An Incremental and Non-binary CSP Solver: The Hyperpolyhedron Search Algorithm

Constraint programming is gaining a great deal of attention because many combinatorial problems especially in areas of planning and scheduling can be expressed in a natural way as a Constraint Satisfaction Problem (CSP). It is well known that a non-binary CSP can be transformed into an equivalent binary CSP using some of the actual techniques. However, when the CSP is not discrete or the number of constraints is high relative to the number of variables, these techniques become impractical. In this paper, we propose an algorithm called "Hyperpolyhedron Search Algorithm" as an incremental and non-binary CSP solver. This non-binary CSP solver does not increase its temporal complexity with the variable domain size. It carries out the search through a hyperpolyhedron that maintains those solutions that satisfy all metric non-binary temporal constraints. Thus, we can manage more complex and expressive problems with high a number of constraints and very large domains.