title: Circumspect descent prevails in solving random constraint satisfaction problems.
abstract: We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios alpha; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.
authors.affiliation: Department of Engineering Physics, Helsinki University of Technology, P.O. Box 1100, FI-02015, Espoo, Finland.
authors.forename: Mikko
authors.initials: M
authors.lastname: Alava
authors.forename: John
authors.initials: J
authors.lastname: Ardelius
authors.forename: Erik
authors.initials: E
authors.lastname: Aurell
authors.forename: Petteri
authors.initials: P
authors.lastname: Kaski
authors.forename: Supriya
authors.initials: S
authors.lastname: Krishnamurthy
authors.forename: Pekka
authors.initials: P
authors.lastname: Orponen
authors.forename: Sakari
authors.initials: S
authors.lastname: Seitz