Projection in Adaptive Constraint Handling

Abstract

Constraint solving in dynamic environments requires an immediate adaptation of the solutions if the constraint problems are changing. Constraint solving with Constraint Handling Rules (CHR) is extended with incremental algorithms, thus supporting the solution of dynamic constraint satisfaction problems (DCSPs). Unfortunately, constraint processing with CHR introduces a lot of new variables which require additional memory space and reduce run-time performance. Most of the variables may be eliminated without any loss of information. Thus, memory may be kept rather small and run-time performance may be improved. This paper describes the use of projection with CHR in order to eliminate irrelevant variable bindings and maintain the constraint store quite small. In detail, some projection algorithms are presented to eliminate variables which are introduced during constraint processing with CHR. Projection is called early projection if it is applied together with each rule application, thus eliminating recently introduced irrelevant variable bindings while keeping the derived constraint store quite small. This kind of projection is well-suited when solving Dynamic Constraint Satisfaction Problems, especially after constraint deletion, when many superfluous variable binding have to be deleted as well. Consequently, the modifications that are required for an adaptation are reduced. This may result in an improved performance of the adaptation algorithms and a better performance for non-adaptive constraint processing with CHR is also expected.