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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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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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