A polynomial algorithm for continuous non-binary disjunctive CSPs: extended DLRs

Nowadays, many real problems can be modelled as Constraint Satisfaction Problems (CSPs). Some CSPs are considered non-binary 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 non-disjunctive problems. We also present a statistical preprocessing step which translates the disjunctive problem into a non-disjunctive and ordered one in each step.