License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2017.9
URN: urn:nbn:de:0030-drops-75355
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7535/
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Scheder, Dominik ; Steinberger, John P.

PPSZ for General k-SAT - Making Hertli's Analysis Simpler and 3-SAT Faster

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Abstract

The currently fastest known algorithm for k-SAT is PPSZ named after its inventors Paturi, Pudlak, Saks, and Zane. Analyzing its running time is much easier for input formulas with a unique satisfying assignment. In this paper, we achieve three goals. First, we simplify Hertli's analysis for input formulas with multiple satisfying assignments. Second, we show a "translation result": if you improve PPSZ for k-CNF formulas with a unique satisfying assignment, you will immediately get a (weaker) improvement for general k-CNF formulas. Combining this with a result by Hertli from 2014, in which he gives an algorithm for Unique-3-SAT slightly beating PPSZ, we obtain an algorithm beating PPSZ for general 3-SAT, thus obtaining the so far best known worst-case bounds for 3-SAT.

BibTeX - Entry

@InProceedings{scheder_et_al:LIPIcs:2017:7535,
  author =	{Dominik Scheder and John P. Steinberger},
  title =	{{PPSZ for General k-SAT - Making Hertli's Analysis Simpler and 3-SAT Faster}},
  booktitle =	{32nd Computational Complexity Conference (CCC 2017)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-040-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{79},
  editor =	{Ryan O'Donnell},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7535},
  URN =		{urn:nbn:de:0030-drops-75355},
  doi =		{10.4230/LIPIcs.CCC.2017.9},
  annote =	{Keywords: Boolean satisfiability, exponential algorithms, randomized algorithms}
}

Keywords: Boolean satisfiability, exponential algorithms, randomized algorithms
Collection: 32nd Computational Complexity Conference (CCC 2017)
Issue Date: 2017
Date of publication: 01.08.2017

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