Guiding CNF-SAT search via efficient constraint partitioning
Vijay Durairaj, Priyank Kalla · 2005
Contemporary techniques to identify a good variable order for SAT rely on identifying minimum tree-width decompositions. However, the problem finding a minimal width tree decomposition for an arbitrary graph is NP complete. The available tools and methods are impratical, as they cannot handle large and hard-to-solve CNF-SAT instances. This paper proposes a novel hypergraph partitioning based constraint decomposition technique as an alternative to contemporary methods. We model the CNF-SAT problem on a hypergraph and apply min-cut based bi-partitioning. Clause-variable statistics across the partitions are analyzed to further decompose the problem, iteratively. The resulting tree-like decomposition provides a variable order for guiding CNF-SAT search. Experiments carried out over a large and varied set of benchmarks demonstrate that our partitioning procedure is very fast and scalable. The variable order derived through the partitioning results in significant increase in performance (often orders of magnitude) of the SAT engine.