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URN: urn:nbn:de:0030-drops-62197
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Analysing Survey Propagation Guided Decimationon Random Formulas

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Abstract

Let vec(theta) be a uniformly distributed random k-SAT formula with n variables and m clauses. For clauses/variables ratio m/n <= r_{k-SAT} ~ 2^k*ln(2) the formula vec(theta) is satisfiable with high probability. However, no efficient algorithm is known to provably find a satisfying assignment beyond m/n ~ 2k*ln(k)/k with a non-vanishing probability. Non-rigorous statistical mechanics work on k-CNF led to the development of a new efficient "message passing algorithm" called Survey Propagation Guided Decimation [Mézard et al., Science 2002]. Experiments conducted for k=3,4,5 suggest that the algorithm finds satisfying assignments close to r_{k-SAT}. However, in the present paper we prove that the basic version of Survey Propagation Guided Decimation fails to solve random k-SAT formulas efficiently already for m/n = 2^{k}(1 + epsilon_k)*ln(k)/k with lim_{k -> infinity} epsilon_k = 0 almost a factor k below r_{k-SAT}.

BibTeX - Entry

@InProceedings{hetterich:LIPIcs:2016:6219,
  author =	{Samuel Hetterich},
  title =	{{Analysing Survey Propagation Guided Decimationon Random Formulas}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{65:1--65:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6219},
  URN =		{urn:nbn:de:0030-drops-62197},
  doi =		{10.4230/LIPIcs.ICALP.2016.65},
  annote =	{Keywords: Survey Propagation Guided Decimation, Message Passing Algorithm, Graph Theory, Random k-SAT}
}

Keywords: Survey Propagation Guided Decimation, Message Passing Algorithm, Graph Theory, Random k-SAT
Seminar: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue date: 2016
Date of publication: 2016


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