Local search methods based on variable focusing for random K-satisfiability

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Journal Title
Journal ISSN
Volume Title
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2015
Major/Subject
Mcode
Degree programme
Language
en
Pages
013305/1-6
Series
Physical Review E, Volume 91, Issue 1
Abstract
We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed.
Description
Keywords
satisfiability problems, local search algorithms, variables
Other note
Citation
Lemoy, Rémi & Alava, Mikko J. & Aurell, Erik. 2015. Local search methods based on variable focusing for random K-satisfiability. Physical Review E. Volume 91, Issue 1. 013305/1-6. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.91.013305.