Satisfying constraint sets through convex envelopes

In this article, we present a general representation for constraint satisfaction problems with disjunctive relations called cluster constraint systems (CCS). For this representation, we develop a novel and simple approach for solving CCSs using convex envelopes. These envelopes can be used to decompose the feasible space of the CCS through convex approximations. We explore interval reasoning as a case study of CCS. Our experimental results demonstrate that such CCS can be effectively and efficiently solved through convex enveloping with very modest branching requirements in comparison to other generic as well as specialized algorithms for interval reasoning. In fact, convex enveloping solves significantly more cases and more efficiently than other methods used in our test bed.