A distribution method for solving SAT in grids

Abstract. The emerging large-scale computational grid infrastructure is providing an interesting platform for massive distributed computations. In this paper the problem of exploiting such computational grids for solving challenging propositional satisfiability problem (SAT) instances is studied. When designing a distributed algorithm for a large loosely coupled computational grid, a number of grid specific problems need to be tackled including the heterogeneity of the resources, inherent communication delays, and high failure probabilities of grid jobs. In this work a novel distribution method for solving SAT problem instances, called scattering, is introduced. The key advantages of scattering are that it can be used in conjunction with any sequential SAT solver (including industrial black box solvers), the distribution heuristic is strictly separated from the heuristic used in sequential solving, and it requires no communication between processes solving subproblems but still allows coordination of such processes. An implementation of the method has been developed for NorduGrid, a large widely distributed production-level grid running in Scandinavia. The implementation has been benchmarked with test cases including random 3SAT and challenging industrial benchmarks used in previous SAT competitions.

Computing Maximal Autarkies with Few and Simple Oracle Queries

We consider the algorithmic task of computing a maximal autarky for a clause-set F, i.e., a partial assignment which satisfies every clause of F it touches, and where this property is destroyed by adding any non-empty set of further assignments.We employ SAT solvers as oracles, using various capabilities. Using the standard SAT oracle, log_2(n(F)) oracle calls suffice, where n(F) is the number of variables, but the drawback is that (translated) cardinality constraints are employed, which makes this approach less efficient in practice.Using an extended SAT oracle, motivated by the capabilities of modern SAT solvers, we show how to compute maximal autarkies with 2 n(F)^{1/2} simpler oracle calls. This novel algorithm combines the previous two main approaches, based on the autarky-resolution duality and on SAT translations