Exploiting a theory of phase transitions in three-satisfiability problems

David M. Pennock, Quentin F. Stout

Research output: Contribution to conferencePaperpeer-review

7 Scopus citations

Abstract

In the past few years there have been several empirical discoveries of phase transitions in constraint satisfaction problems (CSPs), and a growth of interest in the area among the artificial intelligence community. This paper extends a simple analytical theory of phase transitions in three-satisfiability (3-SAT) problems in two directions. First, a more accurate, problem-dependent calculation leads to a new polynomial time probabilistic estimate of the satisfiability of 3-SAT problems called PE-SAT (Probabilistic Estimate SATisfiability algorithm). PE-SAT empirically classifies 3-SAT problems with about 70% accuracy at the hardest region (the so-called crossover point or 50% satisfiable region) of random 3-SAT space. Furthermore, the estimate has a meaningful magnitude such that extreme estimates are much more likely to be correct. Second, the same estimate is used to improve the running time of a backtracking search for a solution to 3-SAT by pruning unlikely branches of the search. The speed-up is achieved at the expense of accuracy - the search remains sound but is no longer complete. The trade-off between speed-up and accuracy is shown to improve as the size of problems increases.

Original languageEnglish (US)
Pages253-258
Number of pages6
StatePublished - 1996
Externally publishedYes
EventProceedings of the 1996 13th National Conference on Artificial Intelligence, AAAI 96. Part 1 (of 2) - Portland, OR, USA
Duration: Aug 4 1996Aug 8 1996

Conference

ConferenceProceedings of the 1996 13th National Conference on Artificial Intelligence, AAAI 96. Part 1 (of 2)
CityPortland, OR, USA
Period8/4/968/8/96

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

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