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DOI: 10.4230/LIPIcs.STACS.2016.10

Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs

Authors: Rahul Arora, Ashu Gupta, Rohit Gurjar, and Raghunath Tewari

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract

The perfect matching problem has a randomized NC algorithm, using the celebrated Isolation Lemma of Mulmuley, Vazirani and Vazirani. The Isolation Lemma states that giving a random weight assignment to the edges of a graph ensures that it has a unique minimum weight perfect matching, with a good probability. We derandomize this lemma for K3,3-free and K5-free bipartite graphs. That is, we give a deterministic log-space construction of such a weight assignment for these graphs. Such a construction was known previously for planar bipartite graphs. Our result implies that the perfect matching problem for K3,3-free and K5-free bipartite graphs is in SPL. It also gives an alternate proof for an already known result – reachability for K3,3-free and K5-free graphs is in UL.

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Rahul Arora, Ashu Gupta, Rohit Gurjar, and Raghunath Tewari. Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 10:1-10:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{arora_et_al:LIPIcs.STACS.2016.10,
  author =	{Arora, Rahul and Gupta, Ashu and Gurjar, Rohit and Tewari, Raghunath},
  title =	{{Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{10:1--10:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.10},
  URN =		{urn:nbn:de:0030-drops-57116},
  doi =		{10.4230/LIPIcs.STACS.2016.10},
  annote =	{Keywords: bipartite matching, derandomization, isolation lemma, SPL, minor-free graph}
}

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Derandomizing Isolation Lemma for K3,3-free and K5-free Bipartite Graphs

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