Guiding CNF-SAT search via efficient constraint partitioning

• Published in: IEEE/ACM International Conference on Computer Aided Design, 2004. ICCAD-2004 pp. 498 - 501
• Main Authors: Durairaj, V., Kalla, P.
• Format: Conference Proceeding
• Language: English
• Published: Washington, DC, USA IEEE Computer Society 07.11.2004; IEEE; ACM
• Series: ACM Conferences
• Subjects: Applied sciences; Circuits; Cities and towns; Computational complexity; Computer aided design; Computer science; control theory; systems; Electronics; Engines; Exact sciences and technology; Information analysis; Integrated circuits; Integrated circuits by function (including memories and processors); Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; Software; Statistical analysis; Tree data structures; Tree graphs; Minimal tree; Hypergraph; Statistical analysis; Probabilistic approach; Circuit design; Complete graph; Constraint satisfaction; Modeling; Treewidth; Propositional logic; Graph decomposition; Conjunctive normal form; NP complete problem; Satisfiability problem; Computer aided design
• ISBN: 0780387023; 9780780387027
• ISSN: 1092-3152; 1558-2434
• DOI: 10.1109/ICCAD.2004.1382629

Contemporary techniques to identify a good variable order for SAT rely on identifying minimum tree-width decompositions. However, the problem of finding a minimal width tree decomposition for an arbitrary graph is NP complete. The available tools and methods are impractical, as they cannot handle large and hard-to-solve CNF-SAT instances. This work proposes a 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 demonstrate that our partitioning procedure is fast, scalable and the derived variable order results in significant increase in performance of the SAT engine.