We study the performance of stochastic local search algorithms for random instances of the Ksatisfiability (K-SAT) problem. We presenta 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 α; 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.
geometry of solutions local search performance random K-SAT
Mikko Alava John Ardelius SwedenErik Aurell Petteri Kaski Supriya Krishnamurthy Pekka Orponen Sakari Seitz
Department of Engineering Physics, Helsinki University of Technology, P.O. Box 1100. FI-02015, Espoo Swedish Institute of Computer Science AB, SE-164 29 Kirta Department of Computational Biology, AibaNova University Centre, SE-106 91 Stockholm, Sweden Linnaeus Centre, KTH-Royal Institute of Technology, SE-100 44 Stockholm, Sweden Helsinki Institute for Information Technology (HUT), Department of Computer Science, University of H School of Information and Communication Technology, KTH-Royal Institute of Technology, SE-164 40 Kis Department of Information and Computer Science, Helsinki University of Technology, P.O. Box 5400, FI