CSE373 notes.pdf - Analysis of Algorithm Median find in an...

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Analysis of Algorithm
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Median find in an )
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Problem : Stable matching - = Given at of N men Met m , .mu mug set of N women WE } wiiwz way list Pim ) for each mean and pews for each wtw find : A stable matching SEWXM defn : A matching semxw is a set of order pairs from MXW such that each mean and WEW occurs m at most I pair in s subset ' µ defn : Perfect nrlatching : S Cnhxw such that each m and w appear In exactly I pair In S - 0--0 notifying . fo¥#€| sit , m prefer w ' to w and W ' prefer m to mi & 0 o there exists ( m , w ' ) ¢S such that m and W ' both prefer each other to be their partners Find a stable matching : a) perfecting matching (2) no instability
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-6*1 : M= { m , m ' ) , W = } w , w ' ) pcm ) = [ w , W ' ] , PCW )=[m , m ' ] PLMY = [ wiw ' ] , p ( w ' ) = Emi m ' ) Solution exists : ( m , w ) a ( m ' , W ' ) Ex 2 : prm )= [ W , w ' ] pcw )=[m ' , m ] pcm 'F [ W ' , w ] pcw ' ) = # , m ' ] No one Is willing to Sol exists : Si = lmiw ) ; ( M ' N " make changes because 52 = ( miw ' ) , ( M 's w ) they can't be " more prefer " . QI : Does it exist a stable matching for an sets ? Yes QZ : Given an Instance , can we find a stable matching ? Yes G- S Algorithm : Initially , mean , wew are free Whole
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