Context in Discrete Constraint Satisfaction Problems

In this paper, we study interchangeability in finite and discrete constraint satisfaction problems (CSPs). In many applications modeled as CSPs, it is important to be able to build on the spot equivalence classes of objects of the world to allow local modifications of the solutions and highlight opportunities for change. The concept of interchangeability, defined by Freuder [4], formalizes equivalence relations among objects. Interchangeability rarely exists in complete problems, but is more frequent when restricted to certain context. We call this new type of interchangeability context dependent interchangeability (CDI). In this paper, we show that CDI is related to neighborhood interchangeability [4] within subproblems of the original CSP and provide polynomial time algorithms for identifying CDI sets.