POLYSA: A Polynomial Algorithm for Non-binary Constraint Satisfaction Problems with ≤ and ≠

Nowadays, many real problems can be naturally modelled as Constraint Satisfaction Problems (CSPs). It is well known that any non-binary CSP can be transformed into an equivalent binary one, using some of the current techniques. However, this transformation may not be practical in problems with certain properties. Therefore, it is necessary to manage these non-binary constraints directly. In this paper, we propose a heuristic called "POLYSA" that solves non-binary constraint satisfaction problems in a natural way as an incremental and non-binary CSP solver. This non-binary CSP solver carries out the search through a polyhedron that maintains in its vertices those solutions that satisfy all non-binary constraints.