id sid tid token lemma pos cana-307 1 1 communications communication NOUN cana-307 1 2 on on ADP cana-307 1 3 applied apply VERB cana-307 1 4 nonlinear nonlinear ADJ cana-307 1 5 analysis analysis NOUN cana-307 1 6 issn issn NOUN cana-307 1 7 : : PUNCT cana-307 1 8 1074 1074 NUM cana-307 1 9 - - PUNCT cana-307 1 10 133x 133x NUM cana-307 1 11 vol vol NOUN cana-307 1 12 30 30 NUM cana-307 1 13 no no NOUN cana-307 1 14 . . NOUN cana-307 1 15 4 4 NUM cana-307 1 16 ( ( PUNCT cana-307 1 17 2023 2023 NUM cana-307 1 18 ) ) PUNCT cana-307 1 19 58 58 NUM cana-307 1 20 https://internationalpubls.com https://internationalpubls.com NUM cana-307 1 21 three three NUM cana-307 1 22 persons person NOUN cana-307 1 23 satisfactory satisfactory ADJ cana-307 1 24 roommates roommate NOUN cana-307 1 25 problem problem VERB cana-307 1 26 with with ADP cana-307 1 27 incomplete incomplete ADJ cana-307 1 28 list list NOUN cana-307 1 29 n. n. NOUN cana-307 1 30 logapriya1 logapriya1 PROPN cana-307 1 31 and and CCONJ cana-307 1 32 t. t. ADJ cana-307 1 33 ramachandran2 ramachandran2 NOUN cana-307 1 34 1department 1department NUM cana-307 1 35 of of ADP cana-307 1 36 mathematics mathematic NOUN cana-307 1 37 , , PUNCT cana-307 1 38 m.v m.v PROPN cana-307 1 39 muthiah muthiah PROPN cana-307 1 40 government government NOUN cana-307 1 41 arts arts PROPN cana-307 1 42 college college PROPN cana-307 1 43 for for ADP cana-307 1 44 women woman NOUN cana-307 1 45 , , PUNCT cana-307 1 46 dindigul dindigul NOUN cana-307 1 47 , , PUNCT cana-307 1 48 tamil tamil PROPN cana-307 1 49 nadu nadu NOUN cana-307 1 50 624001 624001 NUM cana-307 1 51 g g NOUN cana-307 1 52 - - PUNCT cana-307 1 53 mail mail NOUN cana-307 1 54 : : PUNCT cana-307 1 55 logapriya848@gmail.com logapriya848@gmail.com X cana-307 2 1 2department 2department NUM cana-307 2 2 of of ADP cana-307 2 3 mathematics mathematic NOUN cana-307 2 4 , , PUNCT cana-307 2 5 m.v m.v PROPN cana-307 2 6 muthiah muthiah PROPN cana-307 2 7 government government NOUN cana-307 2 8 arts arts PROPN cana-307 2 9 college college PROPN cana-307 2 10 for for ADP cana-307 2 11 women woman NOUN cana-307 2 12 , , PUNCT cana-307 2 13 dindigul dindigul NOUN cana-307 2 14 , , PUNCT cana-307 2 15 tamil tamil PROPN cana-307 2 16 nadu nadu NOUN cana-307 2 17 624001 624001 NUM cana-307 2 18 g g NOUN cana-307 2 19 - - PUNCT cana-307 2 20 mail mail NOUN cana-307 2 21 : : PUNCT cana-307 2 22 yasrams@gmail.com yasrams@gmail.com X cana-307 2 23 article article NOUN cana-307 2 24 history history NOUN cana-307 2 25 : : PUNCT cana-307 2 26 received receive VERB cana-307 2 27 : : PUNCT cana-307 2 28 25 25 NUM cana-307 2 29 - - SYM cana-307 2 30 08 08 NUM cana-307 2 31 - - PUNCT cana-307 2 32 2023 2023 NUM cana-307 2 33 revised revise VERB cana-307 2 34 : : PUNCT cana-307 2 35 28 28 NUM cana-307 2 36 - - SYM cana-307 2 37 09 09 NUM cana-307 2 38 - - PUNCT cana-307 2 39 2023 2023 NUM cana-307 2 40 accepted accept VERB cana-307 2 41 : : PUNCT cana-307 2 42 22 22 NUM cana-307 2 43 - - SYM cana-307 2 44 10 10 NUM cana-307 2 45 - - PUNCT cana-307 2 46 2023 2023 NUM cana-307 2 47 abstract abstract NOUN cana-307 2 48 : : PUNCT cana-307 2 49 the the DET cana-307 2 50 satisfactory satisfactory ADJ cana-307 2 51 roommates roommate NOUN cana-307 2 52 problem problem NOUN cana-307 2 53 ( ( PUNCT cana-307 2 54 sfrp sfrp NOUN cana-307 2 55 ) ) PUNCT cana-307 2 56 is be AUX cana-307 2 57 the the DET cana-307 2 58 problem problem NOUN cana-307 2 59 of of ADP cana-307 2 60 finding find VERB cana-307 2 61 satisfactory satisfactory ADJ cana-307 2 62 matching matching NOUN cana-307 2 63 between between ADP cana-307 2 64 any any DET cana-307 2 65 pair pair NOUN cana-307 2 66 of of ADP cana-307 2 67 roommates roommate NOUN cana-307 2 68 . . PUNCT cana-307 3 1 in in ADP cana-307 3 2 the the DET cana-307 3 3 complete complete ADJ cana-307 3 4 list list NOUN cana-307 3 5 ( ( PUNCT cana-307 3 6 sfrp sfrp NOUN cana-307 3 7 ) ) PUNCT cana-307 3 8 each each DET cana-307 3 9 person person NOUN cana-307 3 10 in in ADP cana-307 3 11 the the DET cana-307 3 12 set set NOUN cana-307 3 13 of of ADP cana-307 3 14 even even ADV cana-307 3 15 cardinality cardinality PROPN cana-307 3 16 2𝑛 2𝑛 PROPN cana-307 3 17 ranks rank VERB cana-307 3 18 the the DET cana-307 3 19 2𝑛 2𝑛 PROPN cana-307 3 20 βˆ’ βˆ’ PROPN cana-307 3 21 1 1 NUM cana-307 3 22 others other NOUN cana-307 3 23 in in ADP cana-307 3 24 order order NOUN cana-307 3 25 of of ADP cana-307 3 26 preference preference NOUN cana-307 3 27 . . PUNCT cana-307 4 1 in in ADP cana-307 4 2 the the DET cana-307 4 3 incomplete incomplete ADJ cana-307 4 4 list list NOUN cana-307 4 5 ( ( PUNCT cana-307 4 6 sfrpi sfrpi PROPN cana-307 4 7 ) ) PUNCT cana-307 4 8 there there PRON cana-307 4 9 is be VERB cana-307 4 10 some some DET cana-307 4 11 member member NOUN cana-307 4 12 in in ADP cana-307 4 13 the the DET cana-307 4 14 group group NOUN cana-307 4 15 prefers prefer VERB cana-307 4 16 less less ADJ cana-307 4 17 than than ADP cana-307 4 18 2𝑛 2𝑛 PROPN cana-307 4 19 βˆ’ βˆ’ PROPN cana-307 4 20 1 1 NUM cana-307 4 21 members member NOUN cana-307 4 22 . . PUNCT cana-307 5 1 there there PRON cana-307 5 2 are be VERB cana-307 5 3 3𝑛 3𝑛 NUM cana-307 5 4 people people NOUN cana-307 5 5 in in ADP cana-307 5 6 this this DET cana-307 5 7 three three NUM cana-307 5 8 persons person NOUN cana-307 5 9 satisfactory satisfactory ADJ cana-307 5 10 roommates roommate NOUN cana-307 5 11 problem problem VERB cana-307 5 12 with with ADP cana-307 5 13 incomplete incomplete ADJ cana-307 5 14 list list NOUN cana-307 5 15 ( ( PUNCT cana-307 5 16 tpsrpi tpsrpi NOUN cana-307 5 17 ) ) PUNCT cana-307 5 18 , , PUNCT cana-307 5 19 and and CCONJ cana-307 5 20 each each DET cana-307 5 21 person person NOUN cana-307 5 22 has have VERB cana-307 5 23 a a DET cana-307 5 24 preference preference NOUN cana-307 5 25 list list NOUN cana-307 5 26 for for ADP cana-307 5 27 their their PRON cana-307 5 28 two two NUM cana-307 5 29 companions companion NOUN cana-307 5 30 . . PUNCT cana-307 6 1 some some DET cana-307 6 2 people people NOUN cana-307 6 3 have have VERB cana-307 6 4 preferences preference NOUN cana-307 6 5 that that PRON cana-307 6 6 are be AUX cana-307 6 7 fewer few ADJ cana-307 6 8 than than ADP cana-307 6 9 3𝑛 3𝑛 NUM cana-307 6 10 βˆ’ βˆ’ NOUN cana-307 6 11 1 1 NUM cana-307 6 12 . . PUNCT cana-307 7 1 a a DET cana-307 7 2 set set NOUN cana-307 7 3 of of ADP cana-307 7 4 triples triple NOUN cana-307 7 5 is be AUX cana-307 7 6 referred refer VERB cana-307 7 7 to to ADP cana-307 7 8 as as ADP cana-307 7 9 a a DET cana-307 7 10 matching matching NOUN cana-307 7 11 . . PUNCT cana-307 8 1 a a DET cana-307 8 2 new new ADJ cana-307 8 3 , , PUNCT cana-307 8 4 complex complex ADJ cana-307 8 5 algorithm algorithm NOUN cana-307 8 6 for for ADP cana-307 8 7 locating locate VERB cana-307 8 8 perfect perfect ADJ cana-307 8 9 triples triple NOUN cana-307 8 10 in in ADP cana-307 8 11 rooms room NOUN cana-307 8 12 is be AUX cana-307 8 13 presented present VERB cana-307 8 14 in in ADP cana-307 8 15 this this DET cana-307 8 16 study study NOUN cana-307 8 17 . . PUNCT cana-307 9 1 keywords keyword NOUN cana-307 9 2 : : PUNCT cana-307 9 3 incomplete incomplete ADJ cana-307 9 4 list list NOUN cana-307 9 5 , , PUNCT cana-307 9 6 preference preference NOUN cana-307 9 7 value value NOUN cana-307 9 8 , , PUNCT cana-307 9 9 satisfactory satisfactory ADJ cana-307 9 10 value value NOUN cana-307 9 11 matrix matrix NOUN cana-307 9 12 , , PUNCT cana-307 9 13 perfect perfect ADJ cana-307 9 14 matching matching NOUN cana-307 9 15 , , PUNCT cana-307 9 16 three three NUM cana-307 9 17 person person NOUN cana-307 9 18 rooms room NOUN cana-307 9 19 , , PUNCT cana-307 9 20 modified modify VERB cana-307 9 21 satisfactory satisfactory ADJ cana-307 9 22 value value NOUN cana-307 9 23 matrix matrix NOUN cana-307 9 24 . . PUNCT cana-307 10 1 1 1 X cana-307 10 2 . . X cana-307 10 3 introduction introduction NOUN cana-307 10 4 the the DET cana-307 10 5 stable stable ADJ cana-307 10 6 marriage marriage NOUN cana-307 10 7 with with ADP cana-307 10 8 incomplete incomplete ADJ cana-307 10 9 preference preference NOUN cana-307 10 10 lists list NOUN cana-307 10 11 ( ( PUNCT cana-307 10 12 smi smi PROPN cana-307 10 13 ) ) PUNCT cana-307 10 14 is be AUX cana-307 10 15 a a DET cana-307 10 16 generalization generalization NOUN cana-307 10 17 of of ADP cana-307 10 18 the the DET cana-307 10 19 sm sm PROPN cana-307 10 20 . . PUNCT cana-307 11 1 in in ADP cana-307 11 2 the the DET cana-307 11 3 event event NOUN cana-307 11 4 that that PRON cana-307 11 5 an an DET cana-307 11 6 individual individual NOUN cana-307 11 7 decides decide VERB cana-307 11 8 that that PRON cana-307 11 9 one one NUM cana-307 11 10 or or CCONJ cana-307 11 11 more more ADJ cana-307 11 12 members member NOUN cana-307 11 13 of of ADP cana-307 11 14 the the DET cana-307 11 15 set set NOUN cana-307 11 16 are be AUX cana-307 11 17 not not PART cana-307 11 18 suitable suitable ADJ cana-307 11 19 as as ADP cana-307 11 20 a a DET cana-307 11 21 mate mate NOUN cana-307 11 22 , , PUNCT cana-307 11 23 those those DET cana-307 11 24 individuals individual NOUN cana-307 11 25 are be AUX cana-307 11 26 removed remove VERB cana-307 11 27 from from ADP cana-307 11 28 their their PRON cana-307 11 29 list list NOUN cana-307 11 30 of of ADP cana-307 11 31 preferences preference NOUN cana-307 11 32 , , PUNCT cana-307 11 33 resulting result VERB cana-307 11 34 in in ADP cana-307 11 35 an an DET cana-307 11 36 incomplete incomplete ADJ cana-307 11 37 preference preference NOUN cana-307 11 38 list list NOUN cana-307 11 39 . . PUNCT cana-307 12 1 the the DET cana-307 12 2 preferences preference NOUN cana-307 12 3 of of ADP cana-307 12 4 agents agent NOUN cana-307 12 5 over over ADP cana-307 12 6 other other ADJ cana-307 12 7 agents agent NOUN cana-307 12 8 as as ADP cana-307 12 9 roommates roommate NOUN cana-307 12 10 , , PUNCT cana-307 12 11 where where SCONJ cana-307 12 12 the the DET cana-307 12 13 preferences preference NOUN cana-307 12 14 may may AUX cana-307 12 15 have have VERB cana-307 12 16 ties tie NOUN cana-307 12 17 or or CCONJ cana-307 12 18 be be AUX cana-307 12 19 incomplete incomplete ADJ cana-307 12 20 , , PUNCT cana-307 12 21 characterize characterize VERB cana-307 12 22 the the DET cana-307 12 23 stable stable ADJ cana-307 12 24 roommates roommate NOUN cana-307 12 25 problem problem VERB cana-307 12 26 with with ADP cana-307 12 27 ties tie NOUN cana-307 12 28 and and CCONJ cana-307 12 29 incomplete incomplete ADJ cana-307 12 30 lists list NOUN cana-307 12 31 ( ( PUNCT cana-307 12 32 srti srti PROPN cana-307 12 33 ) ) PUNCT cana-307 12 34 , , PUNCT cana-307 12 35 a a DET cana-307 12 36 matching matching NOUN cana-307 12 37 problem problem NOUN cana-307 12 38 . . PUNCT cana-307 13 1 the the DET cana-307 13 2 analysis analysis NOUN cana-307 13 3 was be AUX cana-307 13 4 further far ADV cana-307 13 5 developed develop VERB cana-307 13 6 by by ADP cana-307 13 7 brio brio PROPN cana-307 13 8 et et PROPN cana-307 13 9 al al PROPN cana-307 13 10 . . PUNCT cana-307 14 1 [ [ X cana-307 14 2 1 1 X cana-307 14 3 ] ] PUNCT cana-307 14 4 to to PART cana-307 14 5 include include VERB cana-307 14 6 the the DET cana-307 14 7 stable stable ADJ cana-307 14 8 roommates roommate NOUN cana-307 14 9 problem problem VERB cana-307 14 10 with with ADP cana-307 14 11 incomplete incomplete ADJ cana-307 14 12 lists list NOUN cana-307 14 13 . . PUNCT cana-307 15 1 two two NUM cana-307 15 2 variations variation NOUN cana-307 15 3 of of ADP cana-307 15 4 the the DET cana-307 15 5 traditional traditional ADJ cana-307 15 6 stable stable ADJ cana-307 15 7 roommates roommate NOUN cana-307 15 8 ( ( PUNCT cana-307 15 9 sr sr PROPN cana-307 15 10 ) ) PUNCT cana-307 15 11 problem problem NOUN cana-307 15 12 with with ADP cana-307 15 13 incomplete incomplete ADJ cana-307 15 14 ( ( PUNCT cana-307 15 15 but but CCONJ cana-307 15 16 strictly strictly ADV cana-307 15 17 ordered order VERB cana-307 15 18 ) ) PUNCT cana-307 15 19 preference preference NOUN cana-307 15 20 lists list NOUN cana-307 15 21 ( ( PUNCT cana-307 15 22 sri sri PROPN cana-307 15 23 ) ) PUNCT cana-307 15 24 that that PRON cana-307 15 25 are be AUX cana-307 15 26 degree degree NOUN cana-307 15 27 - - PUNCT cana-307 15 28 constrained constrain VERB cana-307 15 29 β€” β€” PUNCT cana-307 15 30 that that ADV cana-307 15 31 is is ADV cana-307 15 32 , , PUNCT cana-307 15 33 preference preference NOUN cana-307 15 34 lists list NOUN cana-307 15 35 with with ADP cana-307 15 36 restricted restricted ADJ cana-307 15 37 length length NOUN cana-307 15 38 β€” β€” PUNCT cana-307 15 39 were be AUX cana-307 15 40 examined examine VERB cana-307 15 41 by by ADP cana-307 15 42 cseh cseh PROPN cana-307 15 43 et et PROPN cana-307 15 44 al al PROPN cana-307 15 45 . . PUNCT cana-307 16 1 [ [ X cana-307 16 2 2 2 NUM cana-307 16 3 ] ] PUNCT cana-307 16 4 . . PUNCT cana-307 17 1 in in ADP cana-307 17 2 the the DET cana-307 17 3 presence presence NOUN cana-307 17 4 of of ADP cana-307 17 5 ties tie NOUN cana-307 17 6 and and CCONJ cana-307 17 7 incomplete incomplete ADJ cana-307 17 8 lists list NOUN cana-307 17 9 , , PUNCT cana-307 17 10 adil adil PROPN cana-307 17 11 et et PROPN cana-307 17 12 al al PROPN cana-307 17 13 . . PUNCT cana-307 18 1 [ [ X cana-307 18 2 3 3 X cana-307 18 3 ] ] PUNCT cana-307 18 4 examined examine VERB cana-307 18 5 the the DET cana-307 18 6 parameterized parameterized ADJ cana-307 18 7 complexity complexity NOUN cana-307 18 8 of of ADP cana-307 18 9 np np NOUN cana-307 18 10 - - PUNCT cana-307 18 11 hard hard ADJ cana-307 18 12 optimization optimization NOUN cana-307 18 13 variants variant NOUN cana-307 18 14 of of ADP cana-307 18 15 stable stable ADJ cana-307 18 16 roommates roommate NOUN cana-307 18 17 and and CCONJ cana-307 18 18 stable stable ADJ cana-307 18 19 matching matching NOUN cana-307 18 20 . . PUNCT cana-307 19 1 fidan fidan NOUN cana-307 19 2 and and CCONJ cana-307 19 3 erdem erdem PROPN cana-307 19 4 [ [ X cana-307 19 5 4 4 X cana-307 19 6 ] ] PUNCT cana-307 19 7 presented present VERB cana-307 19 8 a a DET cana-307 19 9 knowledge knowledge NOUN cana-307 19 10 - - PUNCT cana-307 19 11 based base VERB cana-307 19 12 approach approach NOUN cana-307 19 13 to to ADP cana-307 19 14 srti srti NOUN cana-307 19 15 that that PRON cana-307 19 16 takes take VERB cana-307 19 17 domain domain NOUN cana-307 19 18 - - PUNCT cana-307 19 19 specific specific ADJ cana-307 19 20 knowledge knowledge NOUN cana-307 19 21 into into ADP cana-307 19 22 account account NOUN cana-307 19 23 and and CCONJ cana-307 19 24 looks look VERB cana-307 19 25 into into ADP cana-307 19 26 its its PRON cana-307 19 27 practical practical ADJ cana-307 19 28 use use NOUN cana-307 19 29 for for ADP cana-307 19 30 matching match VERB cana-307 19 31 up up ADP cana-307 19 32 students student NOUN cana-307 19 33 in in ADP cana-307 19 34 a a DET cana-307 19 35 university university NOUN cana-307 19 36 dorm dorm NOUN cana-307 19 37 . . PUNCT cana-307 20 1 a a DET cana-307 20 2 formal formal ADJ cana-307 20 3 framework framework NOUN cana-307 20 4 known know VERB cana-307 20 5 as as ADP cana-307 20 6 srti srti NOUN cana-307 20 7 - - PUNCT cana-307 20 8 asp asp PROPN cana-307 20 9 was be AUX cana-307 20 10 presented present VERB cana-307 20 11 by by ADP cana-307 20 12 erdem erdem NOUN cana-307 20 13 and and CCONJ cana-307 20 14 fidan fidan NOUN cana-307 20 15 [ [ X cana-307 20 16 5 5 NUM cana-307 20 17 ] ] PUNCT cana-307 20 18 . . PUNCT cana-307 21 1 it it PRON cana-307 21 2 makes make VERB cana-307 21 3 use use NOUN cana-307 21 4 of of ADP cana-307 21 5 the the DET cana-307 21 6 answer answer NOUN cana-307 21 7 set set VERB cana-307 21 8 programming programming NOUN cana-307 21 9 logic logic NOUN cana-307 21 10 programming programming NOUN cana-307 21 11 paradigm paradigm NOUN cana-307 21 12 , , PUNCT cana-307 21 13 which which PRON cana-307 21 14 is be AUX cana-307 21 15 proven prove VERB cana-307 21 16 and and CCONJ cana-307 21 17 sufficiently sufficiently ADV cana-307 21 18 generic generic ADJ cana-307 21 19 to to PART cana-307 21 20 handle handle VERB cana-307 21 21 a a DET cana-307 21 22 large large ADJ cana-307 21 23 number number NOUN cana-307 21 24 of of ADP cana-307 21 25 these these DET cana-307 21 26 sr sr PROPN cana-307 21 27 variations variation NOUN cana-307 21 28 . . PUNCT cana-307 22 1 an an DET cana-307 22 2 undirected undirected ADJ cana-307 22 3 non non ADJ cana-307 22 4 - - ADJ cana-307 22 5 bipartite bipartite ADJ cana-307 22 6 graph graph NOUN cana-307 22 7 𝐺 𝐺 PROPN cana-307 22 8 = = SYM cana-307 22 9 ( ( PUNCT cana-307 22 10 𝑉 𝑉 PROPN cana-307 22 11 , , PUNCT cana-307 22 12 𝐸 𝐸 PROPN cana-307 22 13 ) ) PUNCT cana-307 22 14 is be AUX cana-307 22 15 a a DET cana-307 22 16 perfect perfect ADJ cana-307 22 17 illustration illustration NOUN cana-307 22 18 of of ADP cana-307 22 19 the the DET cana-307 22 20 highly highly ADV cana-307 22 21 stable stable ADJ cana-307 22 22 roommates roommate NOUN cana-307 22 23 problem problem VERB cana-307 22 24 with with ADP cana-307 22 25 incomplete incomplete ADJ cana-307 22 26 lists list NOUN cana-307 22 27 and and CCONJ cana-307 22 28 ties tie NOUN cana-307 22 29 ( ( PUNCT cana-307 22 30 srti srti NOUN cana-307 22 31 ) ) PUNCT cana-307 22 32 . . PUNCT cana-307 23 1 an an DET cana-307 23 2 adjacency adjacency NOUN cana-307 23 3 list list NOUN cana-307 23 4 is be AUX cana-307 23 5 a a DET cana-307 23 6 list list NOUN cana-307 23 7 of of ADP cana-307 23 8 ties tie NOUN cana-307 23 9 , , PUNCT cana-307 23 10 or or CCONJ cana-307 23 11 vertices vertex NOUN cana-307 23 12 that that PRON cana-307 23 13 are be AUX cana-307 23 14 equally equally ADV cana-307 23 15 excellent excellent ADJ cana-307 23 16 for for ADP cana-307 23 17 a a DET cana-307 23 18 given give VERB cana-307 23 19 vertex vertex NOUN cana-307 23 20 . . PUNCT cana-307 24 1 the the DET cana-307 24 2 set set NOUN cana-307 24 3 of of ADP cana-307 24 4 all all DET cana-307 24 5 highly highly ADV cana-307 24 6 stable stable ADJ cana-307 24 7 matchings matching NOUN cana-307 24 8 can can AUX cana-307 24 9 be be AUX cana-307 24 10 represented represent VERB cana-307 24 11 by by ADP cana-307 24 12 a a DET cana-307 24 13 partial partial ADJ cana-307 24 14 order order NOUN cana-307 24 15 with with ADP cana-307 24 16 𝑂(π‘š 𝑂(π‘š ADJ cana-307 24 17 ) ) PUNCT cana-307 24 18 elements element NOUN cana-307 24 19 , , PUNCT cana-307 24 20 as as SCONJ cana-307 24 21 demonstrated demonstrate VERB cana-307 24 22 by by ADP cana-307 24 23 kunysz kunysz NOUN cana-307 24 24 [ [ X cana-307 24 25 6 6 NUM cana-307 24 26 ] ] PUNCT cana-307 24 27 and and CCONJ cana-307 24 28 provided provide VERB cana-307 24 29 an an DET cana-307 24 30 𝑂(nm 𝑂(nm NOUN cana-307 24 31 ) ) PUNCT cana-307 24 32 strategy strategy NOUN cana-307 24 33 for for ADP cana-307 24 34 communications communication NOUN cana-307 24 35 on on ADP cana-307 24 36 applied apply VERB cana-307 24 37 nonlinear nonlinear ADJ cana-307 24 38 analysis analysis NOUN cana-307 24 39 issn issn NOUN cana-307 24 40 : : PUNCT cana-307 24 41 1074 1074 NUM cana-307 24 42 - - PUNCT cana-307 24 43 133x 133x NUM cana-307 24 44 vol vol NOUN cana-307 24 45 30 30 NUM cana-307 24 46 no no NOUN cana-307 24 47 . . NOUN cana-307 24 48 4 4 NUM cana-307 24 49 ( ( PUNCT cana-307 24 50 2023 2023 NUM cana-307 24 51 ) ) PUNCT cana-307 24 52 59 59 NUM cana-307 24 53 https://internationalpubls.com https://internationalpubls.com X cana-307 24 54 creating create VERB cana-307 24 55 this this DET cana-307 24 56 kind kind NOUN cana-307 24 57 of of ADP cana-307 24 58 representation representation NOUN cana-307 24 59 . . PUNCT cana-307 25 1 the the DET cana-307 25 2 algorithms algorithm NOUN cana-307 25 3 are be AUX cana-307 25 4 predicated predicate VERB cana-307 25 5 on on ADP cana-307 25 6 a a DET cana-307 25 7 straightforward straightforward ADJ cana-307 25 8 reduction reduction NOUN cana-307 25 9 to to ADP cana-307 25 10 the the DET cana-307 25 11 problem problem NOUN cana-307 25 12 's 's PART cana-307 25 13 bipartite bipartite ADJ cana-307 25 14 form form NOUN cana-307 25 15 . . PUNCT cana-307 26 1 bredereck bredereck NOUN cana-307 26 2 et et PROPN cana-307 26 3 al al PROPN cana-307 26 4 . . PUNCT cana-307 27 1 [ [ X cana-307 27 2 7 7 X cana-307 27 3 ] ] PUNCT cana-307 27 4 examined examine VERB cana-307 27 5 the the DET cana-307 27 6 boundary boundary NOUN cana-307 27 7 between between ADP cana-307 27 8 w[1]-hardness w[1]-hardness NOUN cana-307 27 9 and and CCONJ cana-307 27 10 fixed fix VERB cana-307 27 11 - - PUNCT cana-307 27 12 parameter parameter NOUN cana-307 27 13 tractability tractability NOUN cana-307 27 14 of of ADP cana-307 27 15 stable stable ADJ cana-307 27 16 roommates roommate NOUN cana-307 27 17 with with ADP cana-307 27 18 ties tie NOUN cana-307 27 19 and and CCONJ cana-307 27 20 incomplete incomplete ADJ cana-307 27 21 lists list NOUN cana-307 27 22 from from ADP cana-307 27 23 the the DET cana-307 27 24 perspective perspective NOUN cana-307 27 25 of of ADP cana-307 27 26 parameterized parameterized ADJ cana-307 27 27 graph graph NOUN cana-307 27 28 algorithmics algorithmic NOUN cana-307 27 29 . . PUNCT cana-307 28 1 irving irving PROPN cana-307 29 1 [ [ X cana-307 29 2 8 8 NUM cana-307 29 3 ] ] PUNCT cana-307 29 4 provided provide VERB cana-307 29 5 an an DET cana-307 29 6 𝑂(π‘š 𝑂(π‘š ADJ cana-307 29 7 ) ) PUNCT cana-307 29 8 algorithm algorithm NOUN cana-307 29 9 that that SCONJ cana-307 29 10 , , PUNCT cana-307 29 11 given give VERB cana-307 29 12 an an DET cana-307 29 13 instance instance NOUN cana-307 29 14 𝐼 𝐼 PROPN cana-307 29 15 of of ADP cana-307 29 16 sr sr PROPN cana-307 29 17 , , PUNCT cana-307 29 18 finds find VERB cana-307 29 19 a a DET cana-307 29 20 stable stable ADJ cana-307 29 21 matching matching NOUN cana-307 29 22 or or CCONJ cana-307 29 23 states state NOUN cana-307 29 24 that that SCONJ cana-307 29 25 none none NOUN cana-307 29 26 exists exist VERB cana-307 29 27 . . PUNCT cana-307 30 1 the the DET cana-307 30 2 approach approach NOUN cana-307 30 3 is be AUX cana-307 30 4 predicated predicate VERB cana-307 30 5 on on ADP cana-307 30 6 the the DET cana-307 30 7 assumptions assumption NOUN cana-307 30 8 that that SCONJ cana-307 30 9 all all DET cana-307 30 10 preference preference NOUN cana-307 30 11 lists list NOUN cana-307 30 12 in in ADP cana-307 30 13 𝐼 𝐼 PROPN cana-307 30 14 are be AUX cana-307 30 15 complete complete ADJ cana-307 30 16 ( ( PUNCT cana-307 30 17 that that PRON cana-307 30 18 is be AUX cana-307 30 19 , , PUNCT cana-307 30 20 𝐴𝑖 𝐴𝑖 PROPN cana-307 30 21 = = SYM cana-307 30 22 𝐴 𝐴 PROPN cana-307 30 23 βˆ– βˆ– X cana-307 30 24 { { PUNCT cana-307 30 25 π‘Žπ‘– π‘Žπ‘– X cana-307 30 26 } } PUNCT cana-307 30 27 for for ADP cana-307 30 28 each each DET cana-307 30 29 π‘Žπ‘– π‘Žπ‘– PRON cana-307 30 30 ∈ ∈ PROPN cana-307 30 31 𝐴 𝐴 PROPN cana-307 30 32 ) ) PUNCT cana-307 30 33 and and CCONJ cana-307 30 34 𝑛 𝑛 PROPN cana-307 30 35 is be AUX cana-307 30 36 even even ADV cana-307 30 37 . . PUNCT cana-307 31 1 however however ADV cana-307 31 2 , , PUNCT cana-307 31 3 it it PRON cana-307 31 4 is be AUX cana-307 31 5 simple simple ADJ cana-307 31 6 to to PART cana-307 31 7 apply apply VERB cana-307 31 8 the the DET cana-307 31 9 algorithm algorithm NOUN cana-307 31 10 to to ADP cana-307 31 11 the the DET cana-307 31 12 problem problem NOUN cana-307 31 13 model model NOUN cana-307 31 14 that that PRON cana-307 31 15 is be AUX cana-307 31 16 described describe VERB cana-307 31 17 here here ADV cana-307 31 18 , , PUNCT cana-307 31 19 which which PRON cana-307 31 20 is be AUX cana-307 31 21 the the DET cana-307 31 22 incomplete incomplete ADJ cana-307 31 23 list list NOUN cana-307 31 24 problem problem NOUN cana-307 31 25 [ [ X cana-307 31 26 9 9 NUM cana-307 31 27 ] ] PUNCT cana-307 31 28 . . PUNCT cana-307 32 1 the the DET cana-307 32 2 problem problem NOUN cana-307 32 3 of of ADP cana-307 32 4 finding find VERB cana-307 32 5 large large ADJ cana-307 32 6 weakly weakly ADJ cana-307 32 7 stable stable ADJ cana-307 32 8 matchings matching NOUN cana-307 32 9 in in ADP cana-307 32 10 the the DET cana-307 32 11 presence presence NOUN cana-307 32 12 of of ADP cana-307 32 13 incomplete incomplete ADJ cana-307 32 14 preference preference NOUN cana-307 32 15 lists list NOUN cana-307 32 16 containing contain VERB cana-307 32 17 onesided onesided ADJ cana-307 32 18 ties tie NOUN cana-307 32 19 was be AUX cana-307 32 20 examined examine VERB cana-307 32 21 by by ADP cana-307 32 22 lam lam PROPN cana-307 32 23 and and CCONJ cana-307 32 24 plaxton plaxton VERB cana-307 33 1 [ [ X cana-307 33 2 10 10 NUM cana-307 33 3 ] ] PUNCT cana-307 33 4 . . PUNCT cana-307 34 1 additionally additionally ADV cana-307 34 2 shown show VERB cana-307 34 3 a a DET cana-307 34 4 polynomialtime polynomialtime NOUN cana-307 34 5 approach approach NOUN cana-307 34 6 that that PRON cana-307 34 7 produces produce VERB cana-307 34 8 a a DET cana-307 34 9 1 1 NUM cana-307 34 10 + + NUM cana-307 34 11 1/𝑒 1/𝑒 NUM cana-307 34 12 better well ADJ cana-307 34 13 approximation approximation NOUN cana-307 34 14 ratio ratio NOUN cana-307 34 15 . . PUNCT cana-307 35 1 the the DET cana-307 35 2 approach approach NOUN cana-307 35 3 is be AUX cana-307 35 4 based base VERB cana-307 35 5 on on ADP cana-307 35 6 a a DET cana-307 35 7 proposal proposal NOUN cana-307 35 8 process process NOUN cana-307 35 9 wherein wherein SCONJ cana-307 35 10 numerical numerical ADJ cana-307 35 11 priorities priority NOUN cana-307 35 12 are be AUX cana-307 35 13 utilized utilize VERB cana-307 35 14 for for ADP cana-307 35 15 tiebreaking tiebreake VERB cana-307 35 16 and and CCONJ cana-307 35 17 are be AUX cana-307 35 18 modified modify VERB cana-307 35 19 based base VERB cana-307 35 20 on on ADP cana-307 35 21 the the DET cana-307 35 22 outcome outcome NOUN cana-307 35 23 of of ADP cana-307 35 24 a a DET cana-307 35 25 linear linear ADJ cana-307 35 26 program program NOUN cana-307 35 27 . . PUNCT cana-307 36 1 sr sr PROPN cana-307 36 2 was be AUX cana-307 36 3 expanded expand VERB cana-307 36 4 to to ADP cana-307 36 5 three three NUM cana-307 36 6 - - PUNCT cana-307 36 7 person person NOUN cana-307 36 8 rooms room NOUN cana-307 36 9 by by ADP cana-307 36 10 iwama iwama PROPN cana-307 36 11 et et PROPN cana-307 36 12 al al PROPN cana-307 36 13 . . PUNCT cana-307 37 1 [ [ X cana-307 37 2 11 11 NUM cana-307 37 3 ] ] PUNCT cana-307 37 4 , , PUNCT cana-307 37 5 this this DET cana-307 37 6 system system NOUN cana-307 37 7 is be AUX cana-307 37 8 known know VERB cana-307 37 9 as as ADP cana-307 37 10 3d 3d NOUN cana-307 37 11 - - PUNCT cana-307 37 12 sr sr PROPN cana-307 37 13 ( ( PUNCT cana-307 37 14 3dimensional 3dimensional NUM cana-307 37 15 stable stable ADJ cana-307 37 16 roommates roommate NOUN cana-307 37 17 ) ) PUNCT cana-307 37 18 . . PUNCT cana-307 38 1 the the PRON cana-307 38 2 three three NUM cana-307 38 3 - - PUNCT cana-307 38 4 person person NOUN cana-307 38 5 satisfying satisfy VERB cana-307 38 6 roommate roommate NOUN cana-307 38 7 dilemma dilemma NOUN cana-307 38 8 is be AUX cana-307 38 9 made make VERB cana-307 38 10 up up ADP cana-307 38 11 of of ADP cana-307 38 12 3𝑛 3𝑛 NUM cana-307 38 13 person person NOUN cana-307 38 14 ( ( PUNCT cana-307 38 15 3d 3d PROPN cana-307 38 16 - - PUNCT cana-307 38 17 sr sr PROPN cana-307 38 18 ) ) PUNCT cana-307 38 19 who who PRON cana-307 38 20 may may AUX cana-307 38 21 have have VERB cana-307 38 22 a a DET cana-307 38 23 list list NOUN cana-307 38 24 of of ADP cana-307 38 25 preferences preference NOUN cana-307 38 26 over over ADP cana-307 38 27 the the DET cana-307 38 28 other other ADJ cana-307 38 29 three three NUM cana-307 38 30 persons person NOUN cana-307 38 31 ( ( PUNCT cana-307 38 32 3𝑛 3𝑛 NUM cana-307 38 33 βˆ’ βˆ’ NOUN cana-307 38 34 1 1 NUM cana-307 38 35 ) ) PUNCT cana-307 38 36 . . PUNCT cana-307 39 1 every every DET cana-307 39 2 individual individual NOUN cana-307 39 3 has have VERB cana-307 39 4 a a DET cana-307 39 5 fully fully ADV cana-307 39 6 ordered order VERB cana-307 39 7 preference preference NOUN cana-307 39 8 list list NOUN cana-307 39 9 that that PRON cana-307 39 10 includes include VERB cana-307 39 11 every every DET cana-307 39 12 other other ADJ cana-307 39 13 person person NOUN cana-307 39 14 ranked rank VERB cana-307 39 15 from from ADP cana-307 39 16 1 1 NUM cana-307 39 17 to to ADP cana-307 39 18 3𝑛 3𝑛 NUM cana-307 39 19 βˆ’ βˆ’ PROPN cana-307 39 20 1 1 NUM cana-307 39 21 based base VERB cana-307 39 22 on on ADP cana-307 39 23 his his PRON cana-307 39 24 preferences preference NOUN cana-307 39 25 . . PUNCT cana-307 40 1 this this DET cana-307 40 2 study study NOUN cana-307 40 3 uses use VERB cana-307 40 4 the the DET cana-307 40 5 same same ADJ cana-307 40 6 tpsr tpsr NOUN cana-307 40 7 approach approach NOUN cana-307 40 8 to to PART cana-307 40 9 discover discover VERB cana-307 40 10 a a DET cana-307 40 11 satisfactory satisfactory ADJ cana-307 40 12 match match NOUN cana-307 40 13 for for ADP cana-307 40 14 the the DET cana-307 40 15 roommate roommate NOUN cana-307 40 16 's 's PART cana-307 40 17 problem problem NOUN cana-307 40 18 with with ADP cana-307 40 19 an an DET cana-307 40 20 incomplete incomplete ADJ cana-307 40 21 list list NOUN cana-307 40 22 , , PUNCT cana-307 40 23 which which PRON cana-307 40 24 is be AUX cana-307 40 25 an an DET cana-307 40 26 extension extension NOUN cana-307 40 27 of of ADP cana-307 40 28 the the DET cana-307 40 29 three three NUM cana-307 40 30 - - PUNCT cana-307 40 31 person person NOUN cana-307 40 32 roommate roommate NOUN cana-307 40 33 's 's PART cana-307 40 34 problem problem NOUN cana-307 40 35 . . PUNCT cana-307 41 1 2 2 X cana-307 41 2 . . X cana-307 41 3 satisfactory satisfactory ADJ cana-307 41 4 roommate roommate NOUN cana-307 41 5 ’s ’s PART cana-307 41 6 problem problem NOUN cana-307 41 7 with with ADP cana-307 41 8 incomplete incomplete ADJ cana-307 41 9 list list NOUN cana-307 41 10 in in ADP cana-307 41 11 two two NUM cana-307 41 12 roommates roommate NOUN cana-307 41 13 a a DET cana-307 41 14 traditional traditional ADJ cana-307 41 15 satisfactory satisfactory ADJ cana-307 41 16 roommate roommate NOUN cana-307 41 17 's 's PART cana-307 41 18 problem problem NOUN cana-307 41 19 ( ( PUNCT cana-307 41 20 sfrp sfrp NOUN cana-307 41 21 ) ) PUNCT cana-307 41 22 where where SCONJ cana-307 41 23 each each DET cana-307 41 24 group group NOUN cana-307 41 25 member member NOUN cana-307 41 26 will will AUX cana-307 41 27 receive receive VERB cana-307 41 28 a a DET cana-307 41 29 complete complete ADJ cana-307 41 30 preference preference NOUN cana-307 41 31 list list NOUN cana-307 41 32 . . PUNCT cana-307 42 1 the the DET cana-307 42 2 term term NOUN cana-307 42 3 sfrpi sfrpi NOUN cana-307 42 4 refers refer VERB cana-307 42 5 to to ADP cana-307 42 6 the the DET cana-307 42 7 satisfactory satisfactory ADJ cana-307 42 8 roommates roommate NOUN cana-307 42 9 problem problem NOUN cana-307 42 10 , , PUNCT cana-307 42 11 which which PRON cana-307 42 12 is be AUX cana-307 42 13 characterized characterize VERB cana-307 42 14 by by ADP cana-307 42 15 an an DET cana-307 42 16 incomplete incomplete ADJ cana-307 42 17 preference preference NOUN cana-307 42 18 list list NOUN cana-307 42 19 [ [ X cana-307 42 20 12 12 NUM cana-307 42 21 ] ] PUNCT cana-307 42 22 . . PUNCT cana-307 43 1 in in ADP cana-307 43 2 other other ADJ cana-307 43 3 words word NOUN cana-307 43 4 , , PUNCT cana-307 43 5 some some DET cana-307 43 6 members member NOUN cana-307 43 7 of of ADP cana-307 43 8 the the DET cana-307 43 9 group group NOUN cana-307 43 10 of of ADP cana-307 43 11 2𝑛 2𝑛 PROPN cana-307 43 12 members member NOUN cana-307 43 13 are be AUX cana-307 43 14 preferred prefer VERB cana-307 43 15 above above ADP cana-307 43 16 members member NOUN cana-307 43 17 of of ADP cana-307 43 18 2𝑛 2𝑛 PROPN cana-307 43 19 βˆ’ βˆ’ PROPN cana-307 43 20 1 1 X cana-307 43 21 . . PUNCT cana-307 44 1 the the DET cana-307 44 2 smar smar ADJ cana-307 44 3 procedure procedure NOUN cana-307 44 4 , , PUNCT cana-307 44 5 which which PRON cana-307 44 6 is be AUX cana-307 44 7 detailed detail VERB cana-307 44 8 in in ADP cana-307 44 9 the the DET cana-307 44 10 sfrpi sfrpi NOUN cana-307 44 11 , , PUNCT cana-307 44 12 can can AUX cana-307 44 13 be be AUX cana-307 44 14 used use VERB cana-307 44 15 to to PART cana-307 44 16 produce produce VERB cana-307 44 17 satisfactory satisfactory ADJ cana-307 44 18 matching matching NOUN cana-307 44 19 for for ADP cana-307 44 20 this this DET cana-307 44 21 particular particular ADJ cana-307 44 22 type type NOUN cana-307 44 23 of of ADP cana-307 44 24 sfrpi sfrpi ADJ cana-307 44 25 problem problem NOUN cana-307 44 26 . . PUNCT cana-307 45 1 participant participant PROPN cana-307 45 2 p p NOUN cana-307 45 3 is be AUX cana-307 45 4 acceptable acceptable ADJ cana-307 45 5 to to PART cana-307 45 6 participant participant VERB cana-307 45 7 π‘ž π‘ž PRON cana-307 45 8 if if SCONJ cana-307 45 9 it it PRON cana-307 45 10 appears appear VERB cana-307 45 11 on on ADP cana-307 45 12 π‘ž π‘ž PROPN cana-307 45 13 's 's PART cana-307 45 14 preference preference NOUN cana-307 45 15 list list NOUN cana-307 45 16 and and CCONJ cana-307 45 17 undesirable undesirable ADJ cana-307 45 18 otherwise otherwise ADV cana-307 45 19 . . PUNCT cana-307 46 1 displaying display VERB cana-307 46 2 the the DET cana-307 46 3 members member NOUN cana-307 46 4 ' ' PART cana-307 46 5 preference preference NOUN cana-307 46 6 lists list NOUN cana-307 46 7 as as ADP cana-307 46 8 a a DET cana-307 46 9 satisfactory satisfactory ADJ cana-307 46 10 value value NOUN cana-307 46 11 matrix matrix NOUN cana-307 46 12 . . PUNCT cana-307 47 1 𝑆𝑉𝑀 𝑆𝑉𝑀 PROPN cana-307 47 2 = = PUNCT cana-307 48 1 [ [ X cana-307 48 2 π‘Žπ‘–π‘— π‘Žπ‘–π‘— NOUN cana-307 48 3 ] ] PUNCT cana-307 48 4 , , PUNCT cana-307 48 5 where where SCONJ cana-307 48 6 [ [ X cana-307 48 7 π‘Žπ‘–π‘— π‘Žπ‘–π‘— NOUN cana-307 48 8 ] ] PUNCT cana-307 48 9 is be AUX cana-307 48 10 equal equal ADJ cana-307 48 11 to to ADP cana-307 48 12 the the DET cana-307 48 13 sum sum NOUN cana-307 48 14 of of ADP cana-307 48 15 the the DET cana-307 48 16 preference preference NOUN cana-307 48 17 values value NOUN cana-307 48 18 of of ADP cana-307 48 19 the the DET cana-307 48 20 𝑗th 𝑗th PROPN cana-307 48 21 member member NOUN cana-307 48 22 with with ADP cana-307 48 23 regard regard NOUN cana-307 48 24 to to ADP cana-307 48 25 the the DET cana-307 48 26 ith ith PROPN cana-307 48 27 member member NOUN cana-307 48 28 , , PUNCT cana-307 48 29 the the DET cana-307 48 30 preference preference NOUN cana-307 48 31 value value NOUN cana-307 48 32 of of ADP cana-307 48 33 the the DET cana-307 48 34 𝑖th 𝑖th PROPN cana-307 48 35 member member NOUN cana-307 48 36 with with ADP cana-307 48 37 respect respect NOUN cana-307 48 38 to to ADP cana-307 48 39 the the DET cana-307 48 40 𝑗th 𝑗th PROPN cana-307 48 41 member member NOUN cana-307 48 42 , , PUNCT cana-307 48 43 and and CCONJ cana-307 48 44 the the DET cana-307 48 45 preference preference NOUN cana-307 48 46 value value NOUN cana-307 48 47 of of ADP cana-307 48 48 the the DET cana-307 48 49 𝑖th 𝑖th PROPN cana-307 48 50 member member NOUN cana-307 48 51 with with ADP cana-307 48 52 respect respect NOUN cana-307 48 53 to to ADP cana-307 48 54 the the DET cana-307 48 55 𝑗th 𝑗th PROPN cana-307 48 56 member member NOUN cana-307 48 57 . . PUNCT cana-307 49 1 if if SCONJ cana-307 49 2 𝑖 𝑖 NOUN cana-307 49 3 = = SYM cana-307 49 4 𝑗 𝑗 PROPN cana-307 49 5 , , PUNCT cana-307 49 6 then then ADV cana-307 49 7 [ [ X cana-307 49 8 π‘Žπ‘–π‘— π‘Žπ‘–π‘— NOUN cana-307 49 9 ] ] PUNCT cana-307 49 10 is be AUX cana-307 49 11 not not PART cana-307 49 12 specified specify VERB cana-307 49 13 . . PUNCT cana-307 50 1 this this DET cana-307 50 2 equal equal ADJ cana-307 50 3 𝑆𝑖𝑗 𝑆𝑖𝑗 PROPN cana-307 50 4 = = PROPN cana-307 50 5 𝑃𝑖𝑗 𝑃𝑖𝑗 PROPN cana-307 50 6 + + CCONJ cana-307 50 7 𝑃𝑗𝑖. 𝑃𝑗𝑖. PROPN cana-307 50 8 𝑃 𝑃 PROPN cana-307 50 9 stands stand VERB cana-307 50 10 for for ADP cana-307 50 11 the the DET cana-307 50 12 preference preference NOUN cana-307 50 13 value value NOUN cana-307 50 14 , , PUNCT cana-307 50 15 which which PRON cana-307 50 16 is be AUX cana-307 50 17 defined define VERB cana-307 50 18 as as ADP cana-307 50 19 the the DET cana-307 50 20 value value NOUN cana-307 50 21 that that PRON cana-307 50 22 is be AUX cana-307 50 23 assigned assign VERB cana-307 50 24 to to ADP cana-307 50 25 each each DET cana-307 50 26 member member NOUN cana-307 50 27 in in ADP cana-307 50 28 the the DET cana-307 50 29 preference preference NOUN cana-307 50 30 list list NOUN cana-307 50 31 based base VERB cana-307 50 32 on on ADP cana-307 50 33 their their PRON cana-307 50 34 relative relative ADJ cana-307 50 35 preference preference NOUN cana-307 50 36 . . PUNCT cana-307 51 1 for for ADP cana-307 51 2 example example NOUN cana-307 51 3 , , PUNCT cana-307 51 4 the the DET cana-307 51 5 first first ADJ cana-307 51 6 member member NOUN cana-307 51 7 is be AUX cana-307 51 8 represented represent VERB cana-307 51 9 as as ADP cana-307 51 10 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-307 51 11 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-307 51 12 , , PUNCT cana-307 51 13 the the DET cana-307 51 14 second second ADJ cana-307 51 15 as as ADP cana-307 51 16 π‘›βˆ’2 π‘›βˆ’2 PROPN cana-307 51 17 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-307 51 18 , , PUNCT cana-307 51 19 the the DET cana-307 51 20 third third ADJ cana-307 51 21 as as ADP cana-307 51 22 π‘›βˆ’3 π‘›βˆ’3 PROPN cana-307 51 23 π‘›βˆ’1 π‘›βˆ’1 PROPN cana-307 51 24 and and CCONJ cana-307 51 25 so so ADV cana-307 51 26 on on ADP cana-307 51 27 [ [ PUNCT cana-307 51 28 13 13 NUM cana-307 51 29 ] ] PUNCT cana-307 51 30 . . PUNCT cana-307 52 1 the the DET cana-307 52 2 assignment assignment NOUN cana-307 52 3 technique technique NOUN cana-307 52 4 is be AUX cana-307 52 5 used use VERB cana-307 52 6 to to PART cana-307 52 7 determine determine VERB cana-307 52 8 a a DET cana-307 52 9 satisfactory satisfactory ADJ cana-307 52 10 fit fit NOUN cana-307 52 11 between between ADP cana-307 52 12 roommates roommate NOUN cana-307 52 13 . . PUNCT cana-307 53 1 using use VERB cana-307 53 2 the the DET cana-307 53 3 hungarian hungarian ADJ cana-307 53 4 algorithm algorithm NOUN cana-307 53 5 , , PUNCT cana-307 53 6 svm svm VERB cana-307 53 7 on on ADP cana-307 53 8 oneto oneto NOUN cana-307 53 9 - - PUNCT cana-307 53 10 one one NUM cana-307 53 11 optimum optimum ADJ cana-307 53 12 matching matching NOUN cana-307 53 13 is be AUX cana-307 53 14 obtained obtain VERB cana-307 53 15 . . PUNCT cana-307 54 1 communications communication NOUN cana-307 54 2 on on ADP cana-307 54 3 applied apply VERB cana-307 54 4 nonlinear nonlinear ADJ cana-307 54 5 analysis analysis NOUN cana-307 54 6 issn issn NOUN cana-307 54 7 : : PUNCT cana-307 54 8 1074 1074 NUM cana-307 54 9 - - PUNCT cana-307 54 10 133x 133x NUM cana-307 54 11 vol vol NOUN cana-307 54 12 30 30 NUM cana-307 54 13 no no NOUN cana-307 54 14 . . NOUN cana-307 54 15 4 4 NUM cana-307 54 16 ( ( PUNCT cana-307 54 17 2023 2023 NUM cana-307 54 18 ) ) PUNCT cana-307 55 1 60 60 NUM cana-307 55 2 https://internationalpubls.com https://internationalpubls.com X cana-307 55 3 3 3 NUM cana-307 55 4 . . X cana-307 55 5 three three NUM cana-307 55 6 person person NOUN cana-307 55 7 satisfactory satisfactory ADJ cana-307 55 8 matching matching NOUN cana-307 55 9 ( ( PUNCT cana-307 55 10 tpsm tpsm PROPN cana-307 55 11 ) ) PUNCT cana-307 55 12 in in ADP cana-307 55 13 this this DET cana-307 55 14 paper paper NOUN cana-307 55 15 , , PUNCT cana-307 55 16 we we PRON cana-307 55 17 propose propose VERB cana-307 55 18 an an DET cana-307 55 19 algorithm algorithm NOUN cana-307 55 20 to to PART cana-307 55 21 find find VERB cana-307 55 22 triple triple ADJ cana-307 55 23 roommates roommate NOUN cana-307 55 24 from from ADP cana-307 55 25 a a DET cana-307 55 26 group group NOUN cana-307 55 27 of of ADP cana-307 55 28 3n 3n NUM cana-307 55 29 person person NOUN cana-307 55 30 based base VERB cana-307 55 31 on on ADP cana-307 55 32 their their PRON cana-307 55 33 preference preference NOUN cana-307 55 34 lists list NOUN cana-307 55 35 and and CCONJ cana-307 55 36 some some DET cana-307 55 37 members member NOUN cana-307 55 38 prefer prefer VERB cana-307 55 39 less less ADJ cana-307 55 40 than than ADP cana-307 55 41 3n-1 3n-1 NUM cana-307 55 42 persons person NOUN cana-307 55 43 . . PUNCT cana-307 56 1 this this DET cana-307 56 2 algorithm algorithm NOUN cana-307 56 3 provides provide VERB cana-307 56 4 a a DET cana-307 56 5 3n 3n NUM cana-307 56 6 set set NOUN cana-307 56 7 of of ADP cana-307 56 8 triple triple ADJ cana-307 56 9 roommates roommate NOUN cana-307 56 10 based base VERB cana-307 56 11 on on ADP cana-307 56 12 the the DET cana-307 56 13 individual individual ADJ cana-307 56 14 satisfactory satisfactory ADJ cana-307 56 15 level level NOUN cana-307 56 16 . . PUNCT cana-307 57 1 preference preference NOUN cana-307 57 2 value value NOUN cana-307 57 3 ( ( PUNCT cana-307 57 4 tpsrp tpsrp NOUN cana-307 57 5 ) ) PUNCT cana-307 57 6 is be AUX cana-307 57 7 defined define VERB cana-307 57 8 as as ADP cana-307 57 9 the the DET cana-307 57 10 value value NOUN cana-307 57 11 assigned assign VERB cana-307 57 12 to to ADP cana-307 57 13 the the DET cana-307 57 14 members member NOUN cana-307 57 15 in in ADP cana-307 57 16 the the DET cana-307 57 17 preference preference NOUN cana-307 57 18 list list NOUN cana-307 57 19 according accord VERB cana-307 57 20 to to ADP cana-307 57 21 the the DET cana-307 57 22 order order NOUN cana-307 57 23 of of ADP cana-307 57 24 preference preference NOUN cana-307 57 25 with with ADP cana-307 57 26 respect respect NOUN cana-307 57 27 to to ADP cana-307 57 28 the the DET cana-307 57 29 persons person NOUN cana-307 57 30 by by ADP cana-307 57 31 considering consider VERB cana-307 57 32 the the DET cana-307 57 33 first first ADJ cana-307 57 34 person person NOUN cana-307 57 35 as as ADP cana-307 57 36 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 37 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 38 , , PUNCT cana-307 57 39 the the DET cana-307 57 40 second second ADJ cana-307 57 41 person person NOUN cana-307 57 42 as as ADP cana-307 57 43 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 44 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 45 , , PUNCT cana-307 57 46 the the DET cana-307 57 47 third third ADJ cana-307 57 48 person person NOUN cana-307 57 49 as as ADP cana-307 57 50 3π‘›βˆ’3 3π‘›βˆ’3 NUM cana-307 57 51 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 52 , , PUNCT cana-307 57 53 the the DET cana-307 57 54 fourth fourth ADJ cana-307 57 55 person person NOUN cana-307 57 56 as as ADP cana-307 57 57 3π‘›βˆ’4 3π‘›βˆ’4 NUM cana-307 57 58 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 57 59 and and CCONJ cana-307 57 60 so so ADV cana-307 57 61 on on ADV cana-307 57 62 . . PUNCT cana-307 58 1 if if SCONJ cana-307 58 2 the the DET cana-307 58 3 person person NOUN cana-307 58 4 i i PRON cana-307 58 5 did do AUX cana-307 58 6 not not PART cana-307 58 7 prefer prefer VERB cana-307 58 8 j j PROPN cana-307 58 9 , , PUNCT cana-307 58 10 then then ADV cana-307 58 11 jth jth PROPN cana-307 58 12 place place NOUN cana-307 58 13 in in ADP cana-307 58 14 ith ith PROPN cana-307 58 15 list list NOUN cana-307 58 16 must must AUX cana-307 58 17 be be AUX cana-307 58 18 considered consider VERB cana-307 58 19 as as ADP cana-307 58 20 infinity infinity NOUN cana-307 58 21 . . PUNCT cana-307 59 1 𝑃 𝑃 NOUN cana-307 59 2 : : PUNCT cana-307 60 1 [ [ X cana-307 60 2 𝑃𝑖𝑗 𝑃𝑖𝑗 NOUN cana-307 60 3 ] ] PUNCT cana-307 60 4 defines define VERB cana-307 60 5 the the DET cana-307 60 6 preference preference NOUN cana-307 60 7 value value NOUN cana-307 60 8 matrix matrix NOUN cana-307 60 9 . . PUNCT cana-307 61 1 𝑃𝑖𝑗 𝑃𝑖𝑗 NOUN cana-307 61 2 = = PUNCT cana-307 61 3 { { PUNCT cana-307 61 4 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 61 5 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 61 6 if if SCONJ cana-307 61 7 j j PROPN cana-307 61 8 is be AUX cana-307 61 9 the the DET cana-307 61 10 first first ADJ cana-307 61 11 or or CCONJ cana-307 61 12 second second ADJ cana-307 61 13 preference preference NOUN cana-307 61 14 of of ADP cana-307 61 15 i i PRON cana-307 61 16 3π‘›βˆ’π‘˜ 3π‘›βˆ’π‘˜ NOUN cana-307 61 17 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 61 18 if if SCONJ cana-307 61 19 j j PROPN cana-307 61 20 is be AUX cana-307 61 21 π‘˜th π‘˜th NOUN cana-307 61 22 preference preference NOUN cana-307 61 23 of of ADP cana-307 61 24 i i PRON cana-307 61 25 and and CCONJ cana-307 61 26 k k NOUN cana-307 61 27 = = SYM cana-307 61 28 3,4,5,6 3,4,5,6 NUM cana-307 61 29 … … PUNCT cana-307 61 30 … … PUNCT cana-307 61 31 upto upto INTJ cana-307 61 32 ( ( PUNCT cana-307 61 33 3n 3n NUM cana-307 61 34 βˆ’ βˆ’ NUM cana-307 61 35 1 1 NUM cana-307 61 36 ) ) PUNCT cana-307 61 37 βˆ’ βˆ’ NOUN cana-307 62 1 if if SCONJ cana-307 62 2 i i PRON cana-307 62 3 = = SYM cana-307 62 4 j j X cana-307 62 5 the the DET cana-307 62 6 modified modify VERB cana-307 62 7 preference preference NOUN cana-307 62 8 value value NOUN cana-307 62 9 matrix matrix NOUN cana-307 62 10 is be AUX cana-307 62 11 defined define VERB cana-307 62 12 as as SCONJ cana-307 62 13 follows follow VERB cana-307 62 14 : : PUNCT cana-307 62 15 π‘š(𝑖𝑗),π‘˜ π‘š(𝑖𝑗),π‘˜ PROPN cana-307 62 16 = = PRON cana-307 62 17 { { PUNCT cana-307 63 1 βˆ’ βˆ’ X cana-307 63 2 if if SCONJ cana-307 63 3 k k PROPN cana-307 63 4 = = VERB cana-307 63 5 i i PROPN cana-307 63 6 and and CCONJ cana-307 63 7 k k PROPN cana-307 63 8 = = PUNCT cana-307 63 9 j j PROPN cana-307 64 1 π‘ƒπ‘–π‘˜ π‘ƒπ‘–π‘˜ PROPN cana-307 64 2 + + CCONJ cana-307 64 3 𝑃𝑗𝑖 𝑃𝑗𝑖 PROPN cana-307 64 4 k k NOUN cana-307 64 5 = = SYM cana-307 64 6 1,2 1,2 NUM cana-307 64 7 , , PUNCT cana-307 64 8 … … PUNCT cana-307 64 9 .3n .3n NOUN cana-307 64 10 β‰  β‰  PROPN cana-307 64 11 i i PROPN cana-307 64 12 , , PUNCT cana-307 64 13 j j PROPN cana-307 64 14 3.1 3.1 NUM cana-307 64 15 algorithm algorithm NOUN cana-307 64 16 ( ( PUNCT cana-307 64 17 tpsma tpsma PROPN cana-307 64 18 ) ) PUNCT cana-307 64 19 1 1 NUM cana-307 64 20 . . PUNCT cana-307 64 21 get get VERB cana-307 64 22 the the DET cana-307 64 23 preference preference NOUN cana-307 64 24 lists list NOUN cana-307 64 25 from from ADP cana-307 64 26 each each DET cana-307 64 27 person person NOUN cana-307 64 28 . . PUNCT cana-307 65 1 2 2 X cana-307 65 2 . . X cana-307 65 3 form form VERB cana-307 65 4 a a DET cana-307 65 5 preference preference NOUN cana-307 65 6 value value NOUN cana-307 65 7 matrix matrix NOUN cana-307 65 8 based base VERB cana-307 65 9 on on ADP cana-307 65 10 their their PRON cana-307 65 11 preference preference NOUN cana-307 65 12 lists list NOUN cana-307 65 13 . . PUNCT cana-307 66 1 3 3 X cana-307 66 2 . . X cana-307 66 3 considering consider VERB cana-307 66 4 the the DET cana-307 66 5 preference preference NOUN cana-307 66 6 value value NOUN cana-307 66 7 matrix matrix NOUN cana-307 66 8 as as ADP cana-307 66 9 a a DET cana-307 66 10 maximization maximization NOUN cana-307 66 11 assignment assignment NOUN cana-307 66 12 problem problem NOUN cana-307 66 13 . . PUNCT cana-307 67 1 4 4 X cana-307 67 2 . . X cana-307 67 3 construct construct VERB cana-307 67 4 a a DET cana-307 67 5 minimized minimized ADJ cana-307 67 6 preference preference NOUN cana-307 67 7 value value NOUN cana-307 67 8 matrix matrix NOUN cana-307 67 9 and and CCONJ cana-307 67 10 applying apply VERB cana-307 67 11 hungarian hungarian ADJ cana-307 67 12 algorithm algorithm NOUN cana-307 67 13 for for ADP cana-307 67 14 that that DET cana-307 67 15 matrix matrix NOUN cana-307 67 16 . . PUNCT cana-307 68 1 5 5 X cana-307 68 2 . . X cana-307 68 3 the the DET cana-307 68 4 resultant resultant NOUN cana-307 68 5 pairs pair NOUN cana-307 68 6 must must AUX cana-307 68 7 be be AUX cana-307 68 8 the the DET cana-307 68 9 optimum optimum ADJ cana-307 68 10 pairs pair NOUN cana-307 68 11 like like ADP cana-307 68 12 ( ( PUNCT cana-307 68 13 i i PROPN cana-307 68 14 , , PUNCT cana-307 68 15 j j PROPN cana-307 68 16 ) ) PUNCT cana-307 68 17 , , PUNCT cana-307 68 18 ( ( PUNCT cana-307 68 19 k k X cana-307 68 20 , , PUNCT cana-307 68 21 l l NOUN cana-307 68 22 ) ) PUNCT cana-307 68 23 , , PUNCT cana-307 68 24 ( ( PUNCT cana-307 68 25 m m NOUN cana-307 68 26 , , PUNCT cana-307 68 27 n n CCONJ cana-307 68 28 ) ) PUNCT cana-307 68 29 and and CCONJ cana-307 68 30 so so ADV cana-307 68 31 on on ADP cana-307 68 32 obtained obtain VERB cana-307 68 33 . . PUNCT cana-307 69 1 6 6 X cana-307 69 2 . . X cana-307 69 3 construct construct VERB cana-307 69 4 the the DET cana-307 69 5 modified modify VERB cana-307 69 6 preference preference NOUN cana-307 69 7 value value NOUN cana-307 69 8 matrix matrix NOUN cana-307 69 9 by by ADP cana-307 69 10 considering consider VERB cana-307 69 11 the the DET cana-307 69 12 pairs pair NOUN cana-307 69 13 ( ( PUNCT cana-307 69 14 i i PROPN cana-307 69 15 , , PUNCT cana-307 69 16 j j PROPN cana-307 69 17 ) ) PUNCT cana-307 69 18 , , PUNCT cana-307 69 19 ( ( PUNCT cana-307 69 20 k k X cana-307 69 21 , , PUNCT cana-307 69 22 l l NOUN cana-307 69 23 ) ) PUNCT cana-307 69 24 , , PUNCT cana-307 69 25 ( ( PUNCT cana-307 69 26 m m NOUN cana-307 69 27 , , PUNCT cana-307 69 28 n n CCONJ cana-307 69 29 ) ) PUNCT cana-307 69 30 … … PUNCT cana-307 69 31 as as ADP cana-307 69 32 rows row NOUN cana-307 69 33 and and CCONJ cana-307 69 34 1,2, 1,2, NUM cana-307 69 35 … … SYM cana-307 69 36 .3n .3n NOUN cana-307 69 37 members member NOUN cana-307 69 38 as as ADP cana-307 69 39 column column NOUN cana-307 69 40 . . PUNCT cana-307 70 1 by by ADP cana-307 70 2 using use VERB cana-307 70 3 mpvm mpvm PROPN cana-307 70 4 definition definition NOUN cana-307 70 5 which which PRON cana-307 70 6 is be AUX cana-307 70 7 given give VERB cana-307 70 8 above above ADV cana-307 70 9 . . PUNCT cana-307 71 1 7 7 X cana-307 71 2 . . X cana-307 71 3 considering consider VERB cana-307 71 4 the the DET cana-307 71 5 modified modify VERB cana-307 71 6 preference preference NOUN cana-307 71 7 value value NOUN cana-307 71 8 matrix matrix NOUN cana-307 71 9 as as ADP cana-307 71 10 a a DET cana-307 71 11 minimized minimized ADJ cana-307 71 12 assignment assignment NOUN cana-307 71 13 problem problem NOUN cana-307 71 14 and and CCONJ cana-307 71 15 apply apply VERB cana-307 71 16 hungarian hungarian ADJ cana-307 71 17 algorithm algorithm NOUN cana-307 71 18 for for ADP cana-307 71 19 getting get VERB cana-307 71 20 the the DET cana-307 71 21 optimum optimum ADJ cana-307 71 22 triples triple NOUN cana-307 71 23 . . PUNCT cana-307 72 1 8 8 X cana-307 72 2 . . X cana-307 72 3 list list VERB cana-307 72 4 out out ADP cana-307 72 5 all all DET cana-307 72 6 the the DET cana-307 72 7 triples triple NOUN cana-307 72 8 and and CCONJ cana-307 72 9 let let VERB cana-307 72 10 it it PRON cana-307 72 11 be be AUX cana-307 72 12 ( ( PUNCT cana-307 72 13 i i PROPN cana-307 72 14 , , PUNCT cana-307 72 15 j j PROPN cana-307 72 16 , , PUNCT cana-307 72 17 k k PROPN cana-307 72 18 ) ) PUNCT cana-307 72 19 , , PUNCT cana-307 72 20 ( ( PUNCT cana-307 72 21 l l NOUN cana-307 72 22 , , PUNCT cana-307 72 23 m m PROPN cana-307 72 24 , , PUNCT cana-307 72 25 n n CCONJ cana-307 72 26 ) ) PUNCT cana-307 72 27 , , PUNCT cana-307 72 28 ( ( PUNCT cana-307 72 29 i i PRON cana-307 72 30 , , PUNCT cana-307 72 31 l l PROPN cana-307 72 32 , , PUNCT cana-307 72 33 n n CCONJ cana-307 72 34 ) ) PUNCT cana-307 72 35 … … PUNCT cana-307 72 36 .. .. PUNCT cana-307 73 1 9 9 NUM cana-307 73 2 . . X cana-307 73 3 from from ADP cana-307 73 4 the the DET cana-307 73 5 obtained obtain VERB cana-307 73 6 triples triple NOUN cana-307 73 7 , , PUNCT cana-307 73 8 choose choose VERB cana-307 73 9 one one NUM cana-307 73 10 by by ADP cana-307 73 11 one one NUM cana-307 73 12 and and CCONJ cana-307 73 13 find find VERB cana-307 73 14 the the DET cana-307 73 15 satisfactory satisfactory ADJ cana-307 73 16 value value NOUN cana-307 73 17 of of ADP cana-307 73 18 each each DET cana-307 73 19 member member NOUN cana-307 73 20 of of ADP cana-307 73 21 a a DET cana-307 73 22 group group NOUN cana-307 73 23 . . PUNCT cana-307 74 1 10 10 NUM cana-307 74 2 . . PUNCT cana-307 75 1 if if SCONJ cana-307 75 2 ( ( PUNCT cana-307 75 3 i i PROPN cana-307 75 4 , , PUNCT cana-307 75 5 j j PROPN cana-307 75 6 , , PUNCT cana-307 75 7 k k NOUN cana-307 75 8 ) ) PUNCT cana-307 75 9 be be VERB cana-307 75 10 the the DET cana-307 75 11 first first ADJ cana-307 75 12 triples triple NOUN cana-307 75 13 , , PUNCT cana-307 75 14 find find VERB cana-307 75 15 the the DET cana-307 75 16 preference preference NOUN cana-307 75 17 value value NOUN cana-307 75 18 of of ADP cana-307 75 19 i i PRON cana-307 75 20 with with ADP cana-307 75 21 respect respect NOUN cana-307 75 22 to to ADP cana-307 75 23 j j PROPN cana-307 75 24 and and CCONJ cana-307 75 25 k k PROPN cana-307 75 26 , , PUNCT cana-307 75 27 then then ADV cana-307 75 28 adding add VERB cana-307 75 29 the the DET cana-307 75 30 preference preference NOUN cana-307 75 31 values value NOUN cana-307 75 32 . . PUNCT cana-307 76 1 now now ADV cana-307 76 2 we we PRON cana-307 76 3 get get VERB cana-307 76 4 the the DET cana-307 76 5 overall overall ADJ cana-307 76 6 preference preference NOUN cana-307 76 7 value value NOUN cana-307 76 8 and and CCONJ cana-307 76 9 multiply multiply VERB cana-307 76 10 the the DET cana-307 76 11 value value NOUN cana-307 76 12 by by ADP cana-307 76 13 50 50 NUM cana-307 76 14 . . PUNCT cana-307 77 1 communications communication NOUN cana-307 77 2 on on ADP cana-307 77 3 applied apply VERB cana-307 77 4 nonlinear nonlinear ADJ cana-307 77 5 analysis analysis NOUN cana-307 77 6 issn issn NOUN cana-307 77 7 : : PUNCT cana-307 77 8 1074 1074 NUM cana-307 77 9 - - PUNCT cana-307 77 10 133x 133x NUM cana-307 77 11 vol vol NOUN cana-307 77 12 30 30 NUM cana-307 77 13 no no NOUN cana-307 77 14 . . NOUN cana-307 77 15 4 4 NUM cana-307 77 16 ( ( PUNCT cana-307 77 17 2023 2023 NUM cana-307 77 18 ) ) PUNCT cana-307 77 19 61 61 NUM cana-307 77 20 https://internationalpubls.com https://internationalpubls.com X cana-307 77 21 it it PRON cana-307 77 22 gives give VERB cana-307 77 23 a a DET cana-307 77 24 satisfactory satisfactory ADJ cana-307 77 25 value value NOUN cana-307 77 26 of of ADP cana-307 77 27 i i PRON cana-307 77 28 with with ADP cana-307 77 29 respect respect NOUN cana-307 77 30 to to ADP cana-307 77 31 j j PROPN cana-307 77 32 and and CCONJ cana-307 77 33 k. k. PROPN cana-307 77 34 similarly similarly ADV cana-307 77 35 find find VERB cana-307 77 36 the the DET cana-307 77 37 satisfactory satisfactory ADJ cana-307 77 38 value value NOUN cana-307 77 39 of of ADP cana-307 77 40 j j PROPN cana-307 77 41 w.r.to w.r.to PROPN cana-307 78 1 i i PROPN cana-307 78 2 & & CCONJ cana-307 78 3 k k PROPN cana-307 78 4 , , PUNCT cana-307 78 5 also also ADV cana-307 78 6 for for ADP cana-307 78 7 k k PROPN cana-307 78 8 w.r.to w.r.to PROPN cana-307 79 1 i i PROPN cana-307 79 2 & & CCONJ cana-307 79 3 j. j. PROPN cana-307 79 4 11 11 NUM cana-307 79 5 . . PUNCT cana-307 80 1 after after ADP cana-307 80 2 getting get VERB cana-307 80 3 these these DET cana-307 80 4 three three NUM cana-307 80 5 satisfactory satisfactory ADJ cana-307 80 6 values value NOUN cana-307 80 7 , , PUNCT cana-307 80 8 find find VERB cana-307 80 9 overall overall ADJ cana-307 80 10 satisfaction satisfaction NOUN cana-307 80 11 for for ADP cana-307 80 12 the the DET cana-307 80 13 triple triple ADJ cana-307 80 14 ( ( PUNCT cana-307 80 15 i i PROPN cana-307 80 16 , , PUNCT cana-307 80 17 j j PROPN cana-307 80 18 , , PUNCT cana-307 80 19 k k PROPN cana-307 80 20 ) ) PUNCT cana-307 80 21 . . PUNCT cana-307 81 1 in in ADP cana-307 81 2 the the DET cana-307 81 3 same same ADJ cana-307 81 4 manner manner NOUN cana-307 81 5 repeat repeat VERB cana-307 81 6 the the DET cana-307 81 7 process process NOUN cana-307 81 8 for for ADP cana-307 81 9 all all DET cana-307 81 10 the the DET cana-307 81 11 remaining remain VERB cana-307 81 12 triples triple NOUN cana-307 81 13 . . PUNCT cana-307 82 1 12 12 NUM cana-307 82 2 . . PUNCT cana-307 83 1 now now ADV cana-307 83 2 choose choose VERB cana-307 83 3 mutually mutually ADV cana-307 83 4 exclusive exclusive ADJ cana-307 83 5 and and CCONJ cana-307 83 6 exhaustive exhaustive ADJ cana-307 83 7 triples triple NOUN cana-307 83 8 which which PRON cana-307 83 9 achieves achieve VERB cana-307 83 10 the the DET cana-307 83 11 maximum maximum ADJ cana-307 83 12 level level NOUN cana-307 83 13 of of ADP cana-307 83 14 satisfaction satisfaction NOUN cana-307 83 15 that that PRON cana-307 83 16 is be AUX cana-307 83 17 the the DET cana-307 83 18 optimum optimum ADJ cana-307 83 19 triples triple NOUN cana-307 83 20 . . PUNCT cana-307 84 1 4 4 X cana-307 84 2 . . X cana-307 84 3 example example NOUN cana-307 84 4 : : PUNCT cana-307 84 5 consider consider VERB cana-307 84 6 the the DET cana-307 84 7 problem problem NOUN cana-307 84 8 instance instance NOUN cana-307 84 9 of of ADP cana-307 84 10 tpsrp tpsrp NOUN cana-307 84 11 based base VERB cana-307 84 12 on on ADP cana-307 84 13 order order NOUN cana-307 84 14 of of ADP cana-307 84 15 preference preference NOUN cana-307 84 16 1 1 NUM cana-307 84 17 3 3 NUM cana-307 84 18 4 4 NUM cana-307 84 19 2 2 NUM cana-307 84 20 5 5 NUM cana-307 84 21 6 6 NUM cana-307 84 22 2 2 NUM cana-307 84 23 5 5 NUM cana-307 84 24 3 3 NUM cana-307 84 25 1 1 NUM cana-307 84 26 6 6 NUM cana-307 84 27 4 4 NUM cana-307 84 28 3 3 NUM cana-307 84 29 2 2 NUM cana-307 84 30 4 4 NUM cana-307 84 31 6 6 NUM cana-307 84 32 5 5 NUM cana-307 84 33 1 1 NUM cana-307 84 34 4 4 NUM cana-307 84 35 3 3 NUM cana-307 84 36 1 1 NUM cana-307 84 37 6 6 NUM cana-307 84 38 2 2 NUM cana-307 84 39 5 5 NUM cana-307 84 40 2 2 NUM cana-307 84 41 6 6 NUM cana-307 84 42 3 3 NUM cana-307 84 43 1 1 NUM cana-307 84 44 6 6 NUM cana-307 84 45 3 3 NUM cana-307 84 46 5 5 NUM cana-307 84 47 4 4 NUM cana-307 84 48 2 2 NUM cana-307 84 49 1 1 NUM cana-307 84 50 solution solution NOUN cana-307 84 51 : : PUNCT cana-307 84 52 the the DET cana-307 84 53 given give VERB cana-307 84 54 preference preference NOUN cana-307 84 55 list list NOUN cana-307 84 56 can can AUX cana-307 84 57 be be AUX cana-307 84 58 constructed construct VERB cana-307 84 59 as as ADP cana-307 84 60 a a DET cana-307 84 61 preference preference NOUN cana-307 84 62 value value NOUN cana-307 84 63 matrix matrix NOUN cana-307 84 64 by by ADP cana-307 84 65 considering consider VERB cana-307 84 66 first first ADJ cana-307 84 67 person person NOUN cana-307 84 68 as as ADP cana-307 84 69 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 70 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 71 , , PUNCT cana-307 84 72 second second ADJ cana-307 84 73 person person NOUN cana-307 84 74 as as ADP cana-307 84 75 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 76 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 77 , , PUNCT cana-307 84 78 third third ADJ cana-307 84 79 person person NOUN cana-307 84 80 as as ADP cana-307 84 81 3π‘›βˆ’3 3π‘›βˆ’3 NUM cana-307 84 82 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 83 , , PUNCT cana-307 84 84 , , PUNCT cana-307 84 85 fourth fourth ADJ cana-307 84 86 person person NOUN cana-307 84 87 as as ADP cana-307 84 88 3π‘›βˆ’4 3π‘›βˆ’4 NUM cana-307 84 89 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 90 , , PUNCT cana-307 84 91 fifth fifth ADJ cana-307 84 92 person person NOUN cana-307 84 93 as as ADP cana-307 84 94 3π‘›βˆ’5 3π‘›βˆ’5 NUM cana-307 84 95 3π‘›βˆ’2 3π‘›βˆ’2 NUM cana-307 84 96 . . PUNCT cana-307 85 1 the the DET cana-307 85 2 preference preference NOUN cana-307 85 3 value value NOUN cana-307 85 4 of of ADP cana-307 85 5 the the DET cana-307 85 6 persons person NOUN cana-307 85 7 3,4,2,5,6 3,4,2,5,6 NUM cana-307 85 8 is be AUX cana-307 85 9 4 4 NUM cana-307 85 10 4 4 NUM cana-307 85 11 , , PUNCT cana-307 85 12 4 4 NUM cana-307 85 13 4 4 NUM cana-307 85 14 , , PUNCT cana-307 85 15 3 3 NUM cana-307 85 16 4 4 NUM cana-307 85 17 , , PUNCT cana-307 85 18 2 2 NUM cana-307 85 19 4 4 NUM cana-307 85 20 and and CCONJ cana-307 85 21 1 1 NUM cana-307 85 22 4 4 NUM cana-307 85 23 with with ADP cana-307 85 24 respect respect NOUN cana-307 85 25 to to ADP cana-307 85 26 person person NOUN cana-307 85 27 1 1 NUM cana-307 85 28 . . PUNCT cana-307 86 1 the the DET cana-307 86 2 preference preference NOUN cana-307 86 3 value value NOUN cana-307 86 4 of of ADP cana-307 86 5 persons person NOUN cana-307 86 6 5,3,1,6,4 5,3,1,6,4 NUM cana-307 86 7 is be AUX cana-307 86 8 4 4 NUM cana-307 86 9 4 4 NUM cana-307 86 10 , , PUNCT cana-307 86 11 4 4 NUM cana-307 86 12 4 4 NUM cana-307 86 13 , , PUNCT cana-307 86 14 3 3 NUM cana-307 86 15 4 4 NUM cana-307 86 16 , , PUNCT cana-307 86 17 2 2 NUM cana-307 86 18 4 4 NUM cana-307 86 19 , , PUNCT cana-307 86 20 and and CCONJ cana-307 86 21 1 1 NUM cana-307 86 22 4 4 NUM cana-307 86 23 with with ADP cana-307 86 24 respect respect NOUN cana-307 86 25 to to ADP cana-307 86 26 person person NOUN cana-307 86 27 2 2 NUM cana-307 86 28 . . PUNCT cana-307 87 1 the the DET cana-307 87 2 preference preference NOUN cana-307 87 3 value value NOUN cana-307 87 4 for for ADP cana-307 87 5 persons person NOUN cana-307 87 6 2,4,6,5,1 2,4,6,5,1 NUM cana-307 87 7 is be AUX cana-307 87 8 4 4 NUM cana-307 87 9 4 4 NUM cana-307 87 10 , , PUNCT cana-307 87 11 4 4 NUM cana-307 87 12 4 4 NUM cana-307 87 13 , , PUNCT cana-307 87 14 3 3 NUM cana-307 87 15 4 4 NUM cana-307 87 16 , , PUNCT cana-307 87 17 2 2 NUM cana-307 87 18 4 4 NUM cana-307 87 19 , , PUNCT cana-307 87 20 and and CCONJ cana-307 87 21 1 1 NUM cana-307 87 22 4 4 NUM cana-307 87 23 with with ADP cana-307 87 24 respect respect NOUN cana-307 87 25 to to ADP cana-307 87 26 person person NOUN cana-307 87 27 3 3 NUM cana-307 87 28 . . PUNCT cana-307 88 1 the the DET cana-307 88 2 preference preference NOUN cana-307 88 3 value value NOUN cana-307 88 4 for for ADP cana-307 88 5 persons person NOUN cana-307 88 6 3,1,6,2 3,1,6,2 NUM cana-307 88 7 is be AUX cana-307 88 8 4 4 NUM cana-307 88 9 4 4 NUM cana-307 88 10 , , PUNCT cana-307 88 11 4 4 NUM cana-307 88 12 4 4 NUM cana-307 88 13 , , PUNCT cana-307 88 14 3 3 NUM cana-307 88 15 4 4 NUM cana-307 88 16 , , PUNCT cana-307 88 17 2 2 NUM cana-307 88 18 4 4 NUM cana-307 88 19 , , PUNCT cana-307 88 20 with with ADP cana-307 88 21 respect respect NOUN cana-307 88 22 to to ADP cana-307 88 23 person person NOUN cana-307 88 24 4 4 NUM cana-307 88 25 . . PUNCT cana-307 89 1 the the DET cana-307 89 2 preference preference NOUN cana-307 89 3 value value NOUN cana-307 89 4 for for ADP cana-307 89 5 persons person NOUN cana-307 89 6 2,6,3,1 2,6,3,1 NUM cana-307 89 7 is be AUX cana-307 89 8 4 4 NUM cana-307 89 9 4 4 NUM cana-307 89 10 , , PUNCT cana-307 89 11 4 4 NUM cana-307 89 12 4 4 NUM cana-307 89 13 , , PUNCT cana-307 89 14 3 3 NUM cana-307 89 15 4 4 NUM cana-307 89 16 , , PUNCT cana-307 89 17 2 2 NUM cana-307 89 18 4 4 NUM cana-307 89 19 with with ADP cana-307 89 20 respect respect NOUN cana-307 89 21 to to ADP cana-307 89 22 person person NOUN cana-307 89 23 5 5 NUM cana-307 89 24 . . PUNCT cana-307 90 1 the the DET cana-307 90 2 preference preference NOUN cana-307 90 3 value value NOUN cana-307 90 4 for for ADP cana-307 90 5 members member NOUN cana-307 90 6 3,5,4,2,1 3,5,4,2,1 NUM cana-307 90 7 is be AUX cana-307 90 8 4 4 NUM cana-307 90 9 4 4 NUM cana-307 90 10 , , PUNCT cana-307 90 11 4 4 NUM cana-307 90 12 4 4 NUM cana-307 90 13 , , PUNCT cana-307 90 14 3 3 NUM cana-307 90 15 4 4 NUM cana-307 90 16 , , PUNCT cana-307 90 17 2 2 NUM cana-307 90 18 4 4 NUM cana-307 90 19 and and CCONJ cana-307 90 20 1 1 NUM cana-307 90 21 4 4 NUM cana-307 90 22 with with ADP cana-307 90 23 respect respect NOUN cana-307 90 24 to to ADP cana-307 90 25 person person NOUN cana-307 90 26 6 6 NUM cana-307 90 27 . . PUNCT cana-307 91 1 the the DET cana-307 91 2 preference preference NOUN cana-307 91 3 values value NOUN cana-307 91 4 are be AUX cana-307 91 5 presented present VERB cana-307 91 6 in in ADP cana-307 91 7 the the DET cana-307 91 8 form form NOUN cana-307 91 9 of of ADP cana-307 91 10 matrix matrix NOUN cana-307 91 11 which which PRON cana-307 91 12 is be AUX cana-307 91 13 given give VERB cana-307 91 14 below below ADP cana-307 91 15 communications communication NOUN cana-307 91 16 on on ADP cana-307 91 17 applied apply VERB cana-307 91 18 nonlinear nonlinear ADJ cana-307 91 19 analysis analysis NOUN cana-307 91 20 issn issn NOUN cana-307 91 21 : : PUNCT cana-307 91 22 1074 1074 NUM cana-307 91 23 - - PUNCT cana-307 91 24 133x 133x NUM cana-307 91 25 vol vol NOUN cana-307 91 26 30 30 NUM cana-307 91 27 no no NOUN cana-307 91 28 . . NOUN cana-307 91 29 4 4 NUM cana-307 91 30 ( ( PUNCT cana-307 91 31 2023 2023 NUM cana-307 91 32 ) ) PUNCT cana-307 91 33 62 62 NUM cana-307 91 34 https://internationalpubls.com https://internationalpubls.com X cana-307 91 35 the the DET cana-307 91 36 preference preference NOUN cana-307 91 37 value value NOUN cana-307 91 38 matrix matrix NOUN cana-307 91 39 1 1 NUM cana-307 91 40 2 2 NUM cana-307 91 41 3 3 NUM cana-307 91 42 4 4 NUM cana-307 91 43 5 5 NUM cana-307 91 44 6 6 NUM cana-307 91 45 3 3 NUM cana-307 91 46 4 4 NUM cana-307 91 47 4 4 NUM cana-307 91 48 2 2 NUM cana-307 91 49 1 1 NUM cana-307 91 50 1 1 NUM cana-307 91 51 4 4 NUM cana-307 91 52 4 4 NUM cana-307 91 53 4 4 NUM cana-307 91 54 4 4 NUM cana-307 91 55 4 4 NUM cana-307 91 56 3 3 NUM cana-307 91 57 4 4 NUM cana-307 91 58 1 1 NUM cana-307 91 59 4 4 NUM cana-307 91 60 2 2 NUM cana-307 91 61 2 2 NUM cana-307 91 62 4 4 NUM cana-307 91 63 4 4 NUM cana-307 91 64 4 4 NUM cana-307 91 65 4 4 NUM cana-307 91 66 4 4 NUM cana-307 91 67 1 1 NUM cana-307 91 68 4 4 NUM cana-307 91 69 4 4 NUM cana-307 91 70 2 2 NUM cana-307 91 71 3 3 NUM cana-307 91 72 3 3 NUM cana-307 91 73 4 4 NUM cana-307 91 74 4 4 NUM cana-307 91 75 4 4 NUM cana-307 91 76 4 4 NUM cana-307 91 77 4 4 NUM cana-307 91 78 4 4 NUM cana-307 91 79 2 2 NUM cana-307 91 80 4 4 NUM cana-307 91 81 3 3 NUM cana-307 91 82 4 4 NUM cana-307 91 83 4 4 NUM cana-307 91 84 4 4 NUM cana-307 91 85 4 4 NUM cana-307 91 86 4 4 NUM cana-307 91 87 2 2 NUM cana-307 91 88 4 4 NUM cana-307 91 89 3 3 NUM cana-307 91 90 4 4 NUM cana-307 91 91 5 5 NUM cana-307 91 92 4 4 NUM cana-307 91 93 4 4 NUM cana-307 91 94 4 4 NUM cana-307 91 95 4 4 NUM cana-307 91 96 1 1 NUM cana-307 91 97 2 2 NUM cana-307 91 98 4 4 NUM cana-307 91 99 3 3 NUM cana-307 91 100 4 4 NUM cana-307 91 101 6 6 NUM cana-307 91 102 4 4 NUM cana-307 91 103 4 4 NUM cana-307 91 104 4 4 NUM cana-307 91 105 4 4 NUM cana-307 91 106 4 4 NUM cana-307 91 107 pvm pvm NOUN cana-307 91 108 βˆ’ βˆ’ ADP cana-307 91 109 βˆ’ βˆ’ NOUN cana-307 91 110 βˆ’ βˆ’ PROPN cana-307 92 1 = = SYM cana-307 92 2 βˆ’ βˆ’ PROPN cana-307 92 3 βˆ’ βˆ’ PROPN cana-307 93 1 βˆ’ βˆ’ PROPN cana-307 93 2 βˆ’ βˆ’ PROPN cana-307 93 3 βˆ’ βˆ’ PROPN cana-307 94 1 from from ADP cana-307 94 2 the the DET cana-307 94 3 preference preference NOUN cana-307 94 4 value value NOUN cana-307 94 5 matrix matrix NOUN cana-307 94 6 to to PART cana-307 94 7 construct construct VERB cana-307 94 8 the the DET cana-307 94 9 minimized minimized ADJ cana-307 94 10 preference preference NOUN cana-307 94 11 value value NOUN cana-307 94 12 matrix matrix NOUN cana-307 94 13 by by ADP cana-307 94 14 subtracting subtract VERB cana-307 94 15 all all DET cana-307 94 16 the the DET cana-307 94 17 elements element NOUN cana-307 94 18 in in ADP cana-307 94 19 the the DET cana-307 94 20 matrix matrix NOUN cana-307 94 21 from from ADP cana-307 94 22 the the DET cana-307 94 23 highest high ADJ cana-307 94 24 element element NOUN cana-307 94 25 in in ADP cana-307 94 26 the the DET cana-307 94 27 matrix matrix NOUN cana-307 94 28 . . PUNCT cana-307 95 1 then then ADV cana-307 95 2 the the DET cana-307 95 3 minimized minimized ADJ cana-307 95 4 preference preference NOUN cana-307 95 5 value value NOUN cana-307 95 6 matrix matrix NOUN cana-307 95 7 given give VERB cana-307 95 8 below below ADP cana-307 95 9 the the DET cana-307 95 10 minimized minimized ADJ cana-307 95 11 preference preference NOUN cana-307 95 12 value value NOUN cana-307 95 13 matrix matrix NOUN cana-307 95 14 1 1 NUM cana-307 95 15 2 2 NUM cana-307 95 16 3 3 NUM cana-307 95 17 4 4 NUM cana-307 95 18 5 5 NUM cana-307 95 19 6 6 NUM cana-307 95 20 1 1 NUM cana-307 95 21 2 2 NUM cana-307 95 22 3 3 NUM cana-307 95 23 1 1 NUM cana-307 95 24 0 0 NUM cana-307 95 25 0 0 NUM cana-307 95 26 4 4 NUM cana-307 95 27 4 4 NUM cana-307 95 28 4 4 NUM cana-307 95 29 1 1 NUM cana-307 95 30 3 3 NUM cana-307 95 31 2 2 NUM cana-307 95 32 2 2 NUM cana-307 95 33 0 0 NUM cana-307 95 34 0 0 NUM cana-307 95 35 4 4 NUM cana-307 95 36 4 4 NUM cana-307 95 37 4 4 NUM cana-307 95 38 3 3 NUM cana-307 95 39 2 2 NUM cana-307 95 40 1 1 NUM cana-307 95 41 3 3 NUM cana-307 95 42 0 0 NUM cana-307 95 43 0 0 NUM cana-307 95 44 4 4 NUM cana-307 95 45 4 4 NUM cana-307 95 46 4 4 NUM cana-307 95 47 2 2 NUM cana-307 95 48 1 1 NUM cana-307 95 49 4 4 NUM cana-307 95 50 0 0 NUM cana-307 95 51 0 0 NUM cana-307 95 52 4 4 NUM cana-307 95 53 4 4 NUM cana-307 95 54 2 2 NUM cana-307 95 55 1 1 NUM cana-307 95 56 5 5 NUM cana-307 95 57 0 0 NUM cana-307 95 58 0 0 NUM cana-307 95 59 4 4 NUM cana-307 95 60 4 4 NUM cana-307 95 61 3 3 NUM cana-307 95 62 2 2 NUM cana-307 95 63 1 1 NUM cana-307 95 64 6 6 NUM cana-307 95 65 0 0 NUM cana-307 95 66 0 0 NUM cana-307 95 67 4 4 NUM cana-307 95 68 4 4 NUM cana-307 95 69 4 4 NUM cana-307 95 70 mpvm mpvm NOUN cana-307 95 71 βˆ’ βˆ’ ADP cana-307 95 72 βˆ’ βˆ’ NOUN cana-307 95 73 βˆ’ βˆ’ PROPN cana-307 95 74 = = SYM cana-307 96 1 βˆ’ βˆ’ PROPN cana-307 96 2 βˆ’ βˆ’ PROPN cana-307 97 1 βˆ’ βˆ’ PROPN cana-307 97 2 βˆ’ βˆ’ NOUN cana-307 97 3 βˆ’ βˆ’ NUM cana-307 97 4 considering consider VERB cana-307 97 5 the the DET cana-307 97 6 mpvm mpvm PROPN cana-307 97 7 as as ADP cana-307 97 8 the the DET cana-307 97 9 assignment assignment NOUN cana-307 97 10 problem problem NOUN cana-307 97 11 and and CCONJ cana-307 97 12 applying apply VERB cana-307 97 13 hungarian hungarian ADJ cana-307 97 14 algorithm algorithm NOUN cana-307 97 15 for for ADP cana-307 97 16 finding find VERB cana-307 97 17 the the DET cana-307 97 18 optimum optimum ADJ cana-307 97 19 pairs pair NOUN cana-307 97 20 . . PUNCT cana-307 98 1 ( ( PUNCT cana-307 98 2 1,4),(2,3),(3,2),(4,1),(5,6),(6,5 1,4),(2,3),(3,2),(4,1),(5,6),(6,5 AUX cana-307 98 3 ) ) PUNCT cana-307 98 4 be be AUX cana-307 98 5 the the DET cana-307 98 6 optimum optimum ADJ cana-307 98 7 pairs pair NOUN cana-307 98 8 . . PUNCT cana-307 99 1 communications communication NOUN cana-307 99 2 on on ADP cana-307 99 3 applied apply VERB cana-307 99 4 nonlinear nonlinear ADJ cana-307 99 5 analysis analysis NOUN cana-307 99 6 issn issn NOUN cana-307 99 7 : : PUNCT cana-307 99 8 1074 1074 NUM cana-307 99 9 - - PUNCT cana-307 99 10 133x 133x NUM cana-307 99 11 vol vol NOUN cana-307 99 12 30 30 NUM cana-307 99 13 no no NOUN cana-307 99 14 . . NOUN cana-307 99 15 4 4 NUM cana-307 99 16 ( ( PUNCT cana-307 99 17 2023 2023 NUM cana-307 99 18 ) ) PUNCT cana-307 99 19 63 63 NUM cana-307 99 20 https://internationalpubls.com https://internationalpubls.com X cana-307 99 21 to to PART cana-307 99 22 find find VERB cana-307 99 23 the the DET cana-307 99 24 optimum optimum ADJ cana-307 99 25 triples triple NOUN cana-307 99 26 , , PUNCT cana-307 99 27 from from ADP cana-307 99 28 the the DET cana-307 99 29 mpvm mpvm PROPN cana-307 99 30 choose choose X cana-307 99 31 ( ( PUNCT cana-307 99 32 1,4 1,4 ADJ cana-307 99 33 ) ) PUNCT cana-307 99 34 pair pair NOUN cana-307 99 35 , , PUNCT cana-307 99 36 the the DET cana-307 99 37 first first ADJ cana-307 99 38 row row NOUN cana-307 99 39 fourth fourth ADJ cana-307 99 40 column column NOUN cana-307 99 41 corresponding correspond VERB cana-307 99 42 element element NOUN cana-307 99 43 0 0 PUNCT cana-307 99 44 and and CCONJ cana-307 99 45 add add VERB cana-307 99 46 with with ADP cana-307 99 47 entire entire ADJ cana-307 99 48 first first ADJ cana-307 99 49 row row NOUN cana-307 99 50 and and CCONJ cana-307 99 51 assign assign VERB cana-307 99 52 that that DET cana-307 99 53 particular particular ADJ cana-307 99 54 element element NOUN cana-307 99 55 place place NOUN cana-307 99 56 with with ADP cana-307 99 57 - - PUNCT cana-307 99 58 . . PUNCT cana-307 100 1 likewise likewise ADV cana-307 100 2 , , PUNCT cana-307 100 3 choose choose VERB cana-307 100 4 the the DET cana-307 100 5 next next ADJ cana-307 100 6 pair pair NOUN cana-307 100 7 ( ( PUNCT cana-307 100 8 2,3 2,3 NUM cana-307 100 9 ) ) PUNCT cana-307 100 10 , , PUNCT cana-307 100 11 the the DET cana-307 100 12 second second ADJ cana-307 100 13 row row NOUN cana-307 100 14 third third ADJ cana-307 100 15 column column NOUN cana-307 100 16 element element NOUN cana-307 100 17 0 0 PUNCT cana-307 100 18 and and CCONJ cana-307 100 19 add add VERB cana-307 100 20 with with ADP cana-307 100 21 entire entire ADJ cana-307 100 22 second second ADJ cana-307 100 23 row row NOUN cana-307 100 24 and and CCONJ cana-307 100 25 assign assign VERB cana-307 100 26 that that DET cana-307 100 27 particular particular ADJ cana-307 100 28 element element NOUN cana-307 100 29 place place NOUN cana-307 100 30 with with ADP cana-307 100 31 - - PUNCT cana-307 100 32 . . PUNCT cana-307 100 33 similarly similarly ADV cana-307 100 34 , , PUNCT cana-307 100 35 repeat repeat VERB cana-307 100 36 the the DET cana-307 100 37 process process NOUN cana-307 100 38 for for ADP cana-307 100 39 all all DET cana-307 100 40 optimum optimum ADJ cana-307 100 41 pairs pair NOUN cana-307 100 42 . . PUNCT cana-307 101 1 then then ADV cana-307 101 2 the the DET cana-307 101 3 resultant resultant NOUN cana-307 101 4 matrix matrix NOUN cana-307 101 5 will will AUX cana-307 101 6 be be AUX cana-307 101 7 a a DET cana-307 101 8 modified modify VERB cana-307 101 9 minimum minimum NOUN cana-307 101 10 preference preference NOUN cana-307 101 11 value value NOUN cana-307 101 12 matrix matrix NOUN cana-307 101 13 ( ( PUNCT cana-307 101 14 mmpvm mmpvm NOUN cana-307 101 15 ) ) PUNCT cana-307 101 16 . . PUNCT cana-307 102 1 the the DET cana-307 102 2 modified modify VERB cana-307 102 3 minimum minimum NOUN cana-307 102 4 preference preference NOUN cana-307 102 5 value value NOUN cana-307 102 6 matrix matrix NOUN cana-307 102 7 is be AUX cana-307 102 8 given give VERB cana-307 102 9 below below ADP cana-307 102 10 , , PUNCT cana-307 102 11 1 1 NUM cana-307 102 12 2 2 NUM cana-307 102 13 3 3 NUM cana-307 102 14 4 4 NUM cana-307 102 15 5 5 NUM cana-307 102 16 6 6 NUM cana-307 102 17 1 1 NUM cana-307 102 18 2 2 NUM cana-307 102 19 3 3 NUM cana-307 102 20 ( ( PUNCT cana-307 102 21 1,4 1,4 NUM cana-307 102 22 ) ) PUNCT cana-307 102 23 0 0 NUM cana-307 102 24 4 4 NUM cana-307 102 25 4 4 NUM cana-307 102 26 4 4 NUM cana-307 102 27 1 1 NUM cana-307 102 28 3 3 NUM cana-307 102 29 2 2 NUM cana-307 102 30 ( ( PUNCT cana-307 102 31 2,3 2,3 NUM cana-307 102 32 ) ) PUNCT cana-307 102 33 0 0 NUM cana-307 102 34 4 4 NUM cana-307 102 35 4 4 NUM cana-307 102 36 4 4 NUM cana-307 102 37 3 3 NUM cana-307 102 38 2 2 NUM cana-307 102 39 1 1 NUM cana-307 102 40 ( ( PUNCT cana-307 102 41 3,2 3,2 NUM cana-307 102 42 ) ) PUNCT cana-307 102 43 0 0 NUM cana-307 102 44 4 4 NUM cana-307 102 45 4 4 NUM cana-307 102 46 4 4 NUM cana-307 102 47 2 2 NUM cana-307 102 48 1 1 NUM cana-307 102 49 ( ( PUNCT cana-307 102 50 4,1 4,1 NUM cana-307 102 51 ) ) PUNCT cana-307 102 52 0 0 NUM cana-307 102 53 4 4 NUM cana-307 102 54 4 4 NUM cana-307 102 55 2 2 NUM cana-307 102 56 1 1 NUM cana-307 102 57 ( ( PUNCT cana-307 102 58 5,6 5,6 NUM cana-307 102 59 ) ) PUNCT cana-307 102 60 0 0 NUM cana-307 102 61 4 4 NUM cana-307 102 62 4 4 NUM cana-307 102 63 3 3 NUM cana-307 102 64 2 2 NUM cana-307 102 65 1 1 NUM cana-307 102 66 ( ( PUNCT cana-307 102 67 6,5 6,5 NUM cana-307 102 68 ) ) PUNCT cana-307 102 69 0 0 NUM cana-307 102 70 4 4 NUM cana-307 102 71 4 4 NUM cana-307 102 72 4 4 NUM cana-307 102 73 mmpvm mmpvm NOUN cana-307 102 74 βˆ’ βˆ’ PROPN cana-307 102 75 βˆ’ βˆ’ PROPN cana-307 102 76 βˆ’ βˆ’ PROPN cana-307 102 77 βˆ’ βˆ’ PROPN cana-307 102 78 βˆ’ βˆ’ NOUN cana-307 102 79 βˆ’ βˆ’ PROPN cana-307 102 80 = = SYM cana-307 102 81 βˆ’ βˆ’ PROPN cana-307 102 82 βˆ’ βˆ’ PROPN cana-307 103 1 βˆ’ βˆ’ PROPN cana-307 103 2 βˆ’ βˆ’ PROPN cana-307 103 3 βˆ’ βˆ’ PROPN cana-307 103 4 βˆ’ βˆ’ PROPN cana-307 103 5 βˆ’ βˆ’ NOUN cana-307 104 1 βˆ’ βˆ’ ADP cana-307 104 2 considering consider VERB cana-307 104 3 this this DET cana-307 104 4 above above ADJ cana-307 104 5 matrix matrix NOUN cana-307 104 6 as as ADP cana-307 104 7 the the DET cana-307 104 8 assignment assignment NOUN cana-307 104 9 problem problem NOUN cana-307 104 10 and and CCONJ cana-307 104 11 apply apply VERB cana-307 104 12 hungarian hungarian ADJ cana-307 104 13 algorithm algorithm NOUN cana-307 104 14 then then ADV cana-307 104 15 get get VERB cana-307 104 16 the the DET cana-307 104 17 optimum optimum ADJ cana-307 104 18 triples triple NOUN cana-307 104 19 . . PUNCT cana-307 105 1 the the DET cana-307 105 2 triples triple NOUN cana-307 105 3 are be AUX cana-307 105 4 ( ( PUNCT cana-307 105 5 1,4,2 1,4,2 NUM cana-307 105 6 ) ) PUNCT cana-307 105 7 , , PUNCT cana-307 105 8 ( ( PUNCT cana-307 105 9 2,3,5 2,3,5 NUM cana-307 105 10 ) ) PUNCT cana-307 105 11 , , PUNCT cana-307 105 12 ( ( PUNCT cana-307 105 13 3,2,4 3,2,4 NOUN cana-307 105 14 ) ) PUNCT cana-307 105 15 ( ( PUNCT cana-307 105 16 4,1,6 4,1,6 PROPN cana-307 105 17 ) ) PUNCT cana-307 105 18 , , PUNCT cana-307 105 19 ( ( PUNCT cana-307 105 20 5,6,1 5,6,1 NUM cana-307 105 21 ) ) PUNCT cana-307 105 22 , , PUNCT cana-307 105 23 ( ( PUNCT cana-307 105 24 6,3,5 6,3,5 NUM cana-307 105 25 ) ) PUNCT cana-307 105 26 . . PUNCT cana-307 106 1 to to PART cana-307 106 2 obtain obtain VERB cana-307 106 3 a a DET cana-307 106 4 best good ADJ cana-307 106 5 three three NUM cana-307 106 6 persons person NOUN cana-307 106 7 as as ADP cana-307 106 8 a a DET cana-307 106 9 roommate roommate NOUN cana-307 106 10 , , PUNCT cana-307 106 11 by by ADP cana-307 106 12 calculate calculate NOUN cana-307 106 13 an an DET cana-307 106 14 individual individual ADJ cana-307 106 15 preference preference NOUN cana-307 106 16 value value NOUN cana-307 106 17 and and CCONJ cana-307 106 18 overall overall ADJ cana-307 106 19 satisfaction satisfaction NOUN cana-307 106 20 . . PUNCT cana-307 107 1 choose choose VERB cana-307 107 2 the the DET cana-307 107 3 first first ADJ cana-307 107 4 triple triple ADJ cana-307 107 5 ( ( PUNCT cana-307 107 6 1,4,2 1,4,2 NUM cana-307 107 7 ) ) PUNCT cana-307 107 8 , , PUNCT cana-307 107 9 to to PART cana-307 107 10 get get VERB cana-307 107 11 1st 1st ADJ cana-307 107 12 person person NOUN cana-307 107 13 satisfactory satisfactory ADJ cana-307 107 14 value value NOUN cana-307 107 15 , , PUNCT cana-307 107 16 by by ADP cana-307 107 17 adding add VERB cana-307 107 18 the the DET cana-307 107 19 4th 4th ADJ cana-307 107 20 person person NOUN cana-307 107 21 ’s ’s PART cana-307 107 22 preference preference NOUN cana-307 107 23 value value NOUN cana-307 107 24 in in ADP cana-307 107 25 the the DET cana-307 107 26 preference preference NOUN cana-307 107 27 value value NOUN cana-307 107 28 matrix matrix NOUN cana-307 107 29 with with ADP cana-307 107 30 respect respect NOUN cana-307 107 31 to to ADP cana-307 107 32 4th 4th ADJ cana-307 107 33 person person NOUN cana-307 107 34 and and CCONJ cana-307 107 35 3rd 3rd ADJ cana-307 107 36 person person NOUN cana-307 107 37 and and CCONJ cana-307 107 38 an an DET cana-307 107 39 individual individual ADJ cana-307 107 40 satisfaction satisfaction NOUN cana-307 107 41 level level NOUN cana-307 107 42 can can AUX cana-307 107 43 be be AUX cana-307 107 44 obtained obtain VERB cana-307 107 45 to to ADP cana-307 107 46 multiplying multiply VERB cana-307 107 47 by by ADP cana-307 107 48 50 50 NUM cana-307 107 49 . . PUNCT cana-307 108 1 that that PRON cana-307 108 2 is be AUX cana-307 108 3 1 1 NUM cana-307 108 4 β†’ β†’ SYM cana-307 108 5 4 4 NUM cana-307 108 6 4 4 NUM cana-307 108 7 + + CCONJ cana-307 108 8 3 3 NUM cana-307 108 9 4 4 NUM cana-307 108 10 = = SYM cana-307 108 11 7 7 NUM cana-307 108 12 4 4 NUM cana-307 108 13 Γ— Γ— NOUN cana-307 108 14 50 50 NUM cana-307 108 15 = = SYM cana-307 108 16 87.5 87.5 NUM cana-307 108 17 % % NOUN cana-307 108 18 . . PUNCT cana-307 109 1 4 4 NUM cana-307 109 2 β†’ β†’ SYM cana-307 109 3 4 4 NUM cana-307 109 4 4 4 NUM cana-307 109 5 + + CCONJ cana-307 109 6 2 2 NUM cana-307 109 7 4 4 NUM cana-307 109 8 = = SYM cana-307 109 9 6 6 NUM cana-307 109 10 4 4 NUM cana-307 109 11 Γ— Γ— NOUN cana-307 109 12 50 50 NUM cana-307 109 13 = = SYM cana-307 109 14 75 75 NUM cana-307 109 15 % % NOUN cana-307 109 16 . . PUNCT cana-307 110 1 2 2 NUM cana-307 110 2 β†’ β†’ SYM cana-307 110 3 3 3 NUM cana-307 110 4 4 4 NUM cana-307 110 5 + + CCONJ cana-307 110 6 1 1 NUM cana-307 110 7 4 4 NUM cana-307 110 8 = = SYM cana-307 110 9 1 1 NUM cana-307 110 10 Γ— Γ— NOUN cana-307 110 11 50 50 NUM cana-307 110 12 = = SYM cana-307 110 13 50 50 NUM cana-307 110 14 % % NOUN cana-307 110 15 . . PUNCT cana-307 111 1 find find VERB cana-307 111 2 the the DET cana-307 111 3 average average NOUN cana-307 111 4 for for ADP cana-307 111 5 the the DET cana-307 111 6 individual individual ADJ cana-307 111 7 satisfaction satisfaction NOUN cana-307 111 8 for for ADP cana-307 111 9 getting get VERB cana-307 111 10 the the DET cana-307 111 11 overall overall ADJ cana-307 111 12 satisfaction satisfaction NOUN cana-307 111 13 level level NOUN cana-307 111 14 . . PUNCT cana-307 112 1 that that PRON cana-307 112 2 is be AUX cana-307 112 3 , , PUNCT cana-307 112 4 87.5 87.5 NUM cana-307 112 5 + + NOUN cana-307 112 6 75 75 NUM cana-307 112 7 + + SYM cana-307 112 8 50 50 NUM cana-307 112 9 = = SYM cana-307 113 1 212.5 212.5 NUM cana-307 113 2 3 3 NUM cana-307 113 3 = = SYM cana-307 113 4 70.8 70.8 NUM cana-307 113 5 % % NOUN cana-307 113 6 . . PUNCT cana-307 114 1 9970.8 9970.8 NUM cana-307 114 2 % % NOUN cana-307 114 3 will will AUX cana-307 114 4 be be AUX cana-307 114 5 the the DET cana-307 114 6 overall overall ADJ cana-307 114 7 satisfaction satisfaction NOUN cana-307 114 8 for for ADP cana-307 114 9 the the DET cana-307 114 10 1st 1st ADJ cana-307 114 11 , , PUNCT cana-307 114 12 4th 4th ADJ cana-307 114 13 , , PUNCT cana-307 114 14 2nd 2nd ADJ cana-307 114 15 person person NOUN cana-307 114 16 as as ADP cana-307 114 17 the the DET cana-307 114 18 roommates roommate NOUN cana-307 114 19 . . PUNCT cana-307 115 1 communications communication NOUN cana-307 115 2 on on ADP cana-307 115 3 applied apply VERB cana-307 115 4 nonlinear nonlinear ADJ cana-307 115 5 analysis analysis NOUN cana-307 115 6 issn issn NOUN cana-307 115 7 : : PUNCT cana-307 115 8 1074 1074 NUM cana-307 115 9 - - PUNCT cana-307 115 10 133x 133x NUM cana-307 115 11 vol vol NOUN cana-307 115 12 30 30 NUM cana-307 115 13 no no NOUN cana-307 115 14 . . NOUN cana-307 115 15 4 4 NUM cana-307 115 16 ( ( PUNCT cana-307 115 17 2023 2023 NUM cana-307 115 18 ) ) PUNCT cana-307 115 19 64 64 NUM cana-307 115 20 https://internationalpubls.com https://internationalpubls.com X cana-307 115 21 similarly similarly ADV cana-307 115 22 this this DET cana-307 115 23 process process NOUN cana-307 115 24 can can AUX cana-307 115 25 be be AUX cana-307 115 26 applied apply VERB cana-307 115 27 for for ADP cana-307 115 28 all all DET cana-307 115 29 the the DET cana-307 115 30 triples triple NOUN cana-307 115 31 which which PRON cana-307 115 32 we we PRON cana-307 115 33 have have VERB cana-307 115 34 . . PUNCT cana-307 116 1 now now ADV cana-307 116 2 choose choose VERB cana-307 116 3 mutually mutually ADV cana-307 116 4 exclusive exclusive ADJ cana-307 116 5 and and CCONJ cana-307 116 6 exhaustive exhaustive ADJ cana-307 116 7 triples triple NOUN cana-307 116 8 , , PUNCT cana-307 116 9 then then ADV cana-307 116 10 the the DET cana-307 116 11 result result NOUN cana-307 116 12 as as SCONJ cana-307 116 13 shown show VERB cana-307 116 14 in in ADP cana-307 116 15 the the DET cana-307 116 16 table table NOUN cana-307 116 17 1 1 NUM cana-307 116 18 , , PUNCT cana-307 116 19 table table NOUN cana-307 116 20 1 1 NUM cana-307 116 21 . . PUNCT cana-307 116 22 three three NUM cana-307 116 23 person person NOUN cana-307 116 24 individual individual ADJ cana-307 116 25 and and CCONJ cana-307 116 26 overall overall ADJ cana-307 116 27 satisfactory satisfactory ADJ cana-307 116 28 matching matching NOUN cana-307 116 29 s.no s.no PROPN cana-307 116 30 possible possible ADJ cana-307 116 31 triples triple NOUN cana-307 116 32 individual individual ADJ cana-307 116 33 satisfaction satisfaction NOUN cana-307 116 34 overall overall ADJ cana-307 116 35 satisfaction satisfaction NOUN cana-307 116 36 1 1 NUM cana-307 116 37 ( ( PUNCT cana-307 116 38 1,4,2 1,4,2 NUM cana-307 116 39 ) ) PUNCT cana-307 116 40 1 1 NUM cana-307 116 41 β†’ β†’ SYM cana-307 116 42 2 2 NUM cana-307 116 43 & & CCONJ cana-307 116 44 4 4 NUM cana-307 116 45 = = SYM cana-307 116 46 87.5 87.5 NUM cana-307 116 47 % % NOUN cana-307 116 48 . . PUNCT cana-307 117 1 70.8 70.8 NUM cana-307 117 2 % % NOUN cana-307 117 3 77 77 NUM cana-307 117 4 2 2 NUM cana-307 117 5 β†’ β†’ SYM cana-307 117 6 1 1 NUM cana-307 117 7 & & CCONJ cana-307 117 8 4 4 NUM cana-307 117 9 = = SYM cana-307 117 10 50 50 NUM cana-307 117 11 % % NOUN cana-307 117 12 . . PUNCT cana-307 118 1 4 4 NUM cana-307 118 2 β†’ β†’ SYM cana-307 118 3 1 1 NUM cana-307 118 4 & & CCONJ cana-307 118 5 2 2 NUM cana-307 118 6 = = SYM cana-307 118 7 75 75 NUM cana-307 118 8 % % NOUN cana-307 118 9 . . PUNCT cana-307 119 1 2 2 NUM cana-307 119 2 ( ( PUNCT cana-307 119 3 3,5,6 3,5,6 NUM cana-307 119 4 ) ) PUNCT cana-307 119 5 3 3 NUM cana-307 119 6 β†’ β†’ SYM cana-307 119 7 5 5 NUM cana-307 119 8 & & CCONJ cana-307 119 9 6 6 NUM cana-307 119 10 = = SYM cana-307 119 11 62.5 62.5 NUM cana-307 119 12 % % NOUN cana-307 119 13 . . PUNCT cana-307 120 1 83.33 83.33 NUM cana-307 120 2 % % NOUN cana-307 120 3 5 5 NUM cana-307 120 4 β†’ β†’ SYM cana-307 120 5 3 3 NUM cana-307 120 6 & & CCONJ cana-307 120 7 6 6 NUM cana-307 120 8 = = SYM cana-307 120 9 87.5 87.5 NUM cana-307 120 10 % % NOUN cana-307 120 11 . . PUNCT cana-307 121 1 6 6 NUM cana-307 121 2 β†’ β†’ SYM cana-307 121 3 3 3 NUM cana-307 121 4 & & CCONJ cana-307 121 5 5 5 NUM cana-307 121 6 = = SYM cana-307 121 7 100 100 NUM cana-307 121 8 % % NOUN cana-307 121 9 . . PUNCT cana-307 122 1 3 3 NUM cana-307 122 2 ( ( PUNCT cana-307 122 3 2,3,5 2,3,5 NUM cana-307 122 4 ) ) PUNCT cana-307 122 5 2 2 NUM cana-307 122 6 β†’ β†’ SYM cana-307 122 7 3 3 NUM cana-307 122 8 & & CCONJ cana-307 122 9 5 5 NUM cana-307 122 10 = = SYM cana-307 122 11 100 100 NUM cana-307 122 12 % % NOUN cana-307 122 13 . . PUNCT cana-307 123 1 87.5 87.5 NUM cana-307 123 2 % % NOUN cana-307 123 3 77 77 NUM cana-307 123 4 3 3 NUM cana-307 123 5 β†’ β†’ SYM cana-307 123 6 2 2 NUM cana-307 123 7 & & CCONJ cana-307 123 8 5 5 NUM cana-307 123 9 = = SYM cana-307 123 10 75 75 NUM cana-307 123 11 % % NOUN cana-307 123 12 . . PUNCT cana-307 124 1 5 5 NUM cana-307 124 2 β†’ β†’ SYM cana-307 124 3 2 2 NUM cana-307 124 4 & & CCONJ cana-307 124 5 3 3 NUM cana-307 124 6 = = SYM cana-307 124 7 87.5 87.5 NUM cana-307 124 8 % % NOUN cana-307 124 9 . . PUNCT cana-307 125 1 4 4 NUM cana-307 125 2 ( ( PUNCT cana-307 125 3 4,1,6 4,1,6 NUM cana-307 125 4 ) ) PUNCT cana-307 125 5 4 4 NUM cana-307 125 6 β†’ β†’ SYM cana-307 125 7 1 1 NUM cana-307 125 8 & & CCONJ cana-307 125 9 6 6 NUM cana-307 125 10 = = SYM cana-307 125 11 87.5 87.5 NUM cana-307 125 12 % % NOUN cana-307 125 13 . . PUNCT cana-307 126 1 66.66 66.66 NUM cana-307 126 2 % % NOUN cana-307 126 3 1 1 NUM cana-307 126 4 β†’ β†’ SYM cana-307 126 5 4 4 NUM cana-307 126 6 & & CCONJ cana-307 126 7 6 6 NUM cana-307 126 8 = = SYM cana-307 126 9 62.5 62.5 NUM cana-307 126 10 % % NOUN cana-307 126 11 . . PUNCT cana-307 127 1 6 6 NUM cana-307 127 2 β†’ β†’ SYM cana-307 127 3 1 1 NUM cana-307 127 4 & & CCONJ cana-307 127 5 4 4 NUM cana-307 127 6 = = SYM cana-307 127 7 50 50 NUM cana-307 127 8 % % NOUN cana-307 127 9 . . PUNCT cana-307 128 1 5 5 NUM cana-307 128 2 ( ( PUNCT cana-307 128 3 5,6,1 5,6,1 NUM cana-307 128 4 ) ) PUNCT cana-307 128 5 5 5 NUM cana-307 128 6 β†’ β†’ SYM cana-307 128 7 1 1 NUM cana-307 128 8 & & CCONJ cana-307 128 9 6 6 NUM cana-307 128 10 = = SYM cana-307 128 11 75 75 NUM cana-307 128 12 % % NOUN cana-307 128 13 . . PUNCT cana-307 129 1 58.33 58.33 NUM cana-307 129 2 % % NOUN cana-307 129 3 69 69 NUM cana-307 129 4 6 6 NUM cana-307 129 5 β†’ β†’ SYM cana-307 129 6 1 1 NUM cana-307 129 7 & & CCONJ cana-307 129 8 5 5 NUM cana-307 129 9 = = SYM cana-307 129 10 62.5 62.5 NUM cana-307 129 11 % % NOUN cana-307 129 12 . . PUNCT cana-307 130 1 1 1 NUM cana-307 130 2 β†’ β†’ SYM cana-307 130 3 5 5 NUM cana-307 130 4 & & CCONJ cana-307 130 5 6 6 NUM cana-307 130 6 = = SYM cana-307 130 7 37.5 37.5 NUM cana-307 130 8 % % NOUN cana-307 130 9 . . PUNCT cana-307 131 1 6 6 NUM cana-307 131 2 ( ( PUNCT cana-307 131 3 3,2,4 3,2,4 NOUN cana-307 131 4 ) ) PUNCT cana-307 131 5 3 3 NUM cana-307 131 6 β†’ β†’ SYM cana-307 131 7 2 2 NUM cana-307 131 8 & & CCONJ cana-307 131 9 4 4 NUM cana-307 131 10 = = SYM cana-307 131 11 100 100 NUM cana-307 131 12 % % NOUN cana-307 131 13 . . PUNCT cana-307 132 1 79.16 79.16 NUM cana-307 132 2 % % NOUN cana-307 132 3 2 2 NUM cana-307 132 4 β†’ β†’ SYM cana-307 132 5 3 3 NUM cana-307 132 6 & & CCONJ cana-307 132 7 4 4 NUM cana-307 132 8 = = SYM cana-307 132 9 62.5 62.5 NUM cana-307 132 10 % % NOUN cana-307 132 11 . . PUNCT cana-307 133 1 4 4 NUM cana-307 133 2 β†’ β†’ SYM cana-307 133 3 2 2 NUM cana-307 133 4 & & CCONJ cana-307 133 5 3 3 NUM cana-307 133 6 = = SYM cana-307 133 7 75 75 NUM cana-307 133 8 % % NOUN cana-307 133 9 . . PUNCT cana-307 134 1 from from ADP cana-307 134 2 the the DET cana-307 134 3 above above ADJ cana-307 134 4 table table NOUN cana-307 134 5 , , PUNCT cana-307 134 6 the the DET cana-307 134 7 overall overall ADJ cana-307 134 8 satisfaction satisfaction NOUN cana-307 134 9 of of ADP cana-307 134 10 the the DET cana-307 134 11 triples triple NOUN cana-307 134 12 ( ( PUNCT cana-307 134 13 1,2,4 1,2,4 NUM cana-307 134 14 ) ) PUNCT cana-307 134 15 , , PUNCT cana-307 134 16 ( ( PUNCT cana-307 134 17 3,5,6 3,5,6 NUM cana-307 134 18 ) ) PUNCT cana-307 134 19 and and CCONJ cana-307 134 20 ( ( PUNCT cana-307 134 21 2,3,5 2,3,5 NUM cana-307 134 22 ) ) PUNCT cana-307 134 23 , , PUNCT cana-307 134 24 ( ( PUNCT cana-307 134 25 1,4,6 1,4,6 NUM cana-307 134 26 ) ) PUNCT cana-307 134 27 are be AUX cana-307 134 28 77 77 NUM cana-307 134 29 percentage percentage NOUN cana-307 134 30 , , PUNCT cana-307 134 31 that that PRON cana-307 134 32 is be AUX cana-307 134 33 both both PRON cana-307 134 34 have have VERB cana-307 134 35 the the DET cana-307 134 36 same same ADJ cana-307 134 37 overall overall ADJ cana-307 134 38 satisfaction satisfaction NOUN cana-307 134 39 percentage percentage NOUN cana-307 134 40 . . PUNCT cana-307 135 1 then then ADV cana-307 135 2 we we PRON cana-307 135 3 have have VERB cana-307 135 4 to to PART cana-307 135 5 move move VERB cana-307 135 6 the the DET cana-307 135 7 other other ADJ cana-307 135 8 hand hand NOUN cana-307 135 9 for for ADP cana-307 135 10 finding find VERB cana-307 135 11 the the DET cana-307 135 12 best good ADJ cana-307 135 13 triples triple NOUN cana-307 135 14 as as ADP cana-307 135 15 the the DET cana-307 135 16 roommates roommate NOUN cana-307 135 17 . . PUNCT cana-307 136 1 consider consider VERB cana-307 136 2 the the DET cana-307 136 3 individual individual ADJ cana-307 136 4 satisfaction satisfaction NOUN cana-307 136 5 percentage percentage NOUN cana-307 136 6 for for ADP cana-307 136 7 possible possible ADJ cana-307 136 8 triples triple NOUN cana-307 136 9 , , PUNCT cana-307 136 10 and and CCONJ cana-307 136 11 calculate calculate VERB cana-307 136 12 the the DET cana-307 136 13 range range NOUN cana-307 136 14 of of ADP cana-307 136 15 them they PRON cana-307 136 16 . . PUNCT cana-307 137 1 we we PRON cana-307 137 2 know know VERB cana-307 137 3 that that SCONJ cana-307 137 4 , , PUNCT cana-307 137 5 the the DET cana-307 137 6 lowest low ADJ cana-307 137 7 range range NOUN cana-307 137 8 is be AUX cana-307 137 9 the the DET cana-307 137 10 best good ADJ cana-307 137 11 one one NUM cana-307 137 12 . . PUNCT cana-307 138 1 the the DET cana-307 138 2 range range NOUN cana-307 138 3 can can AUX cana-307 138 4 be be AUX cana-307 138 5 calculated calculate VERB cana-307 138 6 by by ADP cana-307 138 7 subtracting subtract VERB cana-307 138 8 the the DET cana-307 138 9 lowest low ADJ cana-307 138 10 value value NOUN cana-307 138 11 from from ADP cana-307 138 12 the the DET cana-307 138 13 highest high ADJ cana-307 138 14 value value NOUN cana-307 138 15 . . PUNCT cana-307 139 1 in in ADP cana-307 139 2 the the DET cana-307 139 3 possible possible ADJ cana-307 139 4 triple triple ADJ cana-307 139 5 ( ( PUNCT cana-307 139 6 1,2,4 1,2,4 NUM cana-307 139 7 ) ) PUNCT cana-307 139 8 , , PUNCT cana-307 139 9 the the DET cana-307 139 10 highest high ADJ cana-307 139 11 percentage percentage NOUN cana-307 139 12 is be AUX cana-307 139 13 87.5 87.5 NUM cana-307 139 14 and and CCONJ cana-307 139 15 the the DET cana-307 139 16 lowest low ADJ cana-307 139 17 percentage percentage NOUN cana-307 139 18 is be AUX cana-307 139 19 50 50 NUM cana-307 139 20 . . PUNCT cana-307 140 1 then then ADV cana-307 140 2 the the DET cana-307 140 3 range range NOUN cana-307 140 4 is be AUX cana-307 140 5 87.5 87.5 NUM cana-307 140 6 – – PUNCT cana-307 140 7 50 50 NUM cana-307 140 8 = = SYM cana-307 140 9 37.5 37.5 NUM cana-307 140 10 % % NOUN cana-307 140 11 in in ADP cana-307 140 12 the the DET cana-307 140 13 possible possible ADJ cana-307 140 14 triple triple ADJ cana-307 140 15 ( ( PUNCT cana-307 140 16 3,5,6 3,5,6 NUM cana-307 140 17 ) ) PUNCT cana-307 140 18 , , PUNCT cana-307 140 19 the the DET cana-307 140 20 highest high ADJ cana-307 140 21 percentage percentage NOUN cana-307 140 22 is be AUX cana-307 140 23 100 100 NUM cana-307 140 24 and and CCONJ cana-307 140 25 the the DET cana-307 140 26 lowest low ADJ cana-307 140 27 percentage percentage NOUN cana-307 140 28 is be AUX cana-307 140 29 62.5 62.5 NUM cana-307 140 30 . . PUNCT cana-307 141 1 then then ADV cana-307 141 2 the the DET cana-307 141 3 range range NOUN cana-307 141 4 is be AUX cana-307 141 5 100 100 NUM cana-307 141 6 – – PUNCT cana-307 141 7 62.5 62.5 NUM cana-307 141 8 = = SYM cana-307 141 9 37.5 37.5 NUM cana-307 141 10 % % NOUN cana-307 141 11 in in ADP cana-307 141 12 the the DET cana-307 141 13 possible possible ADJ cana-307 141 14 triple triple ADJ cana-307 141 15 ( ( PUNCT cana-307 141 16 2,3,5 2,3,5 NUM cana-307 141 17 ) ) PUNCT cana-307 141 18 , , PUNCT cana-307 141 19 the the DET cana-307 141 20 highest high ADJ cana-307 141 21 percentage percentage NOUN cana-307 141 22 is be AUX cana-307 141 23 100 100 NUM cana-307 141 24 and and CCONJ cana-307 141 25 the the DET cana-307 141 26 lowest low ADJ cana-307 141 27 percentage percentage NOUN cana-307 141 28 is be AUX cana-307 141 29 75 75 NUM cana-307 141 30 . . PUNCT cana-307 142 1 then then ADV cana-307 142 2 the the DET cana-307 142 3 range range NOUN cana-307 142 4 is be AUX cana-307 142 5 100 100 NUM cana-307 142 6 – – PUNCT cana-307 142 7 75 75 NUM cana-307 142 8 = = SYM cana-307 142 9 25 25 NUM cana-307 142 10 % % NOUN cana-307 142 11 communications communication NOUN cana-307 142 12 on on ADP cana-307 142 13 applied apply VERB cana-307 142 14 nonlinear nonlinear ADJ cana-307 142 15 analysis analysis NOUN cana-307 142 16 issn issn NOUN cana-307 142 17 : : PUNCT cana-307 142 18 1074 1074 NUM cana-307 142 19 - - PUNCT cana-307 142 20 133x 133x NUM cana-307 142 21 vol vol NOUN cana-307 142 22 30 30 NUM cana-307 142 23 no no NOUN cana-307 142 24 . . NOUN cana-307 142 25 4 4 NUM cana-307 142 26 ( ( PUNCT cana-307 142 27 2023 2023 NUM cana-307 142 28 ) ) PUNCT cana-307 142 29 65 65 NUM cana-307 142 30 https://internationalpubls.com https://internationalpubls.com X cana-307 142 31 in in ADP cana-307 142 32 the the DET cana-307 142 33 possible possible ADJ cana-307 142 34 triple triple ADJ cana-307 142 35 ( ( PUNCT cana-307 142 36 1,4,6 1,4,6 NUM cana-307 142 37 ) ) PUNCT cana-307 142 38 , , PUNCT cana-307 142 39 the the DET cana-307 142 40 highest high ADJ cana-307 142 41 percentage percentage NOUN cana-307 142 42 is be AUX cana-307 142 43 87.5 87.5 NUM cana-307 142 44 and and CCONJ cana-307 142 45 the the DET cana-307 142 46 lowest low ADJ cana-307 142 47 percentage percentage NOUN cana-307 142 48 is be AUX cana-307 142 49 50 50 NUM cana-307 142 50 . . PUNCT cana-307 143 1 then then ADV cana-307 143 2 the the DET cana-307 143 3 range range NOUN cana-307 143 4 is be AUX cana-307 143 5 87.5 87.5 NUM cana-307 143 6 – – PUNCT cana-307 143 7 50 50 NUM cana-307 143 8 = = SYM cana-307 143 9 37.5 37.5 NUM cana-307 143 10 % % NOUN cana-307 143 11 by by ADP cana-307 143 12 examine examine VERB cana-307 143 13 the the DET cana-307 143 14 range range NOUN cana-307 143 15 of of ADP cana-307 143 16 the the DET cana-307 143 17 triples triple NOUN cana-307 143 18 , , PUNCT cana-307 143 19 ( ( PUNCT cana-307 143 20 2,3,5 2,3,5 NUM cana-307 143 21 ) ) PUNCT cana-307 143 22 have have VERB cana-307 143 23 the the DET cana-307 143 24 lowest low ADJ cana-307 143 25 range range NOUN cana-307 143 26 percentage percentage NOUN cana-307 143 27 . . PUNCT cana-307 144 1 so so ADV cana-307 144 2 , , PUNCT cana-307 144 3 we we PRON cana-307 144 4 conclude conclude VERB cana-307 144 5 that that SCONJ cana-307 144 6 , , PUNCT cana-307 144 7 the the DET cana-307 144 8 triples triple NOUN cana-307 144 9 ( ( PUNCT cana-307 144 10 2,3,5 2,3,5 NUM cana-307 144 11 ) ) PUNCT cana-307 144 12 and and CCONJ cana-307 144 13 ( ( PUNCT cana-307 144 14 1,4,6 1,4,6 NUM cana-307 144 15 ) ) PUNCT cana-307 144 16 best good ADJ cana-307 144 17 triples triple NOUN cana-307 144 18 as as ADP cana-307 144 19 the the DET cana-307 144 20 roommates roommate NOUN cana-307 144 21 . . PUNCT cana-307 145 1 5 5 X cana-307 145 2 . . X cana-307 145 3 conclusion conclusion NOUN cana-307 145 4 in in ADP cana-307 145 5 this this DET cana-307 145 6 paper paper NOUN cana-307 145 7 , , PUNCT cana-307 145 8 we we PRON cana-307 145 9 proposed propose VERB cana-307 145 10 a a DET cana-307 145 11 preference preference NOUN cana-307 145 12 value value NOUN cana-307 145 13 for for ADP cana-307 145 14 the the DET cana-307 145 15 preferred preferred ADJ cana-307 145 16 incomplete incomplete ADJ cana-307 145 17 lists list NOUN cana-307 145 18 of of ADP cana-307 145 19 roommate roommate NOUN cana-307 145 20 ’s ’s PART cana-307 145 21 instances instance NOUN cana-307 145 22 with with ADP cana-307 145 23 three three NUM cana-307 145 24 person person NOUN cana-307 145 25 rooms room NOUN cana-307 145 26 , , PUNCT cana-307 145 27 and and CCONJ cana-307 145 28 described describe VERB cana-307 145 29 an an DET cana-307 145 30 algorithm algorithm NOUN cana-307 145 31 tpsma tpsma NOUN cana-307 145 32 . . PUNCT cana-307 146 1 this this DET cana-307 146 2 algorithm algorithm NOUN cana-307 146 3 yields yield VERB cana-307 146 4 a a DET cana-307 146 5 triple triple ADJ cana-307 146 6 matching matching NOUN cana-307 146 7 in in ADP cana-307 146 8 addition addition NOUN cana-307 146 9 to to ADP cana-307 146 10 a a DET cana-307 146 11 perfect perfect ADJ cana-307 146 12 , , PUNCT cana-307 146 13 satisfactory satisfactory ADJ cana-307 146 14 matching matching NOUN cana-307 146 15 pair pair NOUN cana-307 146 16 in in ADP cana-307 146 17 its its PRON cana-307 146 18 initial initial ADJ cana-307 146 19 place place NOUN cana-307 146 20 . . PUNCT cana-307 147 1 we we PRON cana-307 147 2 determine determine VERB cana-307 147 3 that that SCONJ cana-307 147 4 the the DET cana-307 147 5 acquired acquire VERB cana-307 147 6 matching matching NOUN cana-307 147 7 yields yield NOUN cana-307 147 8 flawless flawless ADJ cana-307 147 9 triple triple ADJ cana-307 147 10 matching matching NOUN cana-307 147 11 after after ADP cana-307 147 12 looking look VERB cana-307 147 13 over over ADP cana-307 147 14 the the DET cana-307 147 15 data datum NOUN cana-307 147 16 . . PUNCT cana-307 148 1 here here ADV cana-307 148 2 , , PUNCT cana-307 148 3 we we PRON cana-307 148 4 've have AUX cana-307 148 5 demonstrated demonstrate VERB cana-307 148 6 the the DET cana-307 148 7 speed speed NOUN cana-307 148 8 and and CCONJ cana-307 148 9 effectiveness effectiveness NOUN cana-307 148 10 of of ADP cana-307 148 11 tpsma tpsma PROPN cana-307 148 12 . . PUNCT cana-307 149 1 this this DET cana-307 149 2 algorithm algorithm NOUN cana-307 149 3 produces produce VERB cana-307 149 4 a a DET cana-307 149 5 matching matching NOUN cana-307 149 6 where where SCONJ cana-307 149 7 every every DET cana-307 149 8 pair pair NOUN cana-307 149 9 reaches reach VERB cana-307 149 10 the the DET cana-307 149 11 highest high ADJ cana-307 149 12 level level NOUN cana-307 149 13 of of ADP cana-307 149 14 satisfaction satisfaction NOUN cana-307 149 15 possible possible ADJ cana-307 149 16 . . PUNCT cana-307 150 1 thus thus ADV cana-307 150 2 , , PUNCT cana-307 150 3 roommates roommate NOUN cana-307 150 4 with with ADP cana-307 150 5 incomplete incomplete ADJ cana-307 150 6 lists list NOUN cana-307 150 7 are be AUX cana-307 150 8 satisfactorily satisfactorily ADV cana-307 150 9 matched match VERB cana-307 150 10 according accord VERB cana-307 150 11 to to ADP cana-307 150 12 tpsma tpsma PROPN cana-307 150 13 results result NOUN cana-307 150 14 . . PUNCT cana-307 151 1 references reference NOUN cana-307 151 2 [ [ X cana-307 151 3 1 1 NUM cana-307 151 4 ] ] PUNCT cana-307 151 5 birΓ³ birΓ³ NOUN cana-307 151 6 , , PUNCT cana-307 151 7 p. p. PROPN cana-307 151 8 , , PUNCT cana-307 151 9 manlove manlove PROPN cana-307 151 10 , , PUNCT cana-307 151 11 d. d. PROPN cana-307 151 12 f. f. PROPN cana-307 151 13 , , PUNCT cana-307 151 14 & & CCONJ cana-307 151 15 mcdermid mcdermid PROPN cana-307 151 16 , , PUNCT cana-307 151 17 e. e. PROPN cana-307 151 18 j. j. PROPN cana-307 151 19 ( ( PUNCT cana-307 151 20 2012 2012 NUM cana-307 151 21 ) ) PUNCT cana-307 151 22 . . PUNCT cana-307 152 1 β€œ " PUNCT cana-307 152 2 almost almost ADV cana-307 152 3 stable stable ADJ cana-307 152 4 ” " PUNCT cana-307 152 5 matchings matching NOUN cana-307 152 6 in in ADP cana-307 152 7 the the DET cana-307 152 8 roommates roommate NOUN cana-307 152 9 problem problem NOUN cana-307 152 10 with with ADP cana-307 152 11 bounded bounded ADJ cana-307 152 12 preference preference NOUN cana-307 152 13 lists list NOUN cana-307 152 14 . . PUNCT cana-307 153 1 theoretical theoretical ADJ cana-307 153 2 computer computer NOUN cana-307 153 3 science science NOUN cana-307 153 4 , , PUNCT cana-307 153 5 432 432 NUM cana-307 153 6 , , PUNCT cana-307 153 7 1020 1020 NUM cana-307 153 8 . . PUNCT cana-307 154 1 [ [ X cana-307 154 2 2 2 NUM cana-307 154 3 ] ] X cana-307 154 4 cseh cseh NOUN cana-307 154 5 , , PUNCT cana-307 154 6 Γ‘ Γ‘ PROPN cana-307 154 7 . . PROPN cana-307 154 8 , , PUNCT cana-307 154 9 irving irving PROPN cana-307 154 10 , , PUNCT cana-307 154 11 r. r. PROPN cana-307 154 12 w. w. PROPN cana-307 154 13 , , PUNCT cana-307 154 14 & & CCONJ cana-307 154 15 manlove manlove PROPN cana-307 154 16 , , PUNCT cana-307 154 17 d. d. PROPN cana-307 154 18 f. f. PROPN cana-307 154 19 ( ( PUNCT cana-307 154 20 2019 2019 NUM cana-307 154 21 ) ) PUNCT cana-307 154 22 . . PUNCT cana-307 155 1 the the DET cana-307 155 2 stable stable ADJ cana-307 155 3 roommates roommate NOUN cana-307 155 4 problem problem VERB cana-307 155 5 with with ADP cana-307 155 6 short short ADJ cana-307 155 7 lists list NOUN cana-307 155 8 . . PUNCT cana-307 156 1 theory theory NOUN cana-307 156 2 of of ADP cana-307 156 3 computing computing NOUN cana-307 156 4 systems system NOUN cana-307 156 5 , , PUNCT cana-307 156 6 63 63 NUM cana-307 156 7 , , PUNCT cana-307 156 8 128 128 NUM cana-307 156 9 - - SYM cana-307 156 10 149 149 NUM cana-307 156 11 . . PUNCT cana-307 157 1 [ [ X cana-307 157 2 3 3 NUM cana-307 157 3 ] ] X cana-307 157 4 adil adil PROPN cana-307 157 5 , , PUNCT cana-307 157 6 d. d. PROPN cana-307 157 7 , , PUNCT cana-307 157 8 gupta gupta PROPN cana-307 157 9 , , PUNCT cana-307 157 10 s. s. PROPN cana-307 157 11 , , PUNCT cana-307 157 12 roy roy PROPN cana-307 157 13 , , PUNCT cana-307 157 14 s. s. PROPN cana-307 157 15 , , PUNCT cana-307 157 16 saurabh saurabh PROPN cana-307 157 17 , , PUNCT cana-307 157 18 s. s. PROPN cana-307 157 19 , , PUNCT cana-307 157 20 & & CCONJ cana-307 157 21 zehavi zehavi PROPN cana-307 157 22 , , PUNCT cana-307 157 23 m. m. NOUN cana-307 157 24 ( ( PUNCT cana-307 157 25 2018 2018 NUM cana-307 157 26 ) ) PUNCT cana-307 157 27 . . PUNCT cana-307 158 1 parameterized parameterized ADJ cana-307 158 2 algorithms algorithm NOUN cana-307 158 3 for for ADP cana-307 158 4 stable stable ADJ cana-307 158 5 matching matching NOUN cana-307 158 6 with with ADP cana-307 158 7 ties tie NOUN cana-307 158 8 and and CCONJ cana-307 158 9 incomplete incomplete ADJ cana-307 158 10 lists list NOUN cana-307 158 11 . . PUNCT cana-307 159 1 theoretical theoretical ADJ cana-307 159 2 computer computer NOUN cana-307 159 3 science science NOUN cana-307 159 4 , , PUNCT cana-307 159 5 723 723 NUM cana-307 159 6 , , PUNCT cana-307 159 7 1 1 NUM cana-307 159 8 - - SYM cana-307 159 9 10 10 NUM cana-307 159 10 . . PUNCT cana-307 160 1 [ [ X cana-307 160 2 4 4 NUM cana-307 160 3 ] ] X cana-307 160 4 fidan fidan PROPN cana-307 160 5 , , PUNCT cana-307 160 6 m. m. NOUN cana-307 160 7 , , PUNCT cana-307 160 8 & & CCONJ cana-307 160 9 erdem erdem PROPN cana-307 160 10 , , PUNCT cana-307 160 11 e. e. PROPN cana-307 160 12 ( ( PUNCT cana-307 160 13 2021 2021 NUM cana-307 160 14 ) ) PUNCT cana-307 160 15 . . PUNCT cana-307 161 1 knowledge knowledge NOUN cana-307 161 2 - - PUNCT cana-307 161 3 based base VERB cana-307 161 4 stable stable ADJ cana-307 161 5 roommates roommate NOUN cana-307 161 6 problem problem NOUN cana-307 161 7 : : PUNCT cana-307 161 8 a a DET cana-307 161 9 real real ADJ cana-307 161 10 - - PUNCT cana-307 161 11 world world NOUN cana-307 161 12 application application NOUN cana-307 161 13 . . PUNCT cana-307 162 1 theory theory NOUN cana-307 162 2 and and CCONJ cana-307 162 3 practice practice NOUN cana-307 162 4 of of ADP cana-307 162 5 logic logic NOUN cana-307 162 6 programming programming NOUN cana-307 162 7 , , PUNCT cana-307 162 8 21(6 21(6 NOUN cana-307 162 9 ) ) PUNCT cana-307 162 10 , , PUNCT cana-307 162 11 852 852 NUM cana-307 162 12 - - SYM cana-307 162 13 869 869 NUM cana-307 162 14 . . PUNCT cana-307 163 1 [ [ X cana-307 163 2 5 5 NUM cana-307 163 3 ] ] X cana-307 163 4 erdem erdem PROPN cana-307 163 5 , , PUNCT cana-307 163 6 e. e. PROPN cana-307 163 7 , , PUNCT cana-307 163 8 fidan fidan PROPN cana-307 163 9 , , PUNCT cana-307 163 10 m. m. NOUN cana-307 163 11 , , PUNCT cana-307 163 12 manlove manlove PROPN cana-307 163 13 , , PUNCT cana-307 163 14 d. d. PROPN cana-307 163 15 , , PUNCT cana-307 163 16 & & CCONJ cana-307 163 17 prosser prosser PROPN cana-307 163 18 , , PUNCT cana-307 163 19 p. p. PROPN cana-307 163 20 ( ( PUNCT cana-307 163 21 2020 2020 NUM cana-307 163 22 ) ) PUNCT cana-307 163 23 . . PUNCT cana-307 164 1 a a DET cana-307 164 2 general general ADJ cana-307 164 3 framework framework NOUN cana-307 164 4 for for ADP cana-307 164 5 stable stable ADJ cana-307 164 6 roommates roommate NOUN cana-307 164 7 problems problem NOUN cana-307 164 8 using use VERB cana-307 164 9 answer answer NOUN cana-307 164 10 set set VERB cana-307 164 11 programming programming NOUN cana-307 164 12 . . PUNCT cana-307 165 1 theory theory NOUN cana-307 165 2 and and CCONJ cana-307 165 3 practice practice NOUN cana-307 165 4 of of ADP cana-307 165 5 logic logic NOUN cana-307 165 6 programming programming NOUN cana-307 165 7 , , PUNCT cana-307 165 8 20(6 20(6 NOUN cana-307 165 9 ) ) PUNCT cana-307 165 10 , , PUNCT cana-307 165 11 911 911 NUM cana-307 165 12 - - SYM cana-307 165 13 925 925 NUM cana-307 165 14 . . PUNCT cana-307 166 1 [ [ X cana-307 166 2 6 6 NUM cana-307 166 3 ] ] PUNCT cana-307 166 4 kunysz kunysz NOUN cana-307 166 5 , , PUNCT cana-307 166 6 a. a. NOUN cana-307 166 7 ( ( PUNCT cana-307 166 8 2016 2016 NUM cana-307 166 9 ) ) PUNCT cana-307 166 10 . . PUNCT cana-307 167 1 the the DET cana-307 167 2 strongly strongly ADV cana-307 167 3 stable stable ADJ cana-307 167 4 roommates roommate NOUN cana-307 167 5 problem problem NOUN cana-307 167 6 . . PUNCT cana-307 168 1 in in ADP cana-307 168 2 24th 24th ADJ cana-307 168 3 annual annual ADJ cana-307 168 4 european european ADJ cana-307 168 5 symposium symposium NOUN cana-307 168 6 on on ADP cana-307 168 7 algorithms algorithms PROPN cana-307 168 8 ( ( PUNCT cana-307 168 9 esa esa PROPN cana-307 168 10 2016 2016 NUM cana-307 168 11 ) ) PUNCT cana-307 168 12 . . PUNCT cana-307 169 1 schloss schloss PROPN cana-307 169 2 dagstuhl dagstuhl PROPN cana-307 169 3 - - PUNCT cana-307 169 4 leibniz leibniz PROPN cana-307 169 5 - - PUNCT cana-307 169 6 zentrum zentrum PROPN cana-307 169 7 fuer fuer PROPN cana-307 169 8 informatik informatik PROPN cana-307 169 9 . . PUNCT cana-307 170 1 [ [ X cana-307 170 2 7 7 NUM cana-307 170 3 ] ] SYM cana-307 170 4 bredereck bredereck NOUN cana-307 170 5 , , PUNCT cana-307 170 6 r. r. PROPN cana-307 170 7 , , PUNCT cana-307 170 8 heeger heeger NOUN cana-307 170 9 , , PUNCT cana-307 170 10 k. k. PROPN cana-307 170 11 , , PUNCT cana-307 170 12 knop knop PROPN cana-307 170 13 , , PUNCT cana-307 170 14 d. d. PROPN cana-307 170 15 , , PUNCT cana-307 170 16 & & CCONJ cana-307 170 17 niedermeier niedermeier PROPN cana-307 170 18 , , PUNCT cana-307 170 19 r. r. PROPN cana-307 170 20 ( ( PUNCT cana-307 170 21 2022 2022 NUM cana-307 170 22 ) ) PUNCT cana-307 170 23 . . PUNCT cana-307 171 1 parameterized parameterized ADJ cana-307 171 2 complexity complexity NOUN cana-307 171 3 of of ADP cana-307 171 4 stable stable ADJ cana-307 171 5 roommates roommate NOUN cana-307 171 6 with with ADP cana-307 171 7 ties tie NOUN cana-307 171 8 and and CCONJ cana-307 171 9 incomplete incomplete ADJ cana-307 171 10 lists list NOUN cana-307 171 11 through through ADP cana-307 171 12 the the DET cana-307 171 13 lens lens NOUN cana-307 171 14 of of ADP cana-307 171 15 graph graph NOUN cana-307 171 16 parameters parameter NOUN cana-307 171 17 . . PUNCT cana-307 172 1 information information NOUN cana-307 172 2 and and CCONJ cana-307 172 3 computation computation NOUN cana-307 172 4 , , PUNCT cana-307 172 5 289 289 NUM cana-307 172 6 , , PUNCT cana-307 172 7 104943 104943 NUM cana-307 172 8 . . PUNCT cana-307 173 1 [ [ X cana-307 173 2 8 8 NUM cana-307 173 3 ] ] SYM cana-307 173 4 irving irving PROPN cana-307 173 5 , , PUNCT cana-307 173 6 r. r. PROPN cana-307 173 7 w. w. PROPN cana-307 173 8 ( ( PUNCT cana-307 173 9 1985 1985 NUM cana-307 173 10 ) ) PUNCT cana-307 173 11 . . PUNCT cana-307 174 1 an an DET cana-307 174 2 efficient efficient ADJ cana-307 174 3 algorithm algorithm NOUN cana-307 174 4 for for ADP cana-307 174 5 the the DET cana-307 174 6 β€œ " PUNCT cana-307 174 7 stable stable ADJ cana-307 174 8 roommates roommate NOUN cana-307 174 9 ” " PUNCT cana-307 174 10 problem problem NOUN cana-307 174 11 . . PUNCT cana-307 175 1 journal journal NOUN cana-307 175 2 of of ADP cana-307 175 3 algorithms algorithms PROPN cana-307 175 4 , , PUNCT cana-307 175 5 6(4 6(4 NOUN cana-307 175 6 ) ) PUNCT cana-307 175 7 , , PUNCT cana-307 175 8 577 577 NUM cana-307 175 9 - - SYM cana-307 175 10 595 595 NUM cana-307 175 11 . . PUNCT cana-307 176 1 [ [ X cana-307 176 2 9 9 NUM cana-307 176 3 ] ] X cana-307 176 4 gusfield gusfield NOUN cana-307 176 5 , , PUNCT cana-307 176 6 d. d. PROPN cana-307 176 7 , , PUNCT cana-307 176 8 & & CCONJ cana-307 176 9 irving irving PROPN cana-307 176 10 , , PUNCT cana-307 176 11 r. r. PROPN cana-307 176 12 w. w. PROPN cana-307 176 13 ( ( PUNCT cana-307 176 14 1989 1989 NUM cana-307 176 15 ) ) PUNCT cana-307 176 16 . . PUNCT cana-307 177 1 the the DET cana-307 177 2 stable stable ADJ cana-307 177 3 marriage marriage NOUN cana-307 177 4 problem problem NOUN cana-307 177 5 : : PUNCT cana-307 177 6 structure structure NOUN cana-307 177 7 and and CCONJ cana-307 177 8 algorithms algorithm NOUN cana-307 177 9 . . PUNCT cana-307 178 1 mit mit PROPN cana-307 178 2 press press NOUN cana-307 178 3 . . PUNCT cana-307 179 1 [ [ X cana-307 179 2 10 10 NUM cana-307 179 3 ] ] X cana-307 179 4 lam lam PROPN cana-307 179 5 , , PUNCT cana-307 179 6 c. c. PROPN cana-307 179 7 k. k. PROPN cana-307 179 8 , , PUNCT cana-307 179 9 & & CCONJ cana-307 179 10 plaxton plaxton PROPN cana-307 179 11 , , PUNCT cana-307 179 12 c. c. PROPN cana-307 179 13 g. g. PROPN cana-307 179 14 ( ( PUNCT cana-307 179 15 2019 2019 NUM cana-307 179 16 ) ) PUNCT cana-307 179 17 . . PUNCT cana-307 180 1 a a DET cana-307 180 2 ( ( PUNCT cana-307 180 3 1 1 NUM cana-307 180 4 + + NUM cana-307 180 5 1 1 NUM cana-307 180 6 / / SYM cana-307 180 7 e)-approximation e)-approximation NOUN cana-307 180 8 algorithm algorithm NOUN cana-307 180 9 for for ADP cana-307 180 10 maximum maximum ADJ cana-307 180 11 stable stable ADJ cana-307 180 12 matching matching NOUN cana-307 180 13 with with ADP cana-307 180 14 one one NUM cana-307 180 15 - - PUNCT cana-307 180 16 sided sided ADJ cana-307 180 17 ties tie NOUN cana-307 180 18 and and CCONJ cana-307 180 19 incomplete incomplete ADJ cana-307 180 20 lists list NOUN cana-307 180 21 . . PUNCT cana-307 181 1 in in ADP cana-307 181 2 proceedings proceeding NOUN cana-307 181 3 of of ADP cana-307 181 4 the the DET cana-307 181 5 thirtieth thirtieth ADJ cana-307 181 6 annual annual ADJ cana-307 181 7 acm acm NOUN cana-307 181 8 - - PUNCT cana-307 181 9 siam siam NOUN cana-307 181 10 symposium symposium NOUN cana-307 181 11 on on ADP cana-307 181 12 discrete discrete ADJ cana-307 181 13 algorithms algorithm NOUN cana-307 181 14 ( ( PUNCT cana-307 181 15 pp pp ADJ cana-307 181 16 . . PUNCT cana-307 181 17 2823 2823 NUM cana-307 181 18 - - SYM cana-307 181 19 2840 2840 NUM cana-307 181 20 ) ) PUNCT cana-307 181 21 . . PUNCT cana-307 182 1 society society NOUN cana-307 182 2 for for ADP cana-307 182 3 industrial industrial ADJ cana-307 182 4 and and CCONJ cana-307 182 5 applied applied ADJ cana-307 182 6 mathematics mathematic NOUN cana-307 182 7 . . PUNCT cana-307 183 1 [ [ X cana-307 183 2 11 11 NUM cana-307 183 3 ] ] PUNCT cana-307 183 4 iwama iwama PROPN cana-307 183 5 , , PUNCT cana-307 183 6 k. k. PROPN cana-307 183 7 , , PUNCT cana-307 183 8 miyazaki miyazaki PROPN cana-307 183 9 , , PUNCT cana-307 183 10 s. s. PROPN cana-307 183 11 , , PUNCT cana-307 183 12 & & CCONJ cana-307 183 13 okamoto okamoto PROPN cana-307 183 14 , , PUNCT cana-307 183 15 k. k. PROPN cana-307 183 16 ( ( PUNCT cana-307 183 17 2007 2007 NUM cana-307 183 18 ) ) PUNCT cana-307 183 19 . . PUNCT cana-307 184 1 stable stable ADJ cana-307 184 2 roommates roommate NOUN cana-307 184 3 problem problem VERB cana-307 184 4 with with ADP cana-307 184 5 triple triple ADJ cana-307 184 6 rooms room NOUN cana-307 184 7 . . PUNCT cana-307 185 1 proceedings proceeding NOUN cana-307 185 2 of of ADP cana-307 185 3 waac waac NOUN cana-307 185 4 , , PUNCT cana-307 185 5 7 7 NUM cana-307 185 6 , , PUNCT cana-307 185 7 105 105 NUM cana-307 185 8 - - SYM cana-307 185 9 112 112 NUM cana-307 185 10 . . PUNCT cana-307 186 1 communications communication NOUN cana-307 186 2 on on ADP cana-307 186 3 applied apply VERB cana-307 186 4 nonlinear nonlinear ADJ cana-307 186 5 analysis analysis NOUN cana-307 186 6 issn issn NOUN cana-307 186 7 : : PUNCT cana-307 186 8 1074 1074 NUM cana-307 186 9 - - PUNCT cana-307 186 10 133x 133x NUM cana-307 186 11 vol vol NOUN cana-307 186 12 30 30 NUM cana-307 186 13 no no NOUN cana-307 186 14 . . NOUN cana-307 186 15 4 4 NUM cana-307 186 16 ( ( PUNCT cana-307 186 17 2023 2023 NUM cana-307 186 18 ) ) PUNCT cana-307 186 19 66 66 NUM cana-307 186 20 https://internationalpubls.com https://internationalpubls.com X cana-307 187 1 [ [ X cana-307 187 2 12 12 NUM cana-307 187 3 ] ] X cana-307 187 4 ramachandran ramachandran PROPN cana-307 187 5 , , PUNCT cana-307 187 6 t. t. PROPN cana-307 187 7 , , PUNCT cana-307 187 8 velusamy velusamy PROPN cana-307 187 9 , , PUNCT cana-307 187 10 k. k. PROPN cana-307 187 11 , , PUNCT cana-307 187 12 & & CCONJ cana-307 187 13 selvakumar selvakumar PROPN cana-307 187 14 , , PUNCT cana-307 187 15 t. t. PROPN cana-307 187 16 ( ( PUNCT cana-307 187 17 2012 2012 NUM cana-307 187 18 ) ) PUNCT cana-307 187 19 . . PUNCT cana-307 188 1 satisfactory satisfactory ADJ cana-307 188 2 roommates roommate NOUN cana-307 188 3 problem problem VERB cana-307 188 4 with with ADP cana-307 188 5 incomplete incomplete ADJ cana-307 188 6 list list NOUN cana-307 188 7 . . PUNCT cana-307 189 1 international international ADJ cana-307 189 2 journal journal PROPN cana-307 189 3 of of ADP cana-307 189 4 computational computational ADJ cana-307 189 5 science science NOUN cana-307 189 6 and and CCONJ cana-307 189 7 mathematics mathematic NOUN cana-307 189 8 . . PUNCT cana-307 190 1 issn issn PROPN cana-307 190 2 , , PUNCT cana-307 190 3 0974 0974 NUM cana-307 190 4 - - SYM cana-307 190 5 3189 3189 NUM cana-307 190 6 , , PUNCT cana-307 190 7 4(1 4(1 NOUN cana-307 190 8 ) ) PUNCT cana-307 190 9 , , PUNCT cana-307 190 10 19 19 NUM cana-307 190 11 - - SYM cana-307 190 12 22 22 NUM cana-307 190 13 . . PUNCT cana-307 191 1 [ [ X cana-307 191 2 13 13 NUM cana-307 191 3 ] ] SYM cana-307 191 4 logapriya logapriya PROPN cana-307 191 5 , , PUNCT cana-307 191 6 n. n. NOUN cana-307 191 7 , , PUNCT cana-307 191 8 & & CCONJ cana-307 191 9 ramachandran ramachandran PROPN cana-307 191 10 , , PUNCT cana-307 191 11 t. t. PROPN cana-307 191 12 ( ( PUNCT cana-307 191 13 2023 2023 NUM cana-307 191 14 ) ) PUNCT cana-307 191 15 . . PUNCT cana-307 192 1 three three NUM cana-307 192 2 persons person NOUN cana-307 192 3 satisfactory satisfactory ADJ cana-307 192 4 roommates roommate NOUN cana-307 192 5 problem problem NOUN cana-307 192 6 . . PUNCT cana-307 193 1 gradiva gradiva PROPN cana-307 193 2 review review PROPN cana-307 193 3 journal journal PROPN cana-307 193 4 , , PUNCT cana-307 193 5 issn0363 issn0363 PROPN cana-307 193 6 8257 8257 NUM cana-307 193 7 , , PUNCT cana-307 193 8 9(8 9(8 NUM cana-307 193 9 ) ) PUNCT cana-307 193 10 . . PUNCT cana-307 194 1 [ [ X cana-307 194 2 14 14 NUM cana-307 194 3 ] ] PUNCT cana-307 194 4 on on ADP cana-307 194 5 the the DET cana-307 194 6 nonlinear nonlinear PROPN cana-307 194 7 volterra volterra PROPN cana-307 194 8 equation equation NOUN cana-307 194 9 with with ADP cana-307 194 10 conformable conformable ADJ cana-307 194 11 derivative derivative NOUN cana-307 194 12 . . PUNCT cana-307 195 1 ( ( PUNCT cana-307 195 2 2023 2023 NUM cana-307 195 3 ) ) PUNCT cana-307 195 4 . . PUNCT cana-307 196 1 advances advance NOUN cana-307 196 2 in in ADP cana-307 196 3 the the DET cana-307 196 4 theory theory NOUN cana-307 196 5 of of ADP cana-307 196 6 nonlinear nonlinear ADJ cana-307 196 7 analysis analysis NOUN cana-307 196 8 and and CCONJ cana-307 196 9 its its PRON cana-307 196 10 application application NOUN cana-307 196 11 , , PUNCT cana-307 196 12 7(2 7(2 NUM cana-307 196 13 ) ) PUNCT cana-307 196 14 , , PUNCT cana-307 196 15 292 292 NUM cana-307 196 16 - - SYM cana-307 196 17 302 302 NUM cana-307 196 18 . . PUNCT