# lect-optional1 - 1 4 1 4 4 4 4 4 4 4 1 1 1 1 1 1 Chinese...

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Optional Lecture Maximum Weight Matching

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Maximum Weight Matching weight. total maximumis with matching a find , : weight edge positive with ) , ( graph bipartite a Given + = R E w E V G 1 3 ?
Minimum Weight Matching weight. toal maximumis with matching a find , : weight edge e nonnegativ with ) , ( graph a Given + = R E c E V G

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Augmenting Path edges. matched on that edges unmatched on weight total with the cycle e alternativ an is cycle augmenting An edges. matched on weight total the edges unmatched on weight total the that, propert path with e alternativ maxinal a is path augmenting An vertex. free a called is matching some in edge an of endpoint not the is hat A vertex t M
Optimality Condition . w.r.t. path/cycle augmenting an contains * Then *). ( ) ( with matchings two be * and Let ) ( Trivial. ) ( M M M M c M c M M < M * M * M * M cycle. augmenting no and path augmenting no has it iff weight - maximum is matching A

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Puzzle mple. counterexa a give Please wrong. is material reading in algorithm The 5 5 5 5

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Unformatted text preview: 1 4 1 4 4 4 4 4 4 4 1 1 1 1 1 1 Chinese Postman 8 9 10 11 12 13 Network G = (N, A) Node set N = {1, 2, 3, 4} Arc Set A = {(1,2), (1,4), (4,2), (4,3), (2,3)} In an undirected graph, (i,j) = (j,i) 14 a a 15 16 17 18 19 20 21 Chinese Postman distance. possible least with the letters, deliver order to in city a in road every along travel to shes Postman wi Chinese The once. least at traversed is edge each in which graph the of walk closed shortest a find weight, edge e nonnegativ graph with a Given Minimum Weight Perfect Matching Minimum Weight Perfect Matching can be transformed to Maximum Weight Matching. Chinese Postman Problem is equivalent to Minimum Weight Perfect Matching in graph on odd nodes....
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## This note was uploaded on 11/03/2010 for the course COMPUTER S CS 6363 taught by Professor Dingzhudu during the Fall '10 term at University of Texas at Dallas, Richardson.

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lect-optional1 - 1 4 1 4 4 4 4 4 4 4 1 1 1 1 1 1 Chinese...

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