Symbiosis of Search and Heuristics for Random 3-SAT

Delft University of Technology, Delft, The NetherlandsAbstract. When combined properly, search techniques can reveal the full poten-tial of sophisticated branching heuristics. We demonstrate this observation on thewell-known class of random 3-SAT formulae. First, a new branching heuristic ispresented, which generalizes existing work on this class. Much smaller searchtrees can be constructed by using this heuristic. Second, we introduce a variantof discrepancy search, called ALDS. Theoretical and practical evidence supportthat ALDS traverses the search tree in a near-optimal order when combined withthe new heuristic. Both techniques, search and heuristic, have been implementedin the look-ahead solvermarch. The SAT 2009 competition results show thatmarch is by far the strongest complete solver on random k-SAT formulae.