Maintaining Global Consistency of Temporal Constraints in a Dynamic Environment

Abstract

Computational problems from many different application areas can be seen as constraint satisfaction problems (CSPs). For example, the problems of scheduling a collection of tasks, or interpreting a visual image, or laying out a silicon chip, can all be seen in this way. Solving a CSP consists of finding an assignment of values to variables such that all the constraints are satisfied. If such assignment (called solution to a CSP) is found, we said that the CSP is globally consistent.

Our aim in this paper is to maintain the global consistency of a constraint satisfaction problem involving temporal constraints during constraint restriction i.e. anytime a new constraint is added. This problem is of practical relevance since it is often required to check whether a solution to a CSP continues to be a solution when a new constraint is added and if not, whether a new solution satisfying the old and new constraints can be found.

The method that we will present here is based on constraint propagation and checks whether the existence of a solution is maintained anytime a new constraint is added. The new constraint is then accepted if the consistency of the problem is maintained and it is rejected otherwise. Experimental tests performed on randomly generated temporal constraint problems demonstrate the efficiency of our method to deal, in a dynamic environment, with large size problems.