Lecture 19-Problem Solving 4 Incremental Method

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Presentation transcript:

Lecture 19-Problem Solving 4 Incremental Method

Min Spanning Tree

Minimum Spanning Tree Could you design an incremental method with the path optimality condition? Could you design an incremental method with the cut optimality condition? What is the running time of each designed algorithm?

Max Weighted Matching

Maximum Weight Matching It is hard to be transformed to maximum flow!!!

Minimum Weight Matching

Augmenting Path

Optimality Condition

Puzzle

Chinese Postman

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)

a a

Chinese Postman

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.