setcoverrounding

setcoverrounding - &ÖÀ#è TeX output...

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Unformatted text preview: ÷##&ÖÀ#;#####è# TeX output 2009.11.18:1302&########################################ÿÿÿÿ #°ç¿^ ý7W² #ª¨N^ ýzW²^ Å###¶##ÕÁG‰\¤#&#g&ó#ÂÖN # ### ####cmbx12ºCSm#&#601/I&`#ITBP&#&#{Randomizedg#&#roundingÅfor^set¸coÈ #vÆerb&#ãyAbhi ram&#&#Ranadeb&¡è&&&&ø#####¶##ÕÁG&&&&¡¡&Input:&#8àó#X«Q## ### ####cmr12¹Collection&#ê¨ó#·ág£# ### ####cmmi12½C&#ÇF¹ofȽn&¹sets^o&¬rv&er&#ê¨theÖunivƬrersez1½::m¹.¡ F— ÿ#Vorãeac&¬rhÅse t&½j&#&{¹w&e÷ha&v&e&a&cost»½cm&#ÌÌó#×##2##########cmmi8¾jÀ&#f ¹.&¢&ºOutput:&#O\¹SubmS&collectionÆ#õæ½C¡b#Ü&&û¥2ó#¾KÈ###########cmsy8Á0 A Ã# ½¹of^½C &#Òȹsuc¡¬rh&that£evÖeryãelemen&tÀ#õåappAS‰ears&in¤atmleast¶1msetbin&½C& ã#Üø&û¥2Á0d ## ½¹andm¢&totalm#ê¨costbof¡sets&in¦½CÈÖ#Ü&Ôû¥2Á0&&#;&¹is&asÃsmall&as¤p^S&ossible.& ¢ÉºIPb#°Ãform& #ulation:&#Ké¹Consider&#ô-matrixÇ#ô,½§&¹in&whic&¬rh&½a&&#Ì̾ij&& d(¹=&##C1cif&½i&¹thøelemen— ¬rt&is3in^thez½j¶ # ÿ¹th&set.b¡øSelected&#GQset:Ö#ò2denot ed&b&¬ryÉa»½nm¹elemenmt&0-1&v&ector&½x&¹where&½x‚ ö#Ì̾i& Å #Wã¹=&#ó 1¸if Öset¢½iø¹is&selected—to¶bmS&eÀin&¡&½CÉ#Ü b&û¥2Á0^m###¹andm#`=0— #`>otherwise.Å#d ¡F&ÿ#Vor#this&w&¬re&w&anÉt»½xm#`=¹sucmh&thatP#`=½Ax&##wó#!",g# ### ####cmsy10À#&½O&S&ne¹,&#} £where&b¡¬ry &#`>½OÆneb¹w9¬re^#`=mean&theA ¢‰ vÖ¬rector^#ê¨whic^h&isball&1s,band&suc#h zthatm½cz3û¥2¾T&a#¢#½x&¹is¿minimized,&where&½c&&û¥2¾T&& öi¹=Ö#UR[½c¶^#ÌÌó#| {Y###########cmr8»1ÈÖ#À#½c¤¶#ÌÌ»2À&½:::cAÃ#Ì̾n&L#¨P¹].&¢3º¦Pm#c#relaxation:&#Ä&¹Wd ÿ#VeÖ#°{cannot&#°| solvÖ¬re¡this&e#cienÖtlyQÿ#V,m#áñso&w&e&relaxbit.Î#¶[So&w3e¶allo¡w—v&ÿXäariablesÅto ã¢Ætak&¬re—#ê¨arbitrary&vªÿXäalues&b&S&etÃw\een&0Îandmone.X#8àSo¡w—e&addãinequaliti esƽxb&#Ì̾j&&#»\À#È#UR¹0½;¶#ÿþxjÀ#Ì̾j&AÀ#\¹1&#ê¨formall3½j^#¬Ó¹.—¢&&#&ôSupp&S&ose ã#¸©wb¬reb#¸¨solv§eÈthis9#¸¨¦P&#¸Àand&getÃa\solution^forz½x¹.m#(5W—ÿ#Ve&need&to&rou nd&it&toa0ãor&1&soãthat&¢bwø¬re&#Í haÆvÖe&aÇsolution##Í toãthe&IPbÿ#V.&Wóe&ha&¬rv2eÜseen}one&#Í w«aÈybof¡doing&thisÈearlier:^#*#round&v&ÿXäalues¾close&¢zto¶#ê¨1¡toø1&andbothersÅto ‚0.¶¢m&#ÅôT¶ÿ#VoãSÆdab¬ryb#ê¨w&e­willbtryªa¶di#eren&t&strategy&ÿ#V.¶^(#Vz3ó#ÂÖN ##G ®# ####cmbx12Ä1&&#(ôRandomized¶ #zárounding&¡ #b#Ö¹Let&# #usÈmak&¬reøa&distinctionÁb• Smetjw&een&the‰ IPb##ÿv¡ ÿXäariables,&##_whic&hbwøe&willd writebin¢capitals£andbthe ²¤¶ lp&#ê¨v&ÿXäariables&whic^¬rhzwXe^willbwrite&in—lo &w&erd case.b¤&ºRounding:Æ#8à¹Setv#꨽XjÀ#Ì̾j&A#»\¹=&#UR1¶withzprobabilitø¬ry &½x—ø#Ì̾j# d #f ¹,&0&with2probabilit&y&1¥#ª¨À#&½xc—#Ì̾jKc#f ¹.ƤÖb#&ôó#&ÎR6# ### ####cmss12ÅdobS&es— #ê¨this— sound¡ goøo&d?K ¢¸Æ#Öô¹Inb¬rtuition:Ö#8à½x v•#Ì̾iÀ&#O &¹closeÖ#ê¨to£ 1^À)&½XX¶ #Ì̾ib— ¹moreãlik&¬relyd...
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This note was uploaded on 01/04/2010 for the course CSE CS601 taught by Professor Prof.ranade during the Summer '09 term at IIT Bombay.

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setcoverrounding - &ÖÀ#è TeX output...

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