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

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

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Rahul Arora
Ashu Gupta
Rohit Gurjar
Raghunath Tewari

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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) https://doi.org/10.4230/LIPIcs.STACS.2016.10

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.

Subject Classification

Keywords
  • bipartite matching
  • derandomization
  • isolation lemma
  • SPL
  • minor-free graph

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