Solution Equivalent Subquadrangle Reformulations of Constraint Satisfaction Problems

Abstract

Constraint Satisfaction Problem instances (CSPs) are a natural way to model real life problems such as image processing, scheduling and natural language understanding. In this paper we are concerned with the modeling of problems as CSPs and how this can affect the performance of different solution algorithms. In particular we are interested in modeling in the language of subquadrangles.

A Quadrangle is essentially an ‘anything-goes’ constraint for some Cartesian product of domains. A Subquadrangle [1] is a constraint all of whose projections to proper subsets of the scope are quadrangles.

Subquadrangles are a very ‘natural’ way in which to represent constraints. This is because they do not place any restrictions on proper subsets of their scope, thus reducing the number of required constraint checks. This leads us to believe that a subquadrangle aware solver could be particularly efficient.