Set Bounds and (Split) Set Domain Propagation Using ROBDDs

Most propagation-based set constraint solvers approximate the set of possible sets that a variable can take by upper and lower bounds, and perform so-called set bounds propagation. However Lagoon and Stuckey have shown that using reduced ordered binary decision diagrams (ROBDDs) one can create a practical set domain propagator that keeps all information (possibly exponential in size) about the set of possible set values for a set variable. In this paper we first show that we can use the same ROBDD approach to build an efficient bounds propagator. The main advantage of this approach to set bounds propagation is that we need not laboriously determine set bounds propagations rules for each new constraint, they can be computed automatically. In addition we can eliminate intermediate variables, and build stronger set bounds propagators than with the usual approach. We then show how we can combine this with the set domain propagation approach of Lagoon and Stuckey to create a more efficient set domain propagation solver.