Efficient SAT-Encoding of Linear CSP Constraints

Propositional satisfiability solving (SAT) has been considerably successful in numerous industrial applications. Whereas the speed and the capacity of SAT solvers significantly improved in the last two decades, the understanding of SAT encodings is still limited and often challenging. Two wellknown variable encodings, namely the order encoding and the sparse encoding, are the most widely used and successfully applied to translate constraint satisfaction problems (CSPs) to equivalent SAT instances. In this paper we analyze the strengths and drawbacks of these encoding in the context of linear CSP problems and propose a new Sp-Or encoding, based on redundant modeling common in Constraint Programming. We show experimentally that the runtime overhead of the Sp-Or encoding is not significant in the worst case compared to the individual encodings whereas it does outperform them in some of the CSPs. The paper concludes with some guidelines regarding the choice of suitable SAT encodings for CSP problems, taking into account several features of these problems.