Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, January 23, 2007, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Jan Hladky (Charles Univ., Prague)

Maximum matching in graphs: an algebraic approach

Edmonds first showed that the problem of finding a maximum cardinality matching in a graph can be solved in polynomial time. The algorithm searches in a fast way for augmenting paths in the graph. Later, faster algorithms appeared (the fastest one running in time O(n^{1/2}m) due to Micali&Vazirani), all of them based on searching augmenting paths.

In the talk, I will explain an approach for finding a maximum matching which is based on the Tutte matrix. I will sketch an elegant (randomized) algorithm of Harvey (2006) which is the most efficient known so far. It runs in time O(n^\omega), where O(n^\omega) is the time necessary to compute the product of two n*n matrices; \omega<2.38.

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