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DOI: 10.4230/LIPIcs.STACS.2011.237

Improving PPSZ for 3-SAT using Critical Variables

Authors: Timon Hertli, Robin A. Moser, and Dominik Scheder

Published in: LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

Abstract

A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. Using a simple case distinction on the fraction of critical variables of a CNF formula, we improve the running time for 3-SAT from O(1.32216^n) [Rolf 2006] to O(1.32153^n). Using a different approach, Iwama et al. very recently achieved a running time of O(1.32113^n). Our method nicely combines with theirs, yielding the currently fastest known algorithm with running time O(1.32065^n). We also improve the bound for 4-SAT from O(1.47390^n) [Hofmeister et al. 2002] to O(1.46928^n), where O(1.46981^n) can be obtained using the methods of Hofmeister and Rolf.

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Timon Hertli, Robin A. Moser, and Dominik Scheder. Improving PPSZ for 3-SAT using Critical Variables. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 237-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{hertli_et_al:LIPIcs.STACS.2011.237,
  author =	{Hertli, Timon and Moser, Robin A. and Scheder, Dominik},
  title =	{{Improving PPSZ for 3-SAT using Critical Variables}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{237--248},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.237},
  URN =		{urn:nbn:de:0030-drops-30147},
  doi =		{10.4230/LIPIcs.STACS.2011.237},
  annote =	{Keywords: SAT, satisfiability, randomized, exponential time, algorithm, 3-SAT, 4-SAT}
}

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Improving PPSZ for 3-SAT using Critical Variables

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