Incremental Method • Transform from a feasible solution to another feasible solution to increase (or decrease) the value of objective function.
Matching in Bipartite Graph Maximum Matching
1. Can we do augmentation directly in bipartite graph? 2. Can we do those augmentation in the same time?
Matching in Graph Maximum Matching
Note • We cannot transform Maximum Matching in Graph into a maximum flow problem. • However, we can solve it with augmenting path method.
2. Can we do those augmentation in the same time?
Hopcroft–Karp algorithm • The Hopcroft–Karp algorithm may therefore be seen as an adaptation of the Edmonds-Karp algorithm for maximum flow.
Running Time Reading Material
Maximum Weight Matching It is hard to be transformed to maximum flow!!!
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.