A Polynomial Algorithm for Continuous Non-binary Disjunctive CSPs

Nowadays, many real problems can be modelled as Constraint Satisfaction Problems (CSPs). Some CSPs are considered nonbinary disjunctive CSPs. Many researchers study the problems of deciding consistency for Disjunctive Linear Relations (DLRs). In this paper, we propose a new class of constraints called Extended DLRs consisting of disjunctions of linear inequalities, linear disequations and non-linear disequations. This new class of constraints extends the class of DLRs. We propose a heuristic algorithm called DPOLYSA that solves Extended DLRs, as a non-binary disjunctive CSP solver. This proposal works on a polyhedron whose vertices are also polyhedra that represent the nondisjunctive problems. We also present a statistical preprocessing step which translates the disjunctive problem into a non-disjunctive and ordered one in each step.