Sequential and parallel algorithms for bipartite matching
Sequential and parallel algorithms for bipartite matching Sequential and parallel algorithms for bipartite matching
Outline Introduction Bipartite Matching Parallel Matching Algorithms 2D Partitioning Parallel Algorithm Weighted Bipartit Bipartite Matching Algorithms Exact Cardinality Algorithms Close relation to Max - Flow Search for augmenting paths Berge’s theorem Let G = (V ,E) be a graph and M a matching in G. Then M is of maximum cardinality if and only if there is no M-augmenting path in G. Obvious Algorithm Repeatedly find single augmenting paths using BFS or DFS Running time: O(mn) Johannes Langguth Sequential and parallel algorithms for bipartite matching
Outline Introduction Bipartite Matching Parallel Matching Algorithms 2D Partitioning Parallel Algorithm Weighted Bipartit Questions Questions ? Johannes Langguth Sequential and parallel algorithms for bipartite matching
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Outline Introduction Bipartite Matching Parallel Matching Algorithms 2D Partitioning Parallel Algorithm Weighted Bipartit<br />
Bipartite Matching Algorithms<br />
Exact Cardinality Algorithms<br />
Close relation to Max - Flow<br />
Search <strong>for</strong> augmenting paths<br />
Berge’s theorem<br />
Let G = (V ,E) be a graph <strong>and</strong> M a <strong>matching</strong> in G. Then M is of<br />
maximum cardinality if <strong>and</strong> only if there is no M-augmenting path<br />
in G.<br />
Obvious Algorithm<br />
Repeatedly find single augmenting paths using BFS or DFS<br />
Running time: O(mn)<br />
Johannes Langguth <strong>Sequential</strong> <strong>and</strong> <strong>parallel</strong> <strong>algorithms</strong> <strong>for</strong> <strong>bipartite</strong> <strong>matching</strong>
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