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DOI: 10.4230/LIPIcs.STACS.2012.254

Improved Bounds for Bipartite Matching on Surfaces

Authors: Samir Datta, Arjun Gopalan, Raghav Kulkarni, and Raghunath Tewari

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)

Abstract

We exhibit the following new upper bounds on the space complexity and the parallel complexity of the Bipartite Perfect Matching (BPM) problem for graphs of small genus: (1) BPM in planar graphs is in UL (improves upon the SPL bound from Datta, Kulkarni, and Roy; (2) BPM in constant genus graphs is in NL (orthogonal to the SPL bound from Datta, Kulkarni, Tewari, and Vinodchandran.; (3) BPM in poly-logarithmic genus graphs is in NC; (extends the NC bound for O(log n) genus graphs from Mahajan and Varadarajan, and Kulkarni, Mahajan, and Varadarajan. For Part (1) we combine the flow technique of Miller and Naor with the double counting technique of Reinhardt and Allender . For Part (2) and (3) we extend Miller and Naor's result to higher genus surfaces in the spirit of Chambers, Erickson and Nayyeri.

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Samir Datta, Arjun Gopalan, Raghav Kulkarni, and Raghunath Tewari. Improved Bounds for Bipartite Matching on Surfaces. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 254-265, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)

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@InProceedings{datta_et_al:LIPIcs.STACS.2012.254,
  author =	{Datta, Samir and Gopalan, Arjun and Kulkarni, Raghav and Tewari, Raghunath},
  title =	{{Improved Bounds for Bipartite Matching on Surfaces}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{254--265},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.254},
  URN =		{urn:nbn:de:0030-drops-34141},
  doi =		{10.4230/LIPIcs.STACS.2012.254},
  annote =	{Keywords: Perfect Matching, Graphs on Surfaces, Space Complexity, NC, UL}
}

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Improved Bounds for Bipartite Matching on Surfaces

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