Disjunction of Non-binary and Numeric Constraint Satisfaction Problems

Abstract

Nowadays, many researchers are working on Constraint Satisfaction Problems (CSPs). Many CSPs can be modelled as non-binary CSPs and, theoretically, they can be transformed into an equivalent binary CSP, using some of the current techniques. However, this transformation may be an inadequate or inefficient way to manage certain types of non-binary constraints. In this paper, we propose an algorithm called DHSA that solves numeric non-binary CSPs with disjunctions in a natural way, as non-binary disjunctive CSP solver. This proposal extends the class of Horn constraint, originally studied by Koubarakis, since DHSA manages disjunctions of linear inequalities and disequations with any number of inequalities per disjunction. This proposal works on a polyhedron whose vertices are also polyhedra that represent the non-disjunctive problems. This non-binary disjunctive CSP solver translates, in a preprocess step, the disjunctive problem into a non-disjunctive one by means of a statistical preprocess step. Furthermore, a Constraint Ordering Algorithm (COA) classifies the resultant constraints from the most restricted to the least restricted one. This preprocess step can be applied to other disjunctive CSP solvers in order to find a solution earlier.