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.ICALP.2020.78
URN: urn:nbn:de:0030-drops-124857
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12485/
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Lincoln, Andrea ; Yedidia, Adam

Faster Random k-CNF Satisfiability

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LIPIcs-ICALP-2020-78.pdf (0.6 MB)

Abstract

We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly.
We build upon the algorithms of Schöning 1999 and Dantsin et al. in 2002. The Schöning algorithm works by trying many possible random assignments, and for each one searching systematically in the neighborhood of that assignment for a satisfying solution. Previous algorithms for this problem run in time O(2^(n (1- Ω(1)/k))).
Our improvement is simple: we count how many clauses are satisfied by each randomly sampled assignment, and only search in the neighborhoods of assignments with abnormally many satisfied clauses. We show that assignments like these are significantly more likely to be near a satisfying assignment. This improvement saves a factor of 2^(n Ω(lg² k)/k), resulting in an overall runtime of O(2^(n (1- Ω(lg² k)/k))) for random k-SAT.

BibTeX - Entry

@InProceedings{lincoln_et_al:LIPIcs:2020:12485,
  author =	{Andrea Lincoln and Adam Yedidia},
  title =	{{Faster Random k-CNF Satisfiability}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{78:1--78:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12485},
  URN =		{urn:nbn:de:0030-drops-124857},
  doi =		{10.4230/LIPIcs.ICALP.2020.78},
  annote =	{Keywords: Random k-SAT, Average-Case, Algorithms}
}

Keywords: Random k-SAT, Average-Case, Algorithms
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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