Variable-Selection Heuristics in Local Search for SAT

One of the important components of a local search strategy for satisfiability testing is the variable selection heuristic, which determines the next variable to be flipped. In a greedy local search such as GSAT, the major decision in variable selection is the strategy for breaking ties between variables that offer the same improvement in the number of unsatisfied clauses. In this paper, we analyze a number of tie-breaking strategies for GSAT and evaluate the strategies empirically using randomly generated 3-SAT instances from a hard distribution of random instances. We find that the property of fairness, which was proposed in the literature as being the critical property of a successful variable strategy, is not a sufficient property, and show that randomness plays a significant role in the success of variable selection heuristics.