A Randomization Strategy for Combinatorial Search

Recent work on the combinatorial search has provided experimental and theoretical evidence that randomization and restart strategies proposed by Gomes, Selman, and Kautz, can be very effective for backtrack search algorithms to solve some hard satisfiable instances of SAT. One difficulty of effectively using the restart strategy is its potential conflict with the branching heuristic. It is well-known that a completely random branching heuristic yields very poor performance. To support the restart strategy, the branching heuristic has to be random (with limitation); otherwise, every restart is a repetition of the first run. In this paper, we propose a new randomization strategy which offers the same advantage of the restart strategy but it can be used with any branching heuristics. The basic idea is to randomly jump in the search space to skip some space. Each jump corresponds to a restart in the restart strategy but there is no repetition. We ensure that no portion of the search space is visited twice during one run and the search will be going on until the allotted time is run out or the search space is exhausted. This new strategy is implemented in SATO, an efficient implementation of the Davis-Putnam-Loveland method for SAT problems. Using the new strategy, we are able to solve several previously open quasigroup problems, which could not be solved using any existing SAT systems.