Séminaire d'équipe(s) Graphs, ALgorithms and Combinatorics

Solving Matching Problems Efficiently in Bipartite Graphs
Selma Djelloul

31 January 2015, 14:30 - 31 January 2015, 15:30 Salle/Bat : 475/PCRI-N
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Activités de recherche : Graph Theory

Résumé :

We investigate the problem maxDMM of computing a largest set
of pairwise disjoint maximum matchings in undirected graphs
We solve maxDMM for bipartite graphs, by providing
an $O(n^{1.5}sqrt{m/log n} + mnlog n)$-time algorithm, where
$n$, $m$ denote respectively the number of vertices and the number of edges.
Bisplit graphs are bipartite graphs with the nested neighborhood property.
For bisplit graphs,
(1) we solve maxDMM in time $O(mnlog n)$, and
(2) we design an $O(n^2log n)$-time algorithm to count all
maximum matchings. This latter time is the same time in which runs the best
known algorithm computing the number of maximum matchings in
bisplit graphs but we claim that our algorithm is much simpler.
The key idea underlying both results is that bisplit graphs have
an $O(n)$-time enumeration of their minimal vertex covers.