L03-bipartite

# L03-bipartite - Bipartite Matching Lecture 3 Jan 17 1...

This preview shows pages 1–7. Sign up to view the full content.

1 Bipartite Matching Lecture 3: Jan 17

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Bipartite Matching A graph is bipartite if its vertex set can be partitioned into two subsets A and B so that each edge has one endpoint in A and the other endpoint in B. A matching M is a subset of edges so that every vertex has degree at most one in M. A B
3 The bipartite matching problem: Find a matching with the maximum number of edges. Maximum Matching A perfect matching is a matching in which every vertex is matched. The perfect matching problem: Is there a perfect matching?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Greedy method? (add an edge with both endpoints unmatched ) First Try
5 Key Questions How to tell if a graph does not have a (perfect) matching? How to determine the size of a maximum matching? How to find a maximum matching efficiently?

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Hall’s Theorem [1935]: A bipartite graph G=(A,B;E) has a matching that “saturates” A if and only if |N(S)| >= |S| for every subset S of A. S
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 20

L03-bipartite - Bipartite Matching Lecture 3 Jan 17 1...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online