Constructive Interval Disjunction

Shaving and constructive disjunction are two main refutation principles used in constraint programming. The shaving principle allows us to compute the singleton arc-consistency (SAC) of finite-domain CSPs and the 3B-consistency of numerical CSPs. Considering the domains as unary disjunctive constraints, one can adapt the constructive disjunction, proposed by Van Hentenryck et al. in the nineties, to provide another general-purpose refutation operator. One advantage over the shaving is that the partial consistency performed to refute values in the domains is not entirely lost. This paper presents a new filtering operator for numerical CSPs, called CID, based on constructive disjunction, and a hybrid algorithm, called 3BCD, mixing shaving and constructive disjunction. Experiments have been performed on 20 benchmarks. Adding CID to bisection, hull or box consistency, and interval Newton, produces a gain in performance of 1, 2 or 3 orders of magnitude on several benchmarks. 3BCD and adap...

• Type: Conference
• Year: 2007
• Where: CP
• Authors: Gilles Trombettoni, Gilles Chabert
• Keywords: Constructive Disjunction, CP 2007, Numerical Csps, Programming Languages, Shaving