12345 efghi UNIVERSITY OF WALES

Applications of graph and hypergraph decomposition techniques to SAT solving have been studied under various conditions. Theoretical research focused on the direction given by tree decompositions, while practical approaches either integrated tree decomposition guidance into existing SAT solver, or studied splitting techniques using hypergraph cuts. In this article we present a uniform and general framework based on the splitting approach. We allow (and study) different graph representations, different graph and hypergraph splitting methods (involving vertices or (hyper)edges), different degrees of integration with the (full) problem structure, and various heuristics for selecting “good” decompositions. Basic is the notion of a decomposable graph representation. We show that resolution graphs (with only non-tautological resolvents(!)) yield a decomposable graph representation. Tree decomposition and variations have theoretical strength, but for practical purposes the (hyper)graph cut approach seems to be more suited, which is of a local nature, yielding one split at a time, while tree decomposition delivers one global scheme, from which all future splittings are derived. For (hyper)graph cuts even the weaker variation of resolution graphs, the conflict graphs (where also tautological resolvents are allowed), yield strictly better splitting possibilities than variable interaction graphs (at the expense of using bigger graphs). Very preliminary experimental results are given (yet mostly of negative nature).