Maintenance Of Solution In A DynamicConstraint Satisfaction Problem

Abstract

Constraint Satisfaction Problems (CSP) have been shown to be a useful way of formulating problems such as design, scene labelling and temporal reasoning. As many problems using constraints need a dynamic environment, the static framework of CSPs extend into DCSP (Dynamic Constraint Satisfaction Problems). Up to now, most papers about DCSPs have dealt with the problem of the existence of a solution and the filtering techniques. The problem of the maintenance of a solution, after the DCSP has evolved, has mainly been approached through re-execution or delay to the computation of the solution. This paper first presents the CSP framework and its dynamic evolution DCSP, and then assigns bounds to the study of the problem of the maintenance of solution: given an instance of a binary DCSP, a solution to it and a new constraint which disables that solution, we achieve the computation (if possible) of a new solution as close as possible to the previous one - with several criteria of closeness. The paper presents an efficient algorithm restricted to acyclic binary DCSPs and new constraints which do not modify the constraint-graph, and then its extension to the cyclic case with any new constraint.