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DOI: 10.4230/LIPIcs.STACS.2011.579
URN: urn:nbn:de:0030-drops-30450
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3045/
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Datta, Samir ; Kulkarni, Raghav ; Tewari, Raghunath ; Vinodchandran, N. Variyam

Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs

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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 oplus L (in fact in mod_k for all k >= 2), C=L, 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.

BibTeX - Entry

@InProceedings{datta_et_al:LIPIcs:2011:3045,
  author =	{Samir Datta and Raghav Kulkarni and Raghunath Tewari and N. Variyam Vinodchandran},
  title =	{{Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{579--590},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3045},
  URN =		{urn:nbn:de:0030-drops-30450},
  doi =		{10.4230/LIPIcs.STACS.2011.579},
  annote =	{Keywords: perfect matching, bounded genus graphs, isolation problem}
}

Keywords: perfect matching, bounded genus graphs, isolation problem
Collection: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue Date: 2011
Date of publication: 11.03.2011

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