Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

Samir Datta; Raghav Kulkarni; Raghunath Tewari; N. V. Vinodchandran

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arXiv · 1004.5080

Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

Samir Datta·Raghav Kulkarni·Raghunath Tewari·N. V. Vinodchandran

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Abstract

We investigate the space complexity of certain perfect matching problems over bipartite graphs embedded on surfaces of constant genus (orientable or non-orientable). We show that the problems of deciding whether such graphs have (1) a perfect matching or not and (2) a unique perfect matching or not, are in the logspace complexity class \SPL. Since \SPL\ is contained in the logspace counting classes $\oplusŁ$ (in fact in \modk\ for all $k\geq 2$), \CeqL, and \PL, our upper bound places the above-mentioned matching problems in these counting classes as well. We also show that the search version, computing a perfect matching, for this class of graphs is in $\FL^{\SPL}$. Our results extend the same upper bounds for these problems over bipartite planar graphs known earlier. As our main technical result, we design a logspace computable and polynomially bounded weight function which isolates a minimum weight perfect matching in bipartite graphs embedded on surfaces of constant genus. We use results from algebraic topology for proving the correctness of the weight function.

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BibTeX RIS

Samir Datta, Raghav Kulkarni, Raghunath Tewari, N. V. Vinodchandran. 2010-04-28. Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs. https://arxiv.org/abs/1004.5080

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