Exploiting Short Supports for Improved Encoding of Arbitrary Constraints into SAT

Abstract

Abstract. Encoding to SAT and applying a highly efficient modern SAT solver is an increasingly popular method of solving finite-domain constraint problems. In this paper we study encodings of arbitrary constraints where unit propagation on the encoding provides strong reasoning. Specifically, unit propagation on the encoding simulates generalised arc consistency on the original constraint. To create compact and efficient encodings we use the concept of short support. Short support has been successfully applied to create efficient propagation algorithms for arbitrary constraints. A short support of a constraint is similar to a satisfying tuple however a short support is not required to assign every variable in scope. Some variables are left free to take any value. In some cases a short support representation is smaller than the table of satisfying tuples by an exponential factor. We present two encodings based on short supports and evaluate them on a set of benchmark problems, demonstrating a substantial improvement over the state of the art.

Theory learning with symmetry breaking

“…The white box nature of the solver allows this kind of novel specialisation to be integrated with ease. The solver has been applied to the consecutive squares packing problem and the results compare well to an approach using a similar straightforward model [1]. Results for constraint solving are often highly model dependent and approaches with more sophisticated modelling [16,27] solve more problems in this class.…”

“…Recently, when considering compilation of tabled constraints into SAT instances, [1] gives a model of the problem using tabled constraints (similar to that used in this paper); the largest non-trivial examples considered have n = 14 and optimal solutions are not addressed.…”