D:\sbornik\...\doc11.DVI Mathematical Problems of Computer Science 33, 111{120, 2010. On the P r oblem of Wir eless Scheduling With Linear P ower Levels Tig r a n To n o ya n Yerevan State University, Faculty of Informatics and Applied Mathematics, Department of Algebra and Discrete Mathematics Abstract In this work we consider the problem of communication scheduling in wireless net- works with respect to the SINR(Signal to Interference plus Noise Ratio) constraint in metric spaces. For the powers of sender nodes we consider the linear power assign- ment, which is one of commonly considered power schemes. We give a constant factor deterministic approximation algorithm for scheduling in wireless networks, which are given in some special class of metric spaces, which contains the Euclidean spaces. To the best of our knowledge, this is the ¯rst constant factor approximation algorithm for this problem. Simultaneously we obtain the approximate value of the optimal schedule length with error at most a constant factor. Refer ences [1 ] A . Fa n g h Äa n e l, T. K e ¼ e lh e im , H . R Äa c ke , B . V Äo kin g , \ Ob livio u s in t e r fe r e n c e s c h e d u lin g " , P roc. 28th Symposium on P rinciples of D istributed Computing (P OD C), 2 0 0 9 . [2 ] A . Fa n g h Äa n e l, T. K e ¼ e lh e im a n d B . V Äo kin g , \ Im p r o ve d A lg o r it h m s o n L a t e n c y Min i- m iz a t io n in W ir e le s s N e t wo r ks " , P roc. 36th International Colloqium on Automata, L an- guages and P rogramming (ICAL P ), 2 0 0 9 . [3 ] O. Go u s s e vs ka ia , M.M. H a lld ¶o r s s o n , R . W a t t e n h o fe r a n d E m o W e lz l. \ Ca p a c it y o f A r b it r a r y W ir e le s s N e t wo r ks " , 28th Annual IE E E Conference on Computer Communi- cations (INF OCOM ), 2 0 0 9 . [4 ] M.M. H a lld ¶o r s s o n , \ W ir e le s s S c h e d u lin g wit h P o we r Co n t r o l" P roc. 17th annual E u- ropean Symposium on Algorithms (E SA), 2 0 0 9 . [5 ] M.M. H a lld ¶o r s s o n a n d R . W a t t e n h o fe r , \ W ir e le s s Co m m u n ic a t io n is in A P X " , P roc. 36th International Colloqium on Automata, L anguages and P rogramming (ICAL P ), 2 0 0 9 . [6 ] G.H . H a r d y, J.E . L it t le wo o d , G. P ¶o lya , In e qu a lit ie s , Ca m b r id g e U n ive r s it y P r e s s , 1 9 3 4 . [7 ] S .O. K r u m ke , M.V . Ma r a t h e a n d S . S . R a vi, \ Mo d e ls a n d a p p r o xim a t io n a lg o r it h m s fo r c h a n n e l a s s ig n m e n t in r a d io n e t wo r ks " , W ir e le s s N e t wo r ks 7 , 2 0 0 1 . [8 ] T. Mo s c ib r o d a , R . W a t t e n h o fe r , \ Th e c o m p le xit y o f c o n n e c t ivit y in wir e le s s n e t wo r ks " , 25th Annual IE E E Conference on Computer Communications (INF OCOM ), 2 0 0 6 . [9 ] T. Mo s c ib r o d a , R . W a t t e n h o fe r a n d Y . W e b e r . \ P r o t o c o l D e s ig n B e yo n d Gr a p h -B a s e d Mo d e ls " , H o t To p ic s in N e t wo r ks ( H o t N e t s ) , 2 0 0 6 . 1 1 1 1 1 2 On the Problem of Wireless Scheduling With Linear Power Levels [1 0 ] T. Mo s c ib r o d a , R . W a t t e n h o fe r a n d A . Zo llin g e r , \ To p o lo g y c o n t r o l m e e t s S IN R : Th e s c h e d u lin g c o m p le xit y o f a r b it r a r y t o p o lo g ie s " , ACM International Symposium on M o- bile Ad Hoc Networking and Computing (M OB IHOC), 2 0 0 7 . [1 1 ] V . S . A . K u m a r , M. V . Ma r a t h e , S . P a r t h a s a r a t h y a n d A . S r in iva s a n , \ A lg o r it h m ic A s p e c t s o f Ca p a c it y in W ir e le s s N e t wo r ks " , ACM International Conference on M ea- surement and M odeling of Computer Systems (SIGM E TR ICS), 2 0 0 5 . ²é³Ýó ɳñÇ ó³Ýó»ñáõÙ ·Í³ÛÇÝ Ñ½áñáõÃÛáõÝÝ»ñáí Ñ»ñó·ñÙ³Ý ËݹñÇ Ù³ëÇÝ î. îáÝáÛ³Ý ²Ù÷á÷áõÙ ²Ûë ³ß˳ï³ÝùáõÙ ¹Çï³ñÏíáõÙ ¿ ³é³Ýó ɳñÇ ó³Ýó»ñáõÙ Ñ»é³ñÓ³ÏáõÙÝ»ñÇ Ñ»ñó·ñÙ³Ý ËݹÇñÁ Ù»ïñÇÏ³Ï³Ý ï³ñ³ÍáõÃÛáõÝÝ»ñáõÙ‘ SINR(Signal to Interference plus Noise Ratio) ë³Ñٳݳ÷³ÏáõÙÝ»ñÇ Ýϳïٳٵ: ò³ÝóÇ Ñ³Ý·áõÛóÝ»ñÇ Ñ½áñáõÃÛáõÝÝ»ñÇ Ñ³Ù³ñ ¹Çï³ñÏíáõÙ ¿ ·Í³ÛÇÝ ë˻ٳÝ, áñÁ Ñ³×³Ë ¹Çï³ñÏíáÕ Ñ½áñáõÃÛ³Ý ë˻ٳݻñÇó ¿: Ø»Ýù µ»ñáõÙ »Ýù ѳëï³ïáõÝ ·áñͳÏóáí Ùáï³ñÏáÕ ³É·áñÇÃÙ Ñ»ñó·ñÙ³Ý ËݹñÇ Ñ³Ù³ñ, ¹Çï³ñÏ»Éáí ËݹÇñÁ áñáß³ÏÇ ïÇåÇ Ù»ïñÇÏ³Ï³Ý ï³ñ³ÍáõÃÛáõÝÝ»ñáõÙ, Ý»ñ³éÛ³É ¾íÏÉÇ¹Û³Ý ï³ñ³ÍáõÃÛáõÝÝ»ñÁ: Àëï Ù»ñ ï»Õ»ÏáõÃÛáõÝÝ»ñÇ‘ ë³ ³é³çÇÝ Ñ³ëï³ïáõÝ ·áñͳÏóáí Ùáï³ñÏáÕ ³É·áñÇÃÙÝ ¿ ³Ûë ËݹñÇ Ñ³Ù³ñ: ØǨÝáõÛÝ Å³Ù³Ý³Ï Ù»Ýù ·ïÝáõÙ »Ýù ûåïÇÙ³É Ñ»ñÃÇ »ñϳñáõÃÛ³Ý Ùáï³íáñ ³ñÅ»ùÁ, ³é³í»É³·áõÛÝÁ ѳëï³ïáõÝ ·áñͳÏóÇ ë˳ɳÝùáí: