Generic Global Constraints based on MDDs

Constraint Programming (CP)[1] has been successfully appl ied to both constraint satisfaction and constraint optimization prob lems. A wide variety of specialized global constraints provide critical assistan ce in achieving a good model that can take advantage of the structure of the problem in the search for a solution. However, a key outstanding issue is the representation of'a d-hoc' constraints that do not have an inherent combinatorial nature, and hence are n ot modelled well using narrowly specialized global constraints. We attempt to address this issue by considering a hybrid of search and compilation. Specificall y we suggest the use of Reduced Ordered Multi-V alued Decision Diagrams (ROMDDs) as the supporting data structure for a generic global constraint. We g ive an algorithm for maintaining generalized arc consistency (GAC) on this cons traint that amortizes the cost of the GAC computation over a root-to-leaf path in th e search tree without requiring asymptotically more space than used for the MD D. Furthermore we present an approach for incrementally maintaining the redu ced property of the MDD during the search, and show how this can be used for provid ing domain entailment detection. Finally we discuss how to apply our ap proach to other similar data structures such as AOMDDs and Case DAGs. The techni que used can be seen as an extension of the GAC algorithm for the regular la nguage constraint on finite length input [2].