Analysis of two simple heuristics on a random instance of k-SAT
Journal of Algorithms
Experimental results on the crossover point in random 3-SAT
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Scaling Properties of Pure Random Walk on Random 3-SAT
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
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We study the scaling properties of sequential and parallel versions of a local search algorithm, WalkSAT, in the easy regions of the easy-hard-easy phase transition (PT) in Random 3-SAT.In the underconstrained region, we study scaling of the sequential version of WalkSAT. We find linear scaling at fixed clause/variable ratio. We also study the case in which a parameter inspired by "finite-size scaling" is held constant. The scaling then also appears to be a simple power law. Combining these results gives a simple prediction for the performance of WalkSAT over most of the easy region. The experimental results suggest that WalkSAT is acting as a threshold algorithm, but with threshold below the satisfiability threshold.Performance of a parallel version of WalkSAT is studied in the over-constrained region. This is more difficult because it is an opumization rather than decision problem. We use the solution quality, the number of unsatisfied clauses, obtained by the sequential algorithm to set a target for its parallel version. We find that qualities obtained by the sequential search with O(n) steps, are achievable by the parallel version in O(log(n)) steps. Thus, the parallelization is efficient for these "easy MAXSAT" problems.