Study of symmetry in Constraint Satisfaction Problems ?

Constraint satisfaction problems (CSP's) involve nding values for variables subject to constraints on which combinations of values are permitted. Symmetrical values of a CSP variable are in a sense redundant. Their removal will simplify the problem space. In this paper we give the principle of symmetry and show that the concept of interchangeability introduced by Freuder, is a particular case of symmetry. Some symmetries can be computed e ciently thanks to the structure of the problem (neighborhood interchangeability is a kind of these symmetries). Therefore we show how such symmetries can be used by existing constraint propagation algorithms and introduce a backtrack procedure exploiting symmetries. Both theoritical analysis and expiriments indicate that our proposed approach is an improvment of neighborhood interchangeability use, and has very good behavior for pigeon-hole problems.