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DOI: 10.4230/LIPIcs.ISAAC.2018.3
URN: urn:nbn:de:0030-drops-99510
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Björklund, Andreas

Exploiting Sparsity for Bipartite Hamiltonicity

LIPIcs-ISAAC-2018-3.pdf (0.4 MB)


We present a Monte Carlo algorithm that detects the presence of a Hamiltonian cycle in an n-vertex undirected bipartite graph of average degree delta >= 3 almost surely and with no false positives, in (2-2^{1-delta})^{n/2}poly(n) time using only polynomial space. With the exception of cubic graphs, this is faster than the best previously known algorithms. Our method is a combination of a variant of Björklund's 2^{n/2}poly(n) time Monte Carlo algorithm for Hamiltonicity detection in bipartite graphs, SICOMP 2014, and a simple fast solution listing algorithm for very sparse CNF-SAT formulas.

BibTeX - Entry

  author =	{Andreas Bj{\"o}rklund},
  title =	{{Exploiting Sparsity for Bipartite Hamiltonicity}},
  booktitle =	{29th International Symposium on Algorithms and Computation  (ISAAC 2018)},
  pages =	{3:1--3:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Wen-Lian Hsu and Der-Tsai Lee and Chung-Shou Liao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-99510},
  doi =		{10.4230/LIPIcs.ISAAC.2018.3},
  annote =	{Keywords: Hamiltonian cycle, bipartite graph}

Keywords: Hamiltonian cycle, bipartite graph
Collection: 29th International Symposium on Algorithms and Computation (ISAAC 2018)
Issue Date: 2018
Date of publication: 06.12.2018

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