A Generalized Two-watched-literal Scheme in a mixed Boolean and Non-linear Arithmetic Constraint Solver

In its combination with conflict-driven clause learning the two-watched-literal scheme led to enormous performance gains in propositional SAT solving. The idea of this approach is to accelerate the deduction phase of a SAT solver by saving a high number of unnecessary and expensive computation steps originating in visits of indefinite clauses. In this paper we give a detailed explanation of the generalized watch scheme, called two-watched-atom scheme, implemented in our interval-based constraint solver HySAT, the latter being a solver for mixed Boolean and non-linear arithmetic constraint formulae. As opposed to the purely Boolean setting, the more general form of atomic formulae to be watched in our solver necessitates an extension of the original scheme and calls for a careful design of the data structures employed in the implementation. We present experimental results to demonstrate the speed-up obtained by the proposed scheme.