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arXiv · 2412.04156

WalkSAT is linear on random 2-SAT

Petra Berenbrink·Amin Coja-Oghlan·Colin Cooper·Thorsten Götte·Lukas Hintze·Pavel Zakharov
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Abstract

In an influential article Papadimitriou [FOCS 1991] proved that a local search algorithm called WalkSAT finds a satisfying assignment of a satisfiable 2-CNF with $n$ variables in $O(n^2)$ expected time. Variants of the WalkSAT algorithm have become a mainstay of practical SAT solving (e.g., [Hoos and St\"utzle 2000]). In the present article we analyse the expected running time of WalkSAT on random 2-SAT instances. Answering a question raised by Alekhnovich and Ben-Sasson [SICOMP 2007], we show that WalkSAT runs in linear expected time for all clause/variable densities up to the random 2-SAT satisfiability threshold.

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Petra Berenbrink, Amin Coja-Oghlan, Colin Cooper, Thorsten Götte, Lukas Hintze, Pavel Zakharov. 2024-12-05. WalkSAT is linear on random 2-SAT. https://arxiv.org/abs/2412.04156

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