Branching Rules for Satisfiability Analysed with Factor Analysis

Abstract. Factor analysis is a statistical technique for reducing the number of factors responsible for a matrix of correlations to a smaller number of factors that may reflect underlying variables. Experiments with constraint satisfaction problems (CSPs) using factor analysis suggest that for some (perhaps many) classes of problems, there are only a few distinct principles of heuristic action. In this paper, this approach is extended to the analysis of branching rules for SAT problems, using the Davis-Putnam algorithm. Tests were carried out with fixed-clause random SAT problems as well as various kinds of structured problems. These experiments show that, just as with CSPs, there appear to be two general kinds of action that distinguish heuristics. These may be characterised as building up of contention and propagation of effects to the remaining, uninstantiated portion of the problem. This work extends and clarifies previous attempts to characterise heuristic performance in terms of fundamental principles of action.