Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k satisfiability problem

Chao, Ming-Te; Franco, John

doi:10.1016/0020-0255(90)90030-e

Cited by 140 publications

(1 citation statement)

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“…Away from the threshold, polynomial-time algorithms for SAT have been found and analyzed, first by Chao and Franco [MTF90], and later by Coja-Oghlan et al [COKV07,CO10]. Additionally, a recent result by Vyas [Vya18] re-analyzes the algorithm of Paturi et al [PPZ99] in the case when the input is drawn from a random distribution, and finds the algorithm to run faster on average in this case by a factor of 2 nΩ(lg k)/k , giving a running time of O(2 n(1−Ω(lg k)/k) ).…”

Section: Introductionmentioning

confidence: 99%

Faster Random $k$-CNF Satisfiability

Lincoln,

Yedidia

2019

Preprint

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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 andDantsin 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 nΩ(lg 2 k)/k , resulting in an overall runtime of O(2 n(1−Ω(lg 2 k)/k) ) for random k-SAT.

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