[en] 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.
Disciplines :
Physics
Author, co-author :
Lemoy, Rémi ; University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Identités, Politiques, Sociétés, Espaces (IPSE)
Local search methods based on variable focusing for random K-satisfiability
Publication date :
2015
Journal title :
Physical Review. E.
ISSN :
1539-3755
Publisher :
Amer Physical Soc, College Pk, Unknown/unspecified
Volume :
91
Issue :
1
Pages :
013305-6
Peer reviewed :
Peer reviewed
Funders :
Center of Excellence program of the Academy of Finland Academy of Finland Distinguished Professor program
Commentary :
The authors thank A. Mozeika and S. Seitz for discussions about variable focusing. Professor P. Orponen (Aalto) is acknowledged for discussions. This work was supported by funding from the Center of Excellence program of the Academy of Finland, for the COIN and COMP Centers, as well as the Academy of Finland Distinguished Professor program (E.A.). We acknowledge the computational resources provided by the Aalto Science-IT project.