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DOI: 10.4230/LIPIcs.ESA.2017.37
URN: urn:nbn:de:0030-drops-78356
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7835/
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Friedrich, Tobias ; Krohmer, Anton ; Rothenberger, Ralf ; Sauerwald, Thomas ; Sutton, Andrew M.

Bounds on the Satisfiability Threshold for Power Law Distributed Random SAT

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Abstract

Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the development of sophisticated rigorous and non-rigorous techniques for analyzing random structures. Despite a long line of research and substantial progress, nearly all theoretical work on random SAT assumes a uniform distribution on the variables. In contrast, real-world instances often exhibit large fluctuations in variable occurrence. This can be modeled by a scale-free distribution of the variables, which results in distributions closer to industrial SAT instances. We study random k-SAT on n variables, m = Theta(n) clauses, and a power law distribution on the variable occurrences with exponent beta. We observe a satisfiability threshold at beta = (2k-1)/(k-1). This threshold is tight in the sense that instances with beta <= (2k-1)/(k-1)-epsilon for any constant epsilon > 0 are unsatisfiable with high probability (w.h.p.). For beta >= (2k-1)/(k-1)+epsilon, the picture is reminiscent of the uniform case: instances are satisfiable w.h.p. for sufficiently small constant clause-variable ratios m/n; they are unsatisfiable above a ratio m/n that depends on beta.

BibTeX - Entry

@InProceedings{friedrich_et_al:LIPIcs:2017:7835,
  author =	{Tobias Friedrich and Anton Krohmer and Ralf Rothenberger and Thomas Sauerwald and Andrew M. Sutton},
  title =	{{Bounds on the Satisfiability Threshold for Power Law Distributed Random SAT}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Kirk Pruhs and Christian Sohler},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7835},
  URN =		{urn:nbn:de:0030-drops-78356},
  doi =		{10.4230/LIPIcs.ESA.2017.37},
  annote =	{Keywords: satisfiability, random structures, random SAT, power law distribution, scale-freeness, phase transitions}
}

Keywords: satisfiability, random structures, random SAT, power law distribution, scale-freeness, phase transitions
Seminar: 25th Annual European Symposium on Algorithms (ESA 2017)
Issue Date: 2017
Date of publication: 31.08.2017


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