Efficient Propagation of Disjunctive Constraints using Watched Literals

Efficient constraint propagation is important for all constraint solvers. One of the key reasons that Boolean Satisfiability solvers are often more efficient than constraint solvers is that they can propagate disjunctive constraints efficiently. This propagation is undertaken using the watched literals mechanism. In a recent paper Gent et al. showed how watched literals can be used in constraint programming, to propagate simple disjunctive constraints. This paper shows through experiment the deficiencies in the existing methods of implementing the disjunction of a set constraints in CP solvers and presents a new algorithm based on watched literals which when applicable massively outperforms all existing algorithms. In particular we show that if variables are not duplicated between the different constraints being considered disjunctively, and a Generalised Arc Consistent (GAC) propagator is known for each of the constraints; then GAC propagation can be efficiently achieved across the entire disjunctive constraint. We end by showing how this new propagation mechanism can be used to produce efficient models of combinatorial problems, including that of finding Hamming codes.