-2479 565 9 2d 2d NOUN iajs-2479 565 10 +2 +2 PROPN iajs-2479 565 11 … … PUNCT iajs-2479 565 12 .. .. PUNCT iajs-2479 565 13 ( ( PUNCT iajs-2479 565 14 b b NOUN iajs-2479 565 15 ) ) PUNCT iajs-2479 565 16 . . PUNCT iajs-2479 566 1 δij= δij= PROPN iajs-2479 566 2 ( ( PUNCT iajs-2479 566 3 a a X iajs-2479 566 4 ) ) PUNCT iajs-2479 566 5 ( ( PUNCT iajs-2479 566 6 b)= b)= X iajs-2479 566 7 2pi 2pi PROPN iajs-2479 567 1 -2pj -2pj PROPN iajs-2479 568 1 ≤0 ≤0 PROPN iajs-2479 568 2 , , PUNCT iajs-2479 568 3 then then ADV iajs-2479 568 4 job job NOUN iajs-2479 568 5 i i PRON iajs-2479 568 6 precede precede VERB iajs-2479 568 7 j. j. PROPN iajs-2479 568 8 case case PROPN iajs-2479 568 9 2 2 X iajs-2479 568 10 . . PUNCT iajs-2479 569 1 if if SCONJ iajs-2479 569 2 d d PROPN iajs-2479 569 3 ≤ ≤ X iajs-2479 569 4 t t NOUN iajs-2479 569 5 + + NOUN iajs-2479 569 6 pi pi NOUN iajs-2479 569 7 , , PUNCT iajs-2479 569 8 t t PROPN iajs-2479 569 9 + + PROPN iajs-2479 569 10 pi pi NOUN iajs-2479 569 11 + + PROPN iajs-2479 569 12 pj pj PROPN iajs-2479 569 13 ≤ ≤ PROPN iajs-2479 569 14 d d PROPN iajs-2479 569 15 ( ( PUNCT iajs-2479 569 16 i.e. i.e. X iajs-2479 569 17 the the DET iajs-2479 569 18 job job NOUN iajs-2479 570 1 i i PRON iajs-2479 570 2 , , PUNCT iajs-2479 570 3 is be AUX iajs-2479 570 4 always always ADV iajs-2479 570 5 tardy tardy ADJ iajs-2479 570 6 and and CCONJ iajs-2479 570 7 the the DET iajs-2479 570 8 job job NOUN iajs-2479 570 9 j j PROPN iajs-2479 570 10 , , PUNCT iajs-2479 570 11 is be AUX iajs-2479 570 12 always always ADV iajs-2479 570 13 early early ADJ iajs-2479 570 14 ) ) PUNCT iajs-2479 570 15 . . PUNCT iajs-2479 571 1 proof proof NOUN iajs-2479 571 2 . . PUNCT iajs-2479 572 1 since since SCONJ iajs-2479 572 2 the the DET iajs-2479 572 3 job job NOUN iajs-2479 572 4 i i PRON iajs-2479 572 5 , , PUNCT iajs-2479 572 6 is be AUX iajs-2479 572 7 always always ADV iajs-2479 572 8 tardy tardy ADJ iajs-2479 572 9 then then ADV iajs-2479 572 10 ei=0 ei=0 PROPN iajs-2479 572 11 , , PUNCT iajs-2479 572 12 ui=1 ui=1 ADV iajs-2479 572 13 , , PUNCT iajs-2479 572 14 and and CCONJ iajs-2479 572 15 if if SCONJ iajs-2479 572 16 job job NOUN iajs-2479 572 17 j j PROPN iajs-2479 572 18 is be AUX iajs-2479 572 19 always always ADV iajs-2479 572 20 early early ADJ iajs-2479 572 21 , , PUNCT iajs-2479 572 22 then then ADV iajs-2479 572 23 tj=0 tj=0 ADJ iajs-2479 572 24 , , PUNCT iajs-2479 572 25 and and CCONJ iajs-2479 572 26 vj={0 vj={0 NUM iajs-2479 572 27 , , PUNCT iajs-2479 572 28 cj cj PROPN iajs-2479 572 29 – – PUNCT iajs-2479 572 30 dj dj NOUN iajs-2479 572 31 } } PUNCT iajs-2479 572 32 ( ( PUNCT iajs-2479 572 33 i.e. i.e. X iajs-2479 572 34 j j PROPN iajs-2479 572 35 , , PUNCT iajs-2479 572 36 is be AUX iajs-2479 572 37 early early ADJ iajs-2479 572 38 or or CCONJ iajs-2479 572 39 partial partial ADJ iajs-2479 572 40 early early ADV iajs-2479 572 41 ) ) PUNCT iajs-2479 572 42 . . PUNCT iajs-2479 573 1   INTJ iajs-2479 573 2 ( ( PUNCT iajs-2479 573 3 when when SCONJ iajs-2479 573 4 vj=0 vj=0 NUM iajs-2479 573 5 ) ) PUNCT iajs-2479 573 6 . . PUNCT iajs-2479 574 1   X iajs-2479 575 1 fij= fij= PROPN iajs-2479 575 2 [ [ PUNCT iajs-2479 575 3 ( ( PUNCT iajs-2479 575 4 t t NOUN iajs-2479 575 5 + + NOUN iajs-2479 575 6 pi pi NOUN iajs-2479 575 7 ) ) PUNCT iajs-2479 576 1 + + CCONJ iajs-2479 576 2 ( ( PUNCT iajs-2479 576 3 t t NOUN iajs-2479 576 4 + + NOUN iajs-2479 576 5 pi pi NOUN iajs-2479 576 6 – – PUNCT iajs-2479 576 7 d d NOUN iajs-2479 576 8 ) ) PUNCT iajs-2479 577 1 +0 +0 ADP iajs-2479 577 2 + + SYM iajs-2479 577 3 1 1 NUM iajs-2479 577 4 + + NOUN iajs-2479 577 5 pi pi NOUN iajs-2479 577 6 + + ADJ iajs-2479 577 7 ( ( PUNCT iajs-2479 577 8 t t NOUN iajs-2479 577 9 + + NOUN iajs-2479 577 10 pi pi PROPN iajs-2479 577 11 + + PROPN iajs-2479 577 12 pj pj X iajs-2479 577 13 ) ) PUNCT iajs-2479 578 1 +0 +0 ADP iajs-2479 578 2 + + SYM iajs-2479 578 3 ( ( PUNCT iajs-2479 578 4 d d PROPN iajs-2479 578 5 – – PUNCT iajs-2479 578 6 t t NOUN iajs-2479 578 7 – – PUNCT iajs-2479 578 8 pi pi NOUN iajs-2479 578 9 – – PUNCT iajs-2479 578 10 pj pj PROPN iajs-2479 578 11 ) ) PUNCT iajs-2479 579 1 +0 +0 ADP iajs-2479 579 2 +0 +0 ADP iajs-2479 579 3 ]= ]= NUM iajs-2479 579 4 2 2 NUM iajs-2479 579 5 t t NOUN iajs-2479 579 6 +3pi +3pi X iajs-2479 579 7 +1 +1 X iajs-2479 579 8 … … PUNCT iajs-2479 579 9 ( ( PUNCT iajs-2479 579 10 a a X iajs-2479 579 11 ) ) PUNCT iajs-2479 579 12   NOUN iajs-2479 579 13 f'ji= f'ji= PROPN iajs-2479 580 1 [ [ X iajs-2479 580 2 ( ( PUNCT iajs-2479 580 3 t t PROPN iajs-2479 580 4 + + PROPN iajs-2479 580 5 pj pj PROPN iajs-2479 580 6 ) ) PUNCT iajs-2479 581 1 +0 +0 ADP iajs-2479 581 2 + + SYM iajs-2479 581 3 ( ( PUNCT iajs-2479 581 4 d d PROPN iajs-2479 581 5 – – PUNCT iajs-2479 581 6 t t PROPN iajs-2479 581 7 – – PUNCT iajs-2479 581 8 pj pj PROPN iajs-2479 581 9 ) ) PUNCT iajs-2479 581 10 +0 +0 ADP iajs-2479 581 11 +0 +0 ADP iajs-2479 581 12 + + PROPN iajs-2479 581 13 ( ( PUNCT iajs-2479 581 14 t t PROPN iajs-2479 581 15 + + PROPN iajs-2479 581 16 pj pj PROPN iajs-2479 581 17 + + PROPN iajs-2479 581 18 pi pi NOUN iajs-2479 581 19 ) ) PUNCT iajs-2479 582 1 + + CCONJ iajs-2479 582 2 ( ( PUNCT iajs-2479 582 3 t t PROPN iajs-2479 582 4 + + PROPN iajs-2479 582 5 pj pj PROPN iajs-2479 582 6 + + PROPN iajs-2479 582 7 pi pi NOUN iajs-2479 582 8 – – PUNCT iajs-2479 582 9 d d NOUN iajs-2479 582 10 ) ) PUNCT iajs-2479 583 1 +0 +0 ADP iajs-2479 583 2 +1 +1 PROPN iajs-2479 584 1 + + NOUN iajs-2479 584 2 pi pi NOUN iajs-2479 584 3 ] ] X iajs-2479 584 4 = = SYM iajs-2479 584 5 2 2 NUM iajs-2479 584 6 t t NOUN iajs-2479 584 7 +3pi +3pi PROPN iajs-2479 584 8 +2pj +2pj PROPN iajs-2479 584 9 +1 +1 PROPN iajs-2479 584 10 … … PUNCT iajs-2479 584 11 (b (b NOUN iajs-2479 584 12 ) ) PUNCT iajs-2479 584 13 δij=(a δij=(a NOUN iajs-2479 584 14 ) ) PUNCT iajs-2479 584 15 – – PUNCT iajs-2479 584 16 ( ( PUNCT iajs-2479 584 17 b)= b)= X iajs-2479 584 18 – – PUNCT iajs-2479 584 19 2pj 2pj NOUN iajs-2479 584 20 < < X iajs-2479 584 21 0 0 NUM iajs-2479 584 22 . . PUNCT iajs-2479 585 1 then then ADV iajs-2479 585 2 job job NOUN iajs-2479 585 3 i i PRON iajs-2479 585 4 precede precede VERB iajs-2479 585 5 j. j. PROPN iajs-2479 585 6   PROPN iajs-2479 585 7 when when SCONJ iajs-2479 585 8 ( ( PUNCT iajs-2479 585 9 when when SCONJ iajs-2479 585 10 vj= vj= PROPN iajs-2479 585 11 cj cj PROPN iajs-2479 585 12 – – PUNCT iajs-2479 585 13 d d NOUN iajs-2479 585 14 ) ) PUNCT iajs-2479 585 15 . . PUNCT iajs-2479 586 1   X iajs-2479 587 1 fij= fij= PROPN iajs-2479 587 2 [ [ PUNCT iajs-2479 587 3 ( ( PUNCT iajs-2479 587 4 t t NOUN iajs-2479 587 5 + + NOUN iajs-2479 587 6 pi pi NOUN iajs-2479 587 7 ) ) PUNCT iajs-2479 588 1 + + CCONJ iajs-2479 588 2 ( ( PUNCT iajs-2479 588 3 t t NOUN iajs-2479 588 4 + + NOUN iajs-2479 588 5 pi pi NOUN iajs-2479 588 6 – – PUNCT iajs-2479 588 7 d d NOUN iajs-2479 588 8 ) ) PUNCT iajs-2479 589 1 +0 +0 ADP iajs-2479 589 2 + + SYM iajs-2479 589 3 1 1 NUM iajs-2479 589 4 + + NOUN iajs-2479 589 5 pi pi NOUN iajs-2479 589 6 + + ADJ iajs-2479 589 7 ( ( PUNCT iajs-2479 589 8 t t NOUN iajs-2479 589 9 + + NOUN iajs-2479 589 10 pi pi PROPN iajs-2479 589 11 + + PROPN iajs-2479 589 12 pj pj X iajs-2479 589 13 ) ) PUNCT iajs-2479 590 1 +0 +0 ADP iajs-2479 590 2 + + SYM iajs-2479 590 3 ( ( PUNCT iajs-2479 590 4 d d PROPN iajs-2479 590 5 – – PUNCT iajs-2479 590 6 t t NOUN iajs-2479 590 7 – – PUNCT iajs-2479 590 8 pi pi NOUN iajs-2479 590 9 – – PUNCT iajs-2479 590 10 pj pj PROPN iajs-2479 590 11 ) ) PUNCT iajs-2479 591 1 +0 +0 ADP iajs-2479 591 2 + + NOUN iajs-2479 591 3 t t NOUN iajs-2479 591 4 + + NUM iajs-2479 591 5 pi pi PROPN iajs-2479 591 6 + + PROPN iajs-2479 591 7 pj pj PROPN iajs-2479 591 8 – – PUNCT iajs-2479 591 9 d]= d]= PROPN iajs-2479 591 10 3 3 NUM iajs-2479 591 11 t t NOUN iajs-2479 591 12 +4pi +4pi PROPN iajs-2479 591 13 + + CCONJ iajs-2479 591 14 pj pj PROPN iajs-2479 591 15 – – PUNCT iajs-2479 591 16 d+1 d+1 PROPN iajs-2479 591 17 … … PUNCT iajs-2479 591 18 .(c .(c NOUN iajs-2479 591 19 ) ) PUNCT iajs-2479 591 20 . . PUNCT iajs-2479 592 1   X iajs-2479 592 2 f'ji= f'ji= PROPN iajs-2479 593 1 [ [ X iajs-2479 593 2 ( ( PUNCT iajs-2479 593 3 t t PROPN iajs-2479 593 4 + + PROPN iajs-2479 593 5 pj pj PROPN iajs-2479 593 6 ) ) PUNCT iajs-2479 594 1 +0 +0 ADP iajs-2479 594 2 + + SYM iajs-2479 594 3 ( ( PUNCT iajs-2479 594 4 d d PROPN iajs-2479 594 5 – – PUNCT iajs-2479 594 6 t t PROPN iajs-2479 594 7 – – PUNCT iajs-2479 594 8 pj pj PROPN iajs-2479 594 9 ) ) PUNCT iajs-2479 595 1 +0 +0 ADP iajs-2479 595 2 + + PROPN iajs-2479 595 3 ( ( PUNCT iajs-2479 595 4 t t PROPN iajs-2479 595 5 + + CCONJ iajs-2479 595 6 pj pj PROPN iajs-2479 595 7 – – PUNCT iajs-2479 595 8 d d NOUN iajs-2479 595 9 ) ) PUNCT iajs-2479 596 1 + + PROPN iajs-2479 596 2 ( ( PUNCT iajs-2479 596 3 t t PROPN iajs-2479 596 4 + + PROPN iajs-2479 596 5 pj pj PROPN iajs-2479 596 6 + + PROPN iajs-2479 596 7 pi pi NOUN iajs-2479 596 8 ) ) PUNCT iajs-2479 597 1 + + CCONJ iajs-2479 597 2 ( ( PUNCT iajs-2479 597 3 t t PROPN iajs-2479 597 4 + + PROPN iajs-2479 597 5 pj pj PROPN iajs-2479 597 6 + + PROPN iajs-2479 597 7 pi pi NOUN iajs-2479 597 8 – – PUNCT iajs-2479 597 9 d d NOUN iajs-2479 597 10 ) ) PUNCT iajs-2479 598 1 +0 +0 ADP iajs-2479 598 2 +1 +1 PROPN iajs-2479 599 1 + + NOUN iajs-2479 599 2 pi pi NOUN iajs-2479 599 3 ] ] X iajs-2479 599 4 = = PUNCT iajs-2479 599 5 3 3 NUM iajs-2479 599 6 t t NOUN iajs-2479 600 1 + + CCONJ iajs-2479 600 2 3pi 3pi NOUN iajs-2479 600 3 +3pj +3pj PUNCT iajs-2479 600 4 – – PUNCT iajs-2479 600 5 d d X iajs-2479 600 6 +1 +1 PROPN iajs-2479 600 7 … … PUNCT iajs-2479 600 8 .. .. PUNCT iajs-2479 600 9 ( ( PUNCT iajs-2479 600 10 e e NOUN iajs-2479 600 11 ) ) PUNCT iajs-2479 600 12 . . PUNCT iajs-2479 601 1 δij=(c δij=(c NUM iajs-2479 601 2 ) ) PUNCT iajs-2479 601 3 – – PUNCT iajs-2479 601 4 ( ( PUNCT iajs-2479 601 5 e)= e)= ADJ iajs-2479 601 6 pi pi NOUN iajs-2479 601 7 – – PUNCT iajs-2479 601 8 2pj 2pj ADJ iajs-2479 601 9 ≤0 ≤0 PROPN iajs-2479 601 10 , , PUNCT iajs-2479 601 11 then then ADV iajs-2479 601 12 job job NOUN iajs-2479 601 13 i i PRON iajs-2479 601 14 precede precede VERB iajs-2479 601 15 j. j. PROPN iajs-2479 601 16 case case PROPN iajs-2479 601 17 4 4 X iajs-2479 601 18 . . PUNCT iajs-2479 602 1 if if SCONJ iajs-2479 602 2 t t PROPN iajs-2479 602 3 + + NOUN iajs-2479 602 4 pi pi NOUN iajs-2479 602 5 + + PROPN iajs-2479 602 6 pj pj PROPN iajs-2479 602 7 ≤ ≤ PROPN iajs-2479 602 8 d d PROPN iajs-2479 602 9 ( ( PUNCT iajs-2479 602 10 i.e. i.e. X iajs-2479 602 11 both both CCONJ iajs-2479 602 12 the the DET iajs-2479 602 13 jobs job NOUN iajs-2479 602 14 i i PRON iajs-2479 602 15 , , PUNCT iajs-2479 602 16 j j PROPN iajs-2479 602 17 are be AUX iajs-2479 602 18 always always ADV iajs-2479 602 19 early early ADJ iajs-2479 602 20 ) ) PUNCT iajs-2479 602 21 . . PUNCT iajs-2479 603 1 proof proof NOUN iajs-2479 603 2 . . PUNCT iajs-2479 604 1   INTJ iajs-2479 604 2 when when SCONJ iajs-2479 604 3 vi vi PROPN iajs-2479 604 4 , , PUNCT iajs-2479 604 5 vj vj X iajs-2479 604 6 = = PROPN iajs-2479 604 7 0 0 PROPN iajs-2479 604 8 . . PUNCT iajs-2479 604 9   PROPN iajs-2479 605 1 fij fij PROPN iajs-2479 605 2 = = PUNCT iajs-2479 606 1 [ [ X iajs-2479 606 2 ( ( PUNCT iajs-2479 606 3 t t NOUN iajs-2479 606 4 + + NOUN iajs-2479 606 5 pi pi NOUN iajs-2479 606 6 ) ) PUNCT iajs-2479 607 1 +0 +0 SCONJ iajs-2479 607 2 + + SYM iajs-2479 607 3 ( ( PUNCT iajs-2479 607 4 d d PROPN iajs-2479 607 5 – – PUNCT iajs-2479 607 6 t t NOUN iajs-2479 607 7 – – PUNCT iajs-2479 607 8 pi pi NOUN iajs-2479 607 9 ) ) PUNCT iajs-2479 607 10 +0 +0 ADP iajs-2479 607 11 +0 +0 ADP iajs-2479 607 12 + + PROPN iajs-2479 607 13 ( ( PUNCT iajs-2479 607 14 t t NOUN iajs-2479 607 15 + + NOUN iajs-2479 607 16 pi pi PROPN iajs-2479 607 17 + + PROPN iajs-2479 607 18 pj pj X iajs-2479 607 19 ) ) PUNCT iajs-2479 608 1 +0 +0 ADP iajs-2479 608 2 + + SYM iajs-2479 608 3 ( ( PUNCT iajs-2479 608 4 d d PROPN iajs-2479 608 5 – – PUNCT iajs-2479 608 6 t t NOUN iajs-2479 608 7 – – PUNCT iajs-2479 608 8 pi pi NOUN iajs-2479 608 9 – – PUNCT iajs-2479 608 10 pj pj PROPN iajs-2479 608 11 ) ) PUNCT iajs-2479 609 1 +0 +0 ADP iajs-2479 609 2 +0 +0 ADP iajs-2479 609 3 ]= ]= NUM iajs-2479 609 4 2d 2d NOUN iajs-2479 609 5 … … PUNCT iajs-2479 609 6 .. .. PUNCT iajs-2479 609 7 ( ( PUNCT iajs-2479 609 8 a a NOUN iajs-2479 609 9 ) ) PUNCT iajs-2479 609 10 . . PUNCT iajs-2479 610 1   X iajs-2479 610 2 f'ji f'ji NOUN iajs-2479 611 1 = = PUNCT iajs-2479 612 1 [ [ X iajs-2479 612 2 ( ( PUNCT iajs-2479 612 3 t t PROPN iajs-2479 612 4 + + PROPN iajs-2479 612 5 pj pj PROPN iajs-2479 612 6 ) ) PUNCT iajs-2479 613 1 +0 +0 ADP iajs-2479 613 2 + + SYM iajs-2479 613 3 ( ( PUNCT iajs-2479 613 4 d d PROPN iajs-2479 613 5 – – PUNCT iajs-2479 613 6 t t PROPN iajs-2479 613 7 – – PUNCT iajs-2479 613 8 pj pj PROPN iajs-2479 613 9 ) ) PUNCT iajs-2479 613 10 +0 +0 ADP iajs-2479 613 11 +0 +0 ADP iajs-2479 613 12 + + PROPN iajs-2479 613 13 ( ( PUNCT iajs-2479 613 14 t t PROPN iajs-2479 613 15 + + PROPN iajs-2479 613 16 pj pj PROPN iajs-2479 613 17 + + PROPN iajs-2479 613 18 pi pi NOUN iajs-2479 613 19 ) ) PUNCT iajs-2479 614 1 +0 +0 ADP iajs-2479 614 2 + + SYM iajs-2479 614 3 ( ( PUNCT iajs-2479 614 4 d d PROPN iajs-2479 614 5 – – PUNCT iajs-2479 614 6 t t PROPN iajs-2479 614 7 – – PUNCT iajs-2479 614 8 pj pj PROPN iajs-2479 614 9 – – PUNCT iajs-2479 614 10 pi)+0 pi)+0 VERB iajs-2479 614 11 +0 +0 ADP iajs-2479 614 12 ] ] X iajs-2479 614 13 = = SYM iajs-2479 614 14 2d 2d NOUN iajs-2479 614 15 … … PUNCT iajs-2479 614 16 .(b .(b NUM iajs-2479 614 17 ) ) PUNCT iajs-2479 614 18 . . PUNCT iajs-2479 615 1 δij=(a δij=(a NOUN iajs-2479 615 2 ) ) PUNCT iajs-2479 615 3 – – PUNCT iajs-2479 615 4 ( ( PUNCT iajs-2479 615 5 b)=0 b)=0 ADV iajs-2479 615 6 , , PUNCT iajs-2479 615 7 then then ADV iajs-2479 615 8 it it PRON iajs-2479 615 9 is be AUX iajs-2479 615 10 indifferent indifferent ADJ iajs-2479 615 11 to to PART iajs-2479 615 12 schedule schedule VERB iajs-2479 615 13 i i PRON iajs-2479 615 14 or or CCONJ iajs-2479 615 15 j j PROPN iajs-2479 615 16 first first ADJ iajs-2479 615 17 . . PUNCT iajs-2479 615 18     SPACE iajs-2479 616 1 152 152 NUM iajs-2479 616 2     SPACE iajs-2479 616 3 ibn ibn PROPN iajs-2479 616 4 al al PROPN iajs-2479 616 5 - - PUNCT iajs-2479 616 6 haitham haitham PROPN iajs-2479 616 7 jour jour X iajs-2479 616 8 . . PROPN iajs-2479 616 9 for for ADP iajs-2479 616 10 pure pure ADJ iajs-2479 616 11 & & CCONJ iajs-2479 616 12 appl appl PROPN iajs-2479 616 13 . . PUNCT iajs-2479 617 1 sci sci PROPN iajs-2479 617 2 . . PROPN iajs-2479 618 1 33 33 NUM iajs-2479 618 2 ( ( PUNCT iajs-2479 618 3 3 3 NUM iajs-2479 618 4 ) ) PUNCT iajs-2479 618 5 2020 2020 NUM iajs-2479 619 1   INTJ iajs-2479 619 2 when when SCONJ iajs-2479 619 3 vi= vi= PROPN iajs-2479 619 4 ci ci PROPN iajs-2479 619 5 – – PUNCT iajs-2479 619 6 d d NOUN iajs-2479 619 7 , , PUNCT iajs-2479 619 8 vj vj PROPN iajs-2479 619 9 = = PUNCT iajs-2479 619 10 cj cj PROPN iajs-2479 619 11 – – PUNCT iajs-2479 619 12 d. d. PROPN iajs-2479 619 13   PROPN iajs-2479 619 14 fij fij PROPN iajs-2479 620 1 = = PUNCT iajs-2479 621 1 [ [ X iajs-2479 621 2 ( ( PUNCT iajs-2479 621 3 t t NOUN iajs-2479 621 4 + + NOUN iajs-2479 621 5 pi pi NOUN iajs-2479 621 6 ) ) PUNCT iajs-2479 622 1 +0 +0 ADP iajs-2479 622 2 + + SYM iajs-2479 622 3 ( ( PUNCT iajs-2479 622 4 d d PROPN iajs-2479 622 5 – – PUNCT iajs-2479 622 6 t t NOUN iajs-2479 622 7 – – PUNCT iajs-2479 622 8 pi pi NOUN iajs-2479 622 9 ) ) PUNCT iajs-2479 623 1 +0 +0 ADP iajs-2479 623 2 + + PROPN iajs-2479 623 3 ( ( PUNCT iajs-2479 623 4 t t NOUN iajs-2479 623 5 + + NOUN iajs-2479 623 6 pi pi NOUN iajs-2479 623 7 – – PUNCT iajs-2479 623 8 d d NOUN iajs-2479 623 9 ) ) PUNCT iajs-2479 624 1 + + PROPN iajs-2479 624 2 ( ( PUNCT iajs-2479 624 3 t t NOUN iajs-2479 624 4 + + NOUN iajs-2479 624 5 pi pi PROPN iajs-2479 624 6 + + PROPN iajs-2479 624 7 pj pj X iajs-2479 624 8 ) ) PUNCT iajs-2479 625 1 +0 +0 ADP iajs-2479 625 2 + + SYM iajs-2479 625 3 ( ( PUNCT iajs-2479 625 4 d d PROPN iajs-2479 625 5 – – PUNCT iajs-2479 625 6 t t NOUN iajs-2479 625 7 – – PUNCT iajs-2479 625 8 pi pi NOUN iajs-2479 625 9 – – PUNCT iajs-2479 625 10 pj pj PROPN iajs-2479 625 11 ) ) PUNCT iajs-2479 626 1 +0 +0 ADP iajs-2479 626 2 + + PROPN iajs-2479 626 3 ( ( PUNCT iajs-2479 626 4 t t NOUN iajs-2479 626 5 + + NUM iajs-2479 626 6 pi pi PROPN iajs-2479 626 7 + + PROPN iajs-2479 626 8 pj pj PROPN iajs-2479 626 9 – – PUNCT iajs-2479 626 10 d)]=2 d)]=2 PROPN iajs-2479 626 11 t t NOUN iajs-2479 626 12 +2pi +2pi SYM iajs-2479 626 13 + + PROPN iajs-2479 626 14 pj pj PROPN iajs-2479 626 15 … … SYM iajs-2479 626 16 .. .. PUNCT iajs-2479 626 17 (c (c NUM iajs-2479 626 18 ) ) PUNCT iajs-2479 626 19 . . PUNCT iajs-2479 627 1   X iajs-2479 627 2 f'ji= f'ji= PROPN iajs-2479 628 1 [ [ X iajs-2479 628 2 ( ( PUNCT iajs-2479 628 3 t t PROPN iajs-2479 628 4 + + PROPN iajs-2479 628 5 pj pj PROPN iajs-2479 628 6 ) ) PUNCT iajs-2479 629 1 +0 +0 ADP iajs-2479 629 2 + + SYM iajs-2479 629 3 ( ( PUNCT iajs-2479 629 4 d d PROPN iajs-2479 629 5 – – PUNCT iajs-2479 629 6 t t PROPN iajs-2479 629 7 – – PUNCT iajs-2479 629 8 pj pj PROPN iajs-2479 629 9 ) ) PUNCT iajs-2479 630 1 +0 +0 ADP iajs-2479 630 2 + + PROPN iajs-2479 630 3 ( ( PUNCT iajs-2479 630 4 t t PROPN iajs-2479 630 5 + + PROPN iajs-2479 630 6 pj pj PROPN iajs-2479 630 7 – – PUNCT iajs-2479 630 8 d d NOUN iajs-2479 630 9 ) ) PUNCT iajs-2479 630 10 + + PROPN iajs-2479 630 11 ( ( PUNCT iajs-2479 630 12 t t PROPN iajs-2479 630 13 + + PROPN iajs-2479 630 14 pj pj PROPN iajs-2479 630 15 + + PROPN iajs-2479 630 16 pi pi NOUN iajs-2479 630 17 ) ) PUNCT iajs-2479 631 1 +0 +0 ADP iajs-2479 631 2 + + SYM iajs-2479 631 3 ( ( PUNCT iajs-2479 631 4 d d PROPN iajs-2479 631 5 – – PUNCT iajs-2479 631 6 t t PROPN iajs-2479 631 7 – – PUNCT iajs-2479 631 8 pj pj PROPN iajs-2479 631 9 – – PUNCT iajs-2479 631 10 pi pi NOUN iajs-2479 631 11 ) ) PUNCT iajs-2479 632 1 +0 +0 ADP iajs-2479 632 2 + + PROPN iajs-2479 632 3 ( ( PUNCT iajs-2479 632 4 t t PROPN iajs-2479 632 5 + + PROPN iajs-2479 632 6 pj pj PROPN iajs-2479 632 7 + + PROPN iajs-2479 632 8 pi pi NOUN iajs-2479 632 9 – – PUNCT iajs-2479 632 10 d)]= d)]= NOUN iajs-2479 632 11 2 2 NUM iajs-2479 632 12 t t NOUN iajs-2479 632 13 + + NOUN iajs-2479 632 14 pi pi NOUN iajs-2479 632 15 +2pj +2pj X iajs-2479 632 16 … … PUNCT iajs-2479 632 17 .(e .(e NUM iajs-2479 632 18 ) ) PUNCT iajs-2479 632 19 . . PUNCT iajs-2479 633 1 δij=(c δij=(c NUM iajs-2479 633 2 ) ) PUNCT iajs-2479 633 3 – – PUNCT iajs-2479 633 4 ( ( PUNCT iajs-2479 633 5 e)= e)= ADJ iajs-2479 633 6 pi pi NOUN iajs-2479 633 7 – – PUNCT iajs-2479 633 8 pj pj PROPN iajs-2479 633 9 ≤ ≤ PROPN iajs-2479 633 10 0 0 NUM iajs-2479 633 11 , , PUNCT iajs-2479 633 12 then then ADV iajs-2479 633 13 job job NOUN iajs-2479 633 14 i i PRON iajs-2479 633 15 precede precede VERB iajs-2479 633 16 j. j. PROPN iajs-2479 633 17 second second PROPN iajs-2479 633 18 : : PUNCT iajs-2479 633 19 if if SCONJ iajs-2479 633 20 r r NOUN iajs-2479 633 21 > > X iajs-2479 633 22 t t PROPN iajs-2479 633 23 , , PUNCT iajs-2479 633 24 then then ADV iajs-2479 633 25 in in ADP iajs-2479 633 26 the the DET iajs-2479 633 27 same same ADJ iajs-2479 633 28 way way NOUN iajs-2479 633 29 above above ADV iajs-2479 633 30 we we PRON iajs-2479 633 31 show show VERB iajs-2479 633 32 that that SCONJ iajs-2479 633 33 the the DET iajs-2479 633 34 theorem theorem NOUN iajs-2479 633 35 is be AUX iajs-2479 633 36 true true ADJ iajs-2479 633 37 ( ( PUNCT iajs-2479 633 38 integral integral ADJ iajs-2479 633 39 ) ) PUNCT iajs-2479 633 40 . . PUNCT iajs-2479 634 1 8 8 X iajs-2479 634 2 . . PUNCT iajs-2479 634 3 computational computational ADJ iajs-2479 634 4 experience experience NOUN iajs-2479 634 5 an an DET iajs-2479 634 6 intensive intensive ADJ iajs-2479 634 7 work work NOUN iajs-2479 634 8 of of ADP iajs-2479 634 9 numerical numerical ADJ iajs-2479 634 10 experimentations experimentation NOUN iajs-2479 634 11 has have AUX iajs-2479 634 12 been be AUX iajs-2479 634 13 performed perform VERB iajs-2479 634 14 subsection subsection NOUN iajs-2479 634 15 ( ( PUNCT iajs-2479 634 16 8.1 8.1 NUM iajs-2479 634 17 ) ) PUNCT iajs-2479 634 18 shows show VERB iajs-2479 634 19 how how SCONJ iajs-2479 634 20 instances instance NOUN iajs-2479 634 21 ( ( PUNCT iajs-2479 634 22 test test NOUN iajs-2479 634 23 problems problem NOUN iajs-2479 634 24 ) ) PUNCT iajs-2479 634 25 can can AUX iajs-2479 634 26 be be AUX iajs-2479 634 27 randomly randomly ADV iajs-2479 634 28 generated generate VERB iajs-2479 634 29 . . PUNCT iajs-2479 635 1 8.1 8.1 NUM iajs-2479 635 2 . . PUNCT iajs-2479 636 1 test test NOUN iajs-2479 636 2 problems problem NOUN iajs-2479 636 3 : : PUNCT iajs-2479 637 1 we we PRON iajs-2479 637 2 created create VERB iajs-2479 637 3 ( ( PUNCT iajs-2479 637 4 10 10 NUM iajs-2479 637 5 ) ) PUNCT iajs-2479 637 6 problems problem NOUN iajs-2479 637 7 randomly randomly ADV iajs-2479 637 8 , , PUNCT iajs-2479 637 9 for for ADP iajs-2479 637 10 each each DET iajs-2479 637 11 problem problem NOUN iajs-2479 637 12 , , PUNCT iajs-2479 637 13 nϵ nϵ X iajs-2479 637 14 { { PUNCT iajs-2479 637 15 5 5 NUM iajs-2479 637 16 , , PUNCT iajs-2479 637 17 … … PUNCT iajs-2479 637 18 , , PUNCT iajs-2479 637 19 16 16 NUM iajs-2479 637 20 } } PUNCT iajs-2479 637 21 jobs job NOUN iajs-2479 637 22 , , PUNCT iajs-2479 637 23 and and CCONJ iajs-2479 637 24 for for ADP iajs-2479 637 25 each each DET iajs-2479 637 26 job job NOUN iajs-2479 637 27 j j PROPN iajs-2479 637 28 has have VERB iajs-2479 637 29 the the DET iajs-2479 637 30 following follow VERB iajs-2479 637 31 data datum NOUN iajs-2479 637 32 : : PUNCT iajs-2479 637 33   X iajs-2479 637 34 the the DET iajs-2479 637 35 processing processing NOUN iajs-2479 637 36 time time NOUN iajs-2479 637 37 pj pj PROPN iajs-2479 637 38 is be AUX iajs-2479 637 39 generated generate VERB iajs-2479 637 40 from from ADP iajs-2479 637 41 the the DET iajs-2479 637 42 discrete discrete ADJ iajs-2479 637 43 uniform uniform ADJ iajs-2479 637 44 distribution distribution NOUN iajs-2479 637 45 [ [ X iajs-2479 637 46 1,10 1,10 NUM iajs-2479 637 47 ] ] PUNCT iajs-2479 637 48 . . PUNCT iajs-2479 638 1   PROPN iajs-2479 638 2 integer integer PROPN iajs-2479 638 3 due due ADJ iajs-2479 638 4 date date NOUN iajs-2479 638 5 dj dj NOUN iajs-2479 638 6 is be AUX iajs-2479 638 7 generated generate VERB iajs-2479 638 8 from from ADP iajs-2479 638 9 the the DET iajs-2479 638 10 uniform uniform ADJ iajs-2479 638 11 distribution distribution NOUN iajs-2479 638 12 [ [ X iajs-2479 638 13 1 1 NUM iajs-2479 638 14 , , PUNCT iajs-2479 638 15 ( ( PUNCT iajs-2479 638 16 1 1 NUM iajs-2479 638 17 - - PUNCT iajs-2479 638 18 tf+rrdd/2)sp tf+rrdd/2)sp PRON iajs-2479 638 19 ] ] PUNCT iajs-2479 638 20 , , PUNCT iajs-2479 638 21 where where SCONJ iajs-2479 638 22 sp= sp= NOUN iajs-2479 638 23 ∑ ∑ SYM iajs-2479 638 24 𝑝 𝑝 NOUN iajs-2479 638 25 , , PUNCT iajs-2479 638 26 ( ( PUNCT iajs-2479 638 27 tf tf X iajs-2479 638 28 ) ) PUNCT iajs-2479 638 29 is be AUX iajs-2479 638 30 the the DET iajs-2479 638 31 " " PUNCT iajs-2479 638 32 tardiness tardiness ADJ iajs-2479 638 33 factor factor NOUN iajs-2479 638 34 " " PUNCT iajs-2479 638 35 , , PUNCT iajs-2479 638 36 and and CCONJ iajs-2479 638 37 ( ( PUNCT iajs-2479 638 38 rrdd rrdd NOUN iajs-2479 638 39 ) ) PUNCT iajs-2479 638 40 is be AUX iajs-2479 638 41 the the DET iajs-2479 638 42 " " PUNCT iajs-2479 638 43 relative relative ADJ iajs-2479 638 44 range range NOUN iajs-2479 638 45 of of ADP iajs-2479 638 46 the the DET iajs-2479 638 47 due due ADJ iajs-2479 638 48 dates date NOUN iajs-2479 638 49 " " PUNCT iajs-2479 638 50 . . PUNCT iajs-2479 639 1 for for ADP iajs-2479 639 2 the the DET iajs-2479 639 3 two two NUM iajs-2479 639 4 parameters parameter NOUN iajs-2479 639 5 ( ( PUNCT iajs-2479 639 6 tf tf PROPN iajs-2479 639 7 ) ) PUNCT iajs-2479 639 8 and and CCONJ iajs-2479 639 9 ( ( PUNCT iajs-2479 639 10 rrdd rrdd NOUN iajs-2479 639 11 ) ) PUNCT iajs-2479 639 12 , , PUNCT iajs-2479 639 13 the the DET iajs-2479 639 14 values value NOUN iajs-2479 639 15 ( ( PUNCT iajs-2479 639 16 0.2 0.2 NUM iajs-2479 639 17 , , PUNCT iajs-2479 639 18 0.4 0.4 NUM iajs-2479 639 19 , , PUNCT iajs-2479 639 20 0.6 0.6 NUM iajs-2479 639 21 , , PUNCT iajs-2479 639 22 0.8 0.8 NUM iajs-2479 639 23 , , PUNCT iajs-2479 639 24 1.0 1.0 NUM iajs-2479 639 25 ) ) PUNCT iajs-2479 639 26 are be AUX iajs-2479 639 27 considered consider VERB iajs-2479 639 28 . . PUNCT iajs-2479 640 1   PRON iajs-2479 640 2 integer integer PROPN iajs-2479 640 3 release release PROPN iajs-2479 640 4 date date NOUN iajs-2479 640 5 rj rj PROPN iajs-2479 640 6 is be AUX iajs-2479 640 7 generated generate VERB iajs-2479 640 8 for for ADP iajs-2479 640 9 each each DET iajs-2479 640 10 j j NOUN iajs-2479 640 11 from from ADP iajs-2479 640 12 the the DET iajs-2479 640 13 uniform uniform ADJ iajs-2479 640 14 distribution distribution NOUN iajs-2479 640 15 [ [ X iajs-2479 640 16 1 1 NUM iajs-2479 640 17 , , PUNCT iajs-2479 640 18 5 5 NUM iajs-2479 640 19 ] ] PUNCT iajs-2479 640 20 . . PUNCT iajs-2479 641 1 8.2 8.2 NUM iajs-2479 641 2 . . PUNCT iajs-2479 641 3 computational computational ADJ iajs-2479 641 4 experience experience NOUN iajs-2479 641 5 with with ADP iajs-2479 641 6 the the DET iajs-2479 641 7 ( ( PUNCT iajs-2479 641 8 ub ub PROPN iajs-2479 641 9 ) ) PUNCT iajs-2479 641 10 and and CCONJ iajs-2479 641 11 ( ( PUNCT iajs-2479 641 12 lb lb NOUN iajs-2479 641 13 ) ) PUNCT iajs-2479 641 14 of of ADP iajs-2479 641 15 ( ( PUNCT iajs-2479 641 16 b&b b&b PROPN iajs-2479 641 17 ) ) PUNCT iajs-2479 641 18 algorithm algorithm NOUN iajs-2479 641 19 the the DET iajs-2479 641 20 ( ( PUNCT iajs-2479 641 21 b&b b&b PROPN iajs-2479 641 22 ) ) PUNCT iajs-2479 641 23 algorithm algorithm NOUN iajs-2479 641 24 was be AUX iajs-2479 641 25 tested test VERB iajs-2479 641 26 by by ADP iajs-2479 641 27 coding code VERB iajs-2479 641 28 in in ADP iajs-2479 641 29 ( ( PUNCT iajs-2479 641 30 mat mat NOUN iajs-2479 641 31 lab lab NOUN iajs-2479 641 32 2018 2018 NUM iajs-2479 641 33 ) ) PUNCT iajs-2479 641 34 and and CCONJ iajs-2479 641 35 running run VERB iajs-2479 641 36 on on ADP iajs-2479 641 37 a a DET iajs-2479 641 38 personal personal ADJ iajs-2479 641 39 computer computer NOUN iajs-2479 641 40 dell dell NOUN iajs-2479 641 41 core core NOUN iajs-2479 641 42 i7 i7 NOUN iajs-2479 641 43 with with ADP iajs-2479 641 44 ram ram NOUN iajs-2479 641 45 8 8 NUM iajs-2479 641 46 gb gb NOUN iajs-2479 641 47 . . PUNCT iajs-2479 642 1 tables table NOUN iajs-2479 642 2 1 1 NUM iajs-2479 642 3 , , PUNCT iajs-2479 642 4 2 2 NUM iajs-2479 642 5 . . PUNCT iajs-2479 642 6 shows show VERB iajs-2479 642 7 the the DET iajs-2479 642 8 results result NOUN iajs-2479 642 9 to to AUX iajs-2479 642 10 problem problem NOUN iajs-2479 642 11 ( ( PUNCT iajs-2479 642 12 p p NOUN iajs-2479 642 13 ) ) PUNCT iajs-2479 642 14 obtained obtain VERB iajs-2479 642 15 by by ADP iajs-2479 642 16 ( ( PUNCT iajs-2479 642 17 b&b b&b PROPN iajs-2479 642 18 ) ) PUNCT iajs-2479 642 19 algorithm algorithm NOUN iajs-2479 642 20 , , PUNCT iajs-2479 642 21 when when SCONJ iajs-2479 642 22 n n DET iajs-2479 642 23 ϵ{5,6, ϵ{5,6, NOUN iajs-2479 642 24 … … PUNCT iajs-2479 642 25 ,10 ,10 PUNCT iajs-2479 642 26 } } PUNCT iajs-2479 642 27 and and CCONJ iajs-2479 642 28 nϵ{11,12, nϵ{11,12, NOUN iajs-2479 642 29 … … PROPN iajs-2479 642 30 ,16 ,16 PUNCT iajs-2479 642 31 } } PUNCT iajs-2479 642 32 respectively respectively ADV iajs-2479 642 33 . . PUNCT iajs-2479 643 1 the the DET iajs-2479 643 2 first first ADJ iajs-2479 643 3 column column NOUN iajs-2479 643 4 ( ( PUNCT iajs-2479 643 5 n n CCONJ iajs-2479 643 6 ) ) PUNCT iajs-2479 643 7 indicate indicate VERB iajs-2479 643 8 to to ADP iajs-2479 643 9 the the DET iajs-2479 643 10 number number NOUN iajs-2479 643 11 of of ADP iajs-2479 643 12 jobs job NOUN iajs-2479 643 13 , , PUNCT iajs-2479 643 14 the the DET iajs-2479 643 15 second second ADJ iajs-2479 643 16 column column NOUN iajs-2479 643 17 ( ( PUNCT iajs-2479 643 18 ex ex NOUN iajs-2479 643 19 ) ) PUNCT iajs-2479 643 20 indicate indicate VERB iajs-2479 643 21 to to ADP iajs-2479 643 22 the the DET iajs-2479 643 23 number number NOUN iajs-2479 643 24 of of ADP iajs-2479 643 25 examples example NOUN iajs-2479 643 26 for for ADP iajs-2479 643 27 each each DET iajs-2479 643 28 instance instance NOUN iajs-2479 643 29 n n CCONJ iajs-2479 643 30 , , PUNCT iajs-2479 643 31 the the DET iajs-2479 643 32 third third ADJ iajs-2479 643 33 column column NOUN iajs-2479 643 34 ( ( PUNCT iajs-2479 643 35 cem cem NOUN iajs-2479 643 36 ) ) PUNCT iajs-2479 643 37 complete complete ADJ iajs-2479 643 38 enumeration enumeration NOUN iajs-2479 643 39 method method NOUN iajs-2479 643 40 only only ADV iajs-2479 643 41 in in ADP iajs-2479 643 42 tables table NOUN iajs-2479 643 43 1 1 NUM iajs-2479 643 44 . . PUNCT iajs-2479 644 1 the the DET iajs-2479 644 2 fourth fourth ADJ iajs-2479 644 3 column column NOUN iajs-2479 644 4 ( ( PUNCT iajs-2479 644 5 optimal optimal ADJ iajs-2479 644 6 ) ) PUNCT iajs-2479 644 7     SPACE iajs-2479 644 8 indicate indicate VERB iajs-2479 644 9 to to ADP iajs-2479 644 10 the the DET iajs-2479 644 11 optimal optimal ADJ iajs-2479 644 12 solution solution NOUN iajs-2479 644 13 obtained obtain VERB iajs-2479 644 14 by(b&b by(b&b PRON iajs-2479 644 15 ) ) PUNCT iajs-2479 644 16 method method NOUN iajs-2479 644 17 , , PUNCT iajs-2479 644 18 the the DET iajs-2479 644 19 fifth fifth ADJ iajs-2479 644 20 and and CCONJ iajs-2479 644 21 sixth sixth ADJ iajs-2479 644 22 columns column NOUN iajs-2479 644 23 indicate indicate VERB iajs-2479 644 24 to to PART iajs-2479 644 25 upper upper ADJ iajs-2479 644 26 bound bind VERB iajs-2479 644 27 ( ( PUNCT iajs-2479 644 28 ub ub ADJ iajs-2479 644 29 ) ) PUNCT iajs-2479 644 30 and and CCONJ iajs-2479 644 31 initial initial ADJ iajs-2479 644 32 lower low ADJ iajs-2479 644 33 bound(ilb bound(ilb NOUN iajs-2479 644 34 ) ) PUNCT iajs-2479 644 35 respectively respectively ADV iajs-2479 644 36 , , PUNCT iajs-2479 644 37 and and CCONJ iajs-2479 644 38 the the DET iajs-2479 644 39 other other ADJ iajs-2479 644 40 columns column NOUN iajs-2479 644 41 ( ( PUNCT iajs-2479 644 42 non non ADJ iajs-2479 644 43 ) ) PUNCT iajs-2479 644 44 are be AUX iajs-2479 644 45     SPACE iajs-2479 644 46 indicate indicate VERB iajs-2479 644 47 to to PART iajs-2479 644 48 number number NOUN iajs-2479 644 49 of of ADP iajs-2479 644 50 nodes node NOUN iajs-2479 644 51 , , PUNCT iajs-2479 644 52 time time NOUN iajs-2479 644 53 ( ( PUNCT iajs-2479 644 54 cem cem NOUN iajs-2479 644 55 ) ) PUNCT iajs-2479 644 56 , , PUNCT iajs-2479 644 57 and and CCONJ iajs-2479 644 58 time(b&b time(b&b NUM iajs-2479 644 59 ) ) PUNCT iajs-2479 644 60 , , PUNCT iajs-2479 644 61 finally finally ADV iajs-2479 644 62 , , PUNCT iajs-2479 644 63 column column NOUN iajs-2479 644 64 ( ( PUNCT iajs-2479 644 65 status status NOUN iajs-2479 644 66 ) ) PUNCT iajs-2479 644 67 indicate indicate VERB iajs-2479 644 68 to to ADP iajs-2479 644 69 the the DET iajs-2479 644 70 problem problem NOUN iajs-2479 644 71 solved solve VERB iajs-2479 644 72 ( ( PUNCT iajs-2479 644 73 0 0 NUM iajs-2479 644 74 ) ) PUNCT iajs-2479 644 75 or or CCONJ iajs-2479 644 76 not not PART iajs-2479 644 77 ( ( PUNCT iajs-2479 644 78 1 1 NUM iajs-2479 644 79 ) ) PUNCT iajs-2479 644 80 . . PUNCT iajs-2479 645 1 the the DET iajs-2479 645 2 symbols symbol NOUN iajs-2479 645 3 ( ( PUNCT iajs-2479 645 4 * * PUNCT iajs-2479 645 5 ) ) PUNCT iajs-2479 645 6 indicate indicate VERB iajs-2479 645 7 to to ADP iajs-2479 645 8 the the DET iajs-2479 645 9 ( ( PUNCT iajs-2479 645 10 ub ub PROPN iajs-2479 645 11 ) ) PUNCT iajs-2479 645 12 given give VERB iajs-2479 645 13 an an DET iajs-2479 645 14 optimal optimal ADJ iajs-2479 645 15 value value NOUN iajs-2479 645 16 and and CCONJ iajs-2479 645 17 ( ( PUNCT iajs-2479 645 18 * * PUNCT iajs-2479 645 19 * * PUNCT iajs-2479 645 20 ) ) PUNCT iajs-2479 645 21 indicate indicate VERB iajs-2479 645 22 to to ADP iajs-2479 645 23 the the DET iajs-2479 645 24 ( ( PUNCT iajs-2479 645 25 ilb ilb NOUN iajs-2479 645 26 ) ) PUNCT iajs-2479 645 27 given give VERB iajs-2479 645 28 an an DET iajs-2479 645 29 optimal optimal ADJ iajs-2479 645 30 value value NOUN iajs-2479 645 31 . . PUNCT iajs-2479 646 1 the the DET iajs-2479 646 2 ( ( PUNCT iajs-2479 646 3 b&b b&b PROPN iajs-2479 646 4 ) ) PUNCT iajs-2479 646 5 algorithm algorithm NOUN iajs-2479 646 6 was be AUX iajs-2479 646 7 stopped stop VERB iajs-2479 646 8 when when SCONJ iajs-2479 646 9 the the DET iajs-2479 646 10 sum sum NOUN iajs-2479 646 11 of of ADP iajs-2479 646 12 ( ( PUNCT iajs-2479 646 13 status status NOUN iajs-2479 646 14 column column NOUN iajs-2479 646 15 ≥3 ≥3 PROPN iajs-2479 646 16 ) ) PUNCT iajs-2479 646 17 . . PUNCT iajs-2479 647 1 a a DET iajs-2479 647 2 condition condition NOUN iajs-2479 647 3 for for ADP iajs-2479 647 4 stopping stop VERB iajs-2479 647 5 the the DET iajs-2479 647 6 ( ( PUNCT iajs-2479 647 7 b&b b&b PROPN iajs-2479 647 8 ) ) PUNCT iajs-2479 647 9 algorithm algorithm NOUN iajs-2479 647 10 was be AUX iajs-2479 647 11 determined determine VERB iajs-2479 647 12 and and CCONJ iajs-2479 647 13 considering consider VERB iajs-2479 647 14 that that SCONJ iajs-2479 647 15 the the DET iajs-2479 647 16 problem problem NOUN iajs-2479 647 17 is be AUX iajs-2479 647 18 unsolved unsolved ADJ iajs-2479 647 19 ( ( PUNCT iajs-2479 647 20 state state NOUN iajs-2479 647 21 is be AUX iajs-2479 647 22 1 1 NUM iajs-2479 647 23 ) ) PUNCT iajs-2479 647 24 . . PUNCT iajs-2479 648 1 here here ADV iajs-2479 648 2 , , PUNCT iajs-2479 648 3 the the DET iajs-2479 648 4 ( ( PUNCT iajs-2479 648 5 b&b b&b PROPN iajs-2479 648 6 ) ) PUNCT iajs-2479 648 7 algorithm algorithm NOUN iajs-2479 648 8 is be AUX iajs-2479 648 9 stopped stop VERB iajs-2479 648 10 , , PUNCT iajs-2479 648 11 after after ADP iajs-2479 648 12 ( ( PUNCT iajs-2479 648 13 1800 1800 NUM iajs-2479 648 14 ) ) PUNCT iajs-2479 648 15 second second NOUN iajs-2479 648 16 . . PUNCT iajs-2479 649 1 from from ADP iajs-2479 649 2 tables table NOUN iajs-2479 649 3 1 1 NUM iajs-2479 649 4 , , PUNCT iajs-2479 649 5 2 2 NUM iajs-2479 649 6 . . X iajs-2479 649 7 we we PRON iajs-2479 649 8 are be AUX iajs-2479 649 9 noticed notice VERB iajs-2479 649 10 that that SCONJ iajs-2479 649 11 the the DET iajs-2479 649 12 six six NUM iajs-2479 649 13 heuristic heuristic NOUN iajs-2479 649 14 of of ADP iajs-2479 649 15 upper upper ADJ iajs-2479 649 16 bound bind VERB iajs-2479 649 17 given give VERB iajs-2479 649 18 good good ADJ iajs-2479 649 19 results result NOUN iajs-2479 649 20 , , PUNCT iajs-2479 649 21 it it PRON iajs-2479 649 22 gives give VERB iajs-2479 649 23 the the DET iajs-2479 649 24 value value NOUN iajs-2479 649 25 for for ADP iajs-2479 649 26 objective objective ADJ iajs-2479 649 27 function function NOUN iajs-2479 649 28 equal equal ADJ iajs-2479 649 29 to to ADP iajs-2479 649 30 optimal optimal ADJ iajs-2479 649 31 or or CCONJ iajs-2479 649 32 near near ADP iajs-2479 649 33 optimal optimal ADJ iajs-2479 649 34 value value NOUN iajs-2479 649 35 . . PUNCT iajs-2479 650 1 we we PRON iajs-2479 650 2 also also ADV iajs-2479 650 3 have have VERB iajs-2479 650 4 two two NUM iajs-2479 650 5 other other ADJ iajs-2479 650 6 tables table NOUN iajs-2479 650 7 3 3 NUM iajs-2479 650 8 , , PUNCT iajs-2479 650 9 4 4 NUM iajs-2479 650 10 . . X iajs-2479 650 11 are be AUX iajs-2479 650 12 the the DET iajs-2479 650 13 summary summary NOUN iajs-2479 650 14 of of ADP iajs-2479 650 15 the the DET iajs-2479 650 16 two two NUM iajs-2479 650 17 previous previous ADJ iajs-2479 650 18 tables table NOUN iajs-2479 650 19 1 1 NUM iajs-2479 650 20 , , PUNCT iajs-2479 650 21 2 2 NUM iajs-2479 650 22 . . PUNCT iajs-2479 650 23 that that PRON iajs-2479 650 24 show show VERB iajs-2479 650 25 the the DET iajs-2479 650 26 average average ADJ iajs-2479 650 27 computational computational ADJ iajs-2479 650 28 time time NOUN iajs-2479 650 29 of of ADP iajs-2479 650 30 ( ( PUNCT iajs-2479 650 31 cem cem NOUN iajs-2479 650 32 ) ) PUNCT iajs-2479 650 33 and and CCONJ iajs-2479 650 34 ( ( PUNCT iajs-2479 650 35 b&b b&b PROPN iajs-2479 650 36 ) ) PUNCT iajs-2479 650 37 , , PUNCT iajs-2479 650 38 the the DET iajs-2479 650 39 average average NOUN iajs-2479 650 40 of of ADP iajs-2479 650 41 nodes node NOUN iajs-2479 650 42 , , PUNCT iajs-2479 650 43 and and CCONJ iajs-2479 650 44 the the DET iajs-2479 650 45 unsolved unsolved ADJ iajs-2479 650 46 problems problem NOUN iajs-2479 650 47 . . PUNCT iajs-2479 650 48     SPACE iajs-2479 651 1 153 153 NUM iajs-2479 651 2     SPACE iajs-2479 651 3 ibn ibn PROPN iajs-2479 651 4 al al PROPN iajs-2479 651 5 - - PUNCT iajs-2479 651 6 haitham haitham PROPN iajs-2479 651 7 jour jour X iajs-2479 651 8 . . PROPN iajs-2479 651 9 for for ADP iajs-2479 651 10 pure pure ADJ iajs-2479 651 11 & & CCONJ iajs-2479 651 12 appl appl PROPN iajs-2479 651 13 . . PUNCT iajs-2479 652 1 sci sci PROPN iajs-2479 652 2 . . PROPN iajs-2479 653 1 33 33 NUM iajs-2479 653 2 ( ( PUNCT iajs-2479 653 3 3 3 NUM iajs-2479 653 4 ) ) PUNCT iajs-2479 653 5 2020 2020 NUM iajs-2479 653 6 table table NOUN iajs-2479 653 7 1 1 NUM iajs-2479 653 8 . . PUNCT iajs-2479 654 1 the the DET iajs-2479 654 2 performance performance NOUN iajs-2479 654 3 of of ADP iajs-2479 654 4 cem cem NOUN iajs-2479 654 5 , , PUNCT iajs-2479 654 6 optimal optimal ADJ iajs-2479 654 7 of of ADP iajs-2479 654 8 ( ( PUNCT iajs-2479 654 9 b&b b&b PROPN iajs-2479 654 10 ) ) PUNCT iajs-2479 654 11 , , PUNCT iajs-2479 654 12 ( ( PUNCT iajs-2479 654 13 ub ub ADP iajs-2479 654 14 ) ) PUNCT iajs-2479 654 15 , , PUNCT iajs-2479 654 16 ( ( PUNCT iajs-2479 654 17 ilb ilb PROPN iajs-2479 654 18 ) ) PUNCT iajs-2479 654 19 , , PUNCT iajs-2479 654 20 number number NOUN iajs-2479 654 21 of of ADP iajs-2479 654 22 node node NOUN iajs-2479 654 23 and and CCONJ iajs-2479 654 24 ( ( PUNCT iajs-2479 654 25 cpu cpu PROPN iajs-2479 654 26 ) ) PUNCT iajs-2479 654 27 in in ADP iajs-2479 654 28 seconds second NOUN iajs-2479 654 29 of of ADP iajs-2479 654 30 ( ( PUNCT iajs-2479 654 31 cem cem NOUN iajs-2479 654 32 ) ) PUNCT iajs-2479 654 33 and and CCONJ iajs-2479 654 34 ( ( PUNCT iajs-2479 654 35 b&b b&b PROPN iajs-2479 654 36 ) ) PUNCT iajs-2479 654 37 , , PUNCT iajs-2479 654 38 for for ADP iajs-2479 654 39 n n NOUN iajs-2479 654 40 = = SYM iajs-2479 654 41 ( ( PUNCT iajs-2479 654 42 5,7,10 5,7,10 PROPN iajs-2479 654 43 ) ) PUNCT iajs-2479 654 44 . . PUNCT iajs-2479 655 1 n n PRON iajs-2479 655 2 ex ex NOUN iajs-2479 655 3 cem cem NOUN iajs-2479 655 4 b&b b&b PROPN iajs-2479 655 5 ub ub PUNCT iajs-2479 655 6 lb lb NUM iajs-2479 655 7 non non ADJ iajs-2479 655 8 t.(cem t.(cem NOUN iajs-2479 655 9 ) ) PUNCT iajs-2479 655 10 t.(b&b t.(b&b NOUN iajs-2479 655 11 ) ) PUNCT iajs-2479 655 12 status status NOUN iajs-2479 655 13 1 1 NUM iajs-2479 655 14 163 163 NUM iajs-2479 655 15 163 163 NUM iajs-2479 655 16 166 166 NUM iajs-2479 655 17 123 123 NUM iajs-2479 655 18 41 41 NUM iajs-2479 655 19 0.0217488 0.0217488 NUM iajs-2479 655 20 0.110176 0.110176 NUM iajs-2479 655 21 0 0 NUM iajs-2479 655 22 2 2 NUM iajs-2479 655 23 160 160 NUM iajs-2479 655 24 160 160 NUM iajs-2479 655 25 160 160 NUM iajs-2479 655 26 * * SYM iajs-2479 655 27 102 102 NUM iajs-2479 655 28 51 51 NUM iajs-2479 655 29 0.0040399 0.0040399 NUM iajs-2479 655 30 0.025487 0.025487 NUM iajs-2479 655 31 0 0 NUM iajs-2479 655 32 3 3 NUM iajs-2479 655 33 207 207 NUM iajs-2479 655 34 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PROPN iajs-2479 659 1 for for ADP iajs-2479 659 2 pure pure ADJ iajs-2479 659 3 & & CCONJ iajs-2479 659 4 appl appl PROPN iajs-2479 659 5 . . PUNCT iajs-2479 660 1 sci sci PROPN iajs-2479 660 2 . . PROPN iajs-2479 661 1 33 33 NUM iajs-2479 661 2 ( ( PUNCT iajs-2479 661 3 3 3 NUM iajs-2479 661 4 ) ) PUNCT iajs-2479 661 5 2020 2020 NUM iajs-2479 661 6 table table NOUN iajs-2479 661 7 2 2 NUM iajs-2479 661 8 . . PUNCT iajs-2479 662 1 the the DET iajs-2479 662 2 performance performance NOUN iajs-2479 662 3 of of ADP iajs-2479 662 4 optimal optimal ADJ iajs-2479 662 5 of of ADP iajs-2479 662 6 ( ( PUNCT iajs-2479 662 7 b&b b&b PROPN iajs-2479 662 8 ) ) PUNCT iajs-2479 662 9 , , PUNCT iajs-2479 662 10 ( ( PUNCT iajs-2479 662 11 ub ub ADP iajs-2479 662 12 ) ) PUNCT iajs-2479 662 13 , , PUNCT iajs-2479 662 14 ( ( PUNCT iajs-2479 662 15 ilb ilb PROPN iajs-2479 662 16 ) ) PUNCT iajs-2479 662 17 , , PUNCT iajs-2479 662 18 number number NOUN iajs-2479 662 19 of of ADP iajs-2479 662 20 node node NOUN iajs-2479 662 21 and and CCONJ iajs-2479 662 22 ( ( PUNCT iajs-2479 662 23 cpu cpu PROPN iajs-2479 662 24 ) ) PUNCT iajs-2479 662 25 in in ADP iajs-2479 662 26 seconds second NOUN iajs-2479 662 27 of of ADP iajs-2479 662 28 ( ( PUNCT iajs-2479 662 29 b&b b&b PROPN iajs-2479 662 30 ) ) PUNCT iajs-2479 662 31 for for ADP iajs-2479 662 32 n=(11 n=(11 NOUN iajs-2479 662 33 , , PUNCT iajs-2479 662 34 13 13 NUM iajs-2479 662 35 , , PUNCT iajs-2479 662 36 16 16 NUM iajs-2479 662 37 ) ) PUNCT iajs-2479 662 38 . . PUNCT iajs-2479 663 1 n n CCONJ iajs-2479 664 1 ex ex PROPN iajs-2479 664 2 b&b b&b PROPN iajs-2479 664 3 ub ub PUNCT iajs-2479 664 4 lb lb PRON iajs-2479 664 5 non non ADJ iajs-2479 664 6 t.(b&b t.(b&b NOUN iajs-2479 664 7 ) ) PUNCT iajs-2479 664 8 status status NOUN iajs-2479 664 9 11 11 NUM iajs-2479 664 10 1 1 NUM iajs-2479 664 11 504 504 NUM iajs-2479 664 12 559 559 NUM iajs-2479 664 13 404 404 NUM iajs-2479 664 14 28164 28164 NUM iajs-2479 664 15 1.798678 1.798678 NUM iajs-2479 664 16 0 0 NUM iajs-2479 664 17 2 2 NUM iajs-2479 664 18 597 597 NUM iajs-2479 664 19 597 597 NUM iajs-2479 664 20 * * NUM iajs-2479 664 21 494 494 NUM iajs-2479 664 22 16666 16666 NUM iajs-2479 664 23 1.1426506 1.1426506 NUM iajs-2479 664 24 0 0 NUM iajs-2479 664 25 3 3 NUM iajs-2479 664 26 412 412 NUM iajs-2479 664 27 412 412 NUM iajs-2479 664 28 * * SYM iajs-2479 664 29 339 339 NUM iajs-2479 664 30 37043 37043 NUM iajs-2479 664 31 2.4015924 2.4015924 NUM iajs-2479 664 32 0 0 NUM iajs-2479 664 33 4 4 NUM 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1800.000598 1800.000598 NUM iajs-2479 666 123 1 1 NUM iajs-2479 666 124 7 7 NUM iajs-2479 666 125 950 950 NUM iajs-2479 666 126 1092 1092 NUM iajs-2479 666 127 836 836 NUM iajs-2479 666 128 8260306 8260306 NUM iajs-2479 666 129 504.8303402 504.8303402 NUM iajs-2479 666 130 0 0 NUM iajs-2479 666 131 8 8 NUM iajs-2479 666 132 1182 1182 NUM iajs-2479 666 133 1183 1183 NUM iajs-2479 666 134 1061 1061 NUM iajs-2479 666 135 23951871 23951871 NUM iajs-2479 667 1 1800.000418 1800.000418 NUM iajs-2479 667 2 1 1 NUM iajs-2479 667 3 9 9 NUM iajs-2479 667 4 1067 1067 NUM iajs-2479 667 5 1086 1086 NUM iajs-2479 667 6 951 951 NUM iajs-2479 667 7 21206817 21206817 NUM iajs-2479 667 8 1800.000022 1800.000022 NOUN iajs-2479 667 9 1 1 NUM iajs-2479 667 10 10 10 NUM iajs-2479 667 11 1004 1004 NUM iajs-2479 667 12 1059 1059 NUM iajs-2479 667 13 879 879 NUM iajs-2479 667 14 20173233 20173233 NUM iajs-2479 667 15 1676.25391 1676.25391 NUM iajs-2479 667 16 0 0 NUM iajs-2479 667 17     SPACE iajs-2479 667 18 155 155 NUM iajs-2479 667 19     SPACE iajs-2479 667 20 ibn ibn PROPN iajs-2479 667 21 al al PROPN iajs-2479 667 22 - - PUNCT iajs-2479 667 23 haitham haitham PROPN iajs-2479 667 24 jour jour X iajs-2479 667 25 . . PROPN iajs-2479 668 1 for for ADP iajs-2479 668 2 pure pure ADJ iajs-2479 668 3 & & CCONJ iajs-2479 668 4 appl appl PROPN iajs-2479 668 5 . . PUNCT iajs-2479 669 1 sci sci PROPN iajs-2479 669 2 . . PROPN iajs-2479 670 1 33 33 NUM iajs-2479 670 2 ( ( PUNCT iajs-2479 670 3 3 3 NUM iajs-2479 670 4 ) ) PUNCT iajs-2479 670 5 2020 2020 NUM iajs-2479 671 1 in in ADP iajs-2479 671 2 the the DET iajs-2479 671 3 tables table NOUN iajs-2479 671 4 1 1 NUM iajs-2479 671 5 , , PUNCT iajs-2479 671 6 2 2 NUM iajs-2479 671 7 . . X iajs-2479 671 8 we we PRON iajs-2479 671 9 have have VERB iajs-2479 671 10 : : PUNCT iajs-2479 671 11 n n NUM iajs-2479 671 12 : : PUNCT iajs-2479 671 13 number number NOUN iajs-2479 671 14 of of ADP iajs-2479 671 15 jobs job NOUN iajs-2479 671 16 . . PUNCT iajs-2479 672 1 ex ex PRON iajs-2479 672 2 : : PUNCT iajs-2479 672 3 example example NOUN iajs-2479 672 4 number number NOUN iajs-2479 672 5 . . PUNCT iajs-2479 673 1 cem cem NOUN iajs-2479 673 2 : : PUNCT iajs-2479 673 3 the the DET iajs-2479 673 4 optimal optimal ADJ iajs-2479 673 5 solution solution NOUN iajs-2479 673 6 obtained obtain VERB iajs-2479 673 7 by by ADP iajs-2479 673 8 ( ( PUNCT iajs-2479 673 9 cem cem NOUN iajs-2479 673 10 ) ) PUNCT iajs-2479 673 11 . . PUNCT iajs-2479 674 1 b&b b&b PROPN iajs-2479 674 2 : : PUNCT iajs-2479 674 3 the the DET iajs-2479 674 4 optimal optimal ADJ iajs-2479 674 5 solution solution NOUN iajs-2479 674 6 obtained obtain VERB iajs-2479 674 7 by by ADP iajs-2479 674 8 ( ( PUNCT iajs-2479 674 9 b&b b&b PROPN iajs-2479 674 10 ) ) PUNCT iajs-2479 674 11 method method NOUN iajs-2479 674 12 . . PUNCT iajs-2479 675 1 ub ub ADP iajs-2479 675 2 : : PUNCT iajs-2479 675 3 the the DET iajs-2479 675 4 upper upper ADJ iajs-2479 675 5 bound bind VERB iajs-2479 675 6 obtained obtain VERB iajs-2479 675 7 from from ADP iajs-2479 675 8 ( ( PUNCT iajs-2479 675 9 section section NOUN iajs-2479 675 10 6.1 6.1 NUM iajs-2479 675 11 ) ) PUNCT iajs-2479 675 12 . . PUNCT iajs-2479 676 1 lb lb X iajs-2479 676 2 : : PUNCT iajs-2479 676 3 the the DET iajs-2479 676 4 lower lower ADV iajs-2479 676 5 bound bind VERB iajs-2479 676 6 obtained obtain VERB iajs-2479 676 7 from from ADP iajs-2479 676 8 ( ( PUNCT iajs-2479 676 9 section section NOUN iajs-2479 676 10 6.2 6.2 NUM iajs-2479 676 11 ) ) PUNCT iajs-2479 676 12 . . PUNCT iajs-2479 677 1 non non ADJ iajs-2479 677 2 : : PUNCT iajs-2479 677 3 number number NOUN iajs-2479 677 4 of of ADP iajs-2479 677 5 nodes node NOUN iajs-2479 677 6 . . PUNCT iajs-2479 678 1 t.cem t.cem ADP iajs-2479 678 2 : : PUNCT iajs-2479 678 3 the the DET iajs-2479 678 4 time time NOUN iajs-2479 678 5 ( ( PUNCT iajs-2479 678 6 in in ADP iajs-2479 678 7 seconds second NOUN iajs-2479 678 8 ) ) PUNCT iajs-2479 678 9 which which PRON iajs-2479 678 10 is be AUX iajs-2479 678 11 required require VERB iajs-2479 678 12 for for ADP iajs-2479 678 13 ( ( PUNCT iajs-2479 678 14 cem cem NOUN iajs-2479 678 15 ) ) PUNCT iajs-2479 678 16 , , PUNCT iajs-2479 678 17 only only ADV iajs-2479 678 18 in in ADP iajs-2479 678 19 table table NOUN iajs-2479 678 20 1 1 NUM iajs-2479 678 21 . . PUNCT iajs-2479 679 1 t.bab t.bab PRON iajs-2479 679 2 : : PUNCT iajs-2479 679 3 the the DET iajs-2479 679 4 time time NOUN iajs-2479 679 5 ( ( PUNCT iajs-2479 679 6 in in ADP iajs-2479 679 7 seconds second NOUN iajs-2479 679 8 ) ) PUNCT iajs-2479 679 9 which which PRON iajs-2479 679 10 is be AUX iajs-2479 679 11 required require VERB iajs-2479 679 12 for for ADP iajs-2479 679 13 ( ( PUNCT iajs-2479 679 14 b&b b&b PROPN iajs-2479 679 15 ) ) PUNCT iajs-2479 679 16 . . PUNCT iajs-2479 680 1 status= status= NOUN iajs-2479 680 2 𝟎 𝟎 NUM iajs-2479 680 3 𝒊𝒇 𝒊𝒇 VERB iajs-2479 680 4 𝒕𝒉𝒆 𝒕𝒉𝒆 NOUN iajs-2479 680 5 𝒑𝒓𝒐𝒃𝒍𝒆𝒎 𝒑𝒓𝒐𝒃𝒍𝒆𝒎 NOUN iajs-2479 681 1 𝒊𝒔 𝒊𝒔 PRON iajs-2479 681 2 𝒔𝒐𝒍𝒗𝒆𝒅 𝒔𝒐𝒍𝒗𝒆𝒅 VERB iajs-2479 681 3 𝟏 𝟏 NUM iajs-2479 681 4 𝒐. 𝒐. NOUN iajs-2479 681 5 𝒘. 𝒘. NOUN iajs-2479 682 1 * * PUNCT iajs-2479 682 2 = = PUNCT iajs-2479 682 3 the the DET iajs-2479 682 4 upper upper ADJ iajs-2479 682 5 bound bind VERB iajs-2479 682 6 givens given NOUN iajs-2479 682 7 the the DET iajs-2479 682 8 optimal optimal ADJ iajs-2479 682 9 value value NOUN iajs-2479 682 10 . . PUNCT iajs-2479 683 1 * * PUNCT iajs-2479 683 2 * * PUNCT iajs-2479 683 3 = = SYM iajs-2479 683 4 the the DET iajs-2479 683 5 ( ( PUNCT iajs-2479 683 6 ilb ilb NOUN iajs-2479 683 7 ) ) PUNCT iajs-2479 683 8 given give VERB iajs-2479 683 9 an an DET iajs-2479 683 10 optimal optimal ADJ iajs-2479 683 11 value value NOUN iajs-2479 683 12 . . PUNCT iajs-2479 684 1 the the DET iajs-2479 684 2 following follow VERB iajs-2479 684 3 tables table NOUN iajs-2479 684 4 summarize summarize VERB iajs-2479 684 5 tables table NOUN iajs-2479 684 6 1 1 NUM iajs-2479 684 7 , , PUNCT iajs-2479 684 8 2 2 NUM iajs-2479 684 9 . . PUNCT iajs-2479 684 10 table table NOUN iajs-2479 684 11 3 3 NUM iajs-2479 684 12 . . PUNCT iajs-2479 685 1 summary summary NOUN iajs-2479 685 2 of of ADP iajs-2479 685 3 the the DET iajs-2479 685 4 table table NOUN iajs-2479 685 5 1 1 NUM iajs-2479 685 6 . . PUNCT iajs-2479 685 7 table table NOUN iajs-2479 685 8 4 4 NUM iajs-2479 685 9 . . PUNCT iajs-2479 686 1 summary summary NOUN iajs-2479 686 2 of of ADP iajs-2479 686 3 the the DET iajs-2479 686 4 table table NOUN iajs-2479 686 5 2 2 NUM iajs-2479 686 6 . . PUNCT iajs-2479 687 1 in in ADP iajs-2479 687 2 table table NOUN iajs-2479 687 3 3 3 NUM iajs-2479 687 4 , , PUNCT iajs-2479 687 5 4 4 NUM iajs-2479 687 6 . . X iajs-2479 688 1 we we PRON iajs-2479 688 2 have have VERB iajs-2479 688 3 : : PUNCT iajs-2479 688 4 n n NUM iajs-2479 688 5 : : PUNCT iajs-2479 688 6 number number VERB iajs-2479 688 7 the the DET iajs-2479 688 8 jobs job NOUN iajs-2479 688 9 . . PUNCT iajs-2479 689 1 av.t av.t PROPN iajs-2479 689 2 . . PUNCT iajs-2479 690 1 ( ( PUNCT iajs-2479 690 2 cem cem NOUN iajs-2479 690 3 ) ) PUNCT iajs-2479 690 4 : : PUNCT iajs-2479 690 5 average average ADJ iajs-2479 690 6 computational computational ADJ iajs-2479 690 7 time time NOUN iajs-2479 690 8 of of ADP iajs-2479 690 9 ( ( PUNCT iajs-2479 690 10 cem cem NOUN iajs-2479 690 11 ) ) PUNCT iajs-2479 690 12 . . PUNCT iajs-2479 691 1 av.t av.t PROPN iajs-2479 691 2 . . PUNCT iajs-2479 692 1 ( ( PUNCT iajs-2479 692 2 b&b):average b&b):average PROPN iajs-2479 692 3 computational computational ADJ iajs-2479 692 4 time time NOUN iajs-2479 692 5 of of ADP iajs-2479 692 6 ( ( PUNCT iajs-2479 692 7 b&b b&b PROPN iajs-2479 692 8 ) ) PUNCT iajs-2479 692 9 . . PUNCT iajs-2479 693 1 uns un NOUN iajs-2479 693 2 . . PUNCT iajs-2479 694 1 p p X iajs-2479 694 2 : : PUNCT iajs-2479 694 3 the the DET iajs-2479 694 4 unsolved unsolved ADJ iajs-2479 694 5 problem problem NOUN iajs-2479 694 6 8 8 NUM iajs-2479 694 7 . . PUNCT iajs-2479 695 1 conclusion conclusion NOUN iajs-2479 695 2 and and CCONJ iajs-2479 695 3 future future ADJ iajs-2479 695 4 work work NOUN iajs-2479 695 5 in in ADP iajs-2479 695 6 this this DET iajs-2479 695 7 paper paper NOUN iajs-2479 696 1 , , PUNCT iajs-2479 696 2 we we PRON iajs-2479 696 3 been been AUX iajs-2479 696 4 developed develop VERB iajs-2479 696 5 exact exact ADJ iajs-2479 696 6 solutions solution NOUN iajs-2479 696 7 for for ADP iajs-2479 696 8 the the DET iajs-2479 696 9 problem problem NOUN iajs-2479 696 10 of of ADP iajs-2479 696 11 scheduling scheduling NOUN iajs-2479 696 12 ( ( PUNCT iajs-2479 696 13 n n CCONJ iajs-2479 696 14 ) ) PUNCT iajs-2479 696 15 jobs job NOUN iajs-2479 696 16 on on ADP iajs-2479 696 17 onemachine onemachine NOUN iajs-2479 696 18 to to PART iajs-2479 696 19 minimize minimize VERB iajs-2479 696 20 the the DET iajs-2479 696 21 sum sum NOUN iajs-2479 696 22 total total ADJ iajs-2479 696 23 completion completion NOUN iajs-2479 696 24 time time NOUN iajs-2479 696 25 , , PUNCT iajs-2479 696 26 total total ADJ iajs-2479 696 27 tardiness tardiness NOUN iajs-2479 696 28 , , PUNCT iajs-2479 696 29 total total ADJ iajs-2479 696 30 earliness earliness NOUN iajs-2479 696 31 , , PUNCT iajs-2479 696 32 number number NOUN iajs-2479 696 33 of of ADP iajs-2479 696 34 tardy tardy ADJ iajs-2479 696 35 jobs job NOUN iajs-2479 696 36 and and CCONJ iajs-2479 696 37 total total ADJ iajs-2479 696 38 late late ADJ iajs-2479 696 39 work work NOUN iajs-2479 696 40 with with ADP iajs-2479 696 41 unequal unequal ADJ iajs-2479 696 42 release release NOUN iajs-2479 696 43 dates date NOUN iajs-2479 696 44 . . 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