WalkSAT is linear on random 2-SAT
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915236572823552 |
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| author | Berenbrink, Petra Coja-Oghlan, Amin Cooper, Colin Götte, Thorsten Hintze, Lukas Zakharov, Pavel |
| author_facet | Berenbrink, Petra Coja-Oghlan, Amin Cooper, Colin Götte, Thorsten Hintze, Lukas Zakharov, Pavel |
| contents | 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 Stützle 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04156 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | WalkSAT is linear on random 2-SAT Berenbrink, Petra Coja-Oghlan, Amin Cooper, Colin Götte, Thorsten Hintze, Lukas Zakharov, Pavel Combinatorics Discrete Mathematics 68Q87, 60C05 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 Stützle 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. |
| title | WalkSAT is linear on random 2-SAT |
| topic | Combinatorics Discrete Mathematics 68Q87, 60C05 |
| url | https://arxiv.org/abs/2412.04156 |