A Generic Global Constraint based on MDDs

TL;DR

This paper introduces a novel global constraint framework using Multi-Valued Decision Diagrams (MDDs), providing an efficient GAC maintenance algorithm that supports skipped variables, dynamic reduction, and domain entailment detection, applicable to related constraint types.

Contribution

It presents a new MDD-based global constraint with an efficient GAC algorithm supporting skipped variables and dynamic reduction, extending to related data structures.

Findings

Efficient GAC maintenance algorithm for MDD-based constraints

Supports skipped variables and dynamic MDD reduction

Applicable to related structures like AOMDDs and Case DAGs

Abstract

The paper suggests the use of Multi-Valued Decision Diagrams (MDDs) as the supporting data structure for a generic global constraint. We give an algorithm for maintaining generalized arc consistency (GAC) on this constraint that amortizes the cost of the GAC computation over a root-to-terminal path in the search tree. The technique used is an extension of the GAC algorithm for the regular language constraint on finite length input. Our approach adds support for skipped variables, maintains the reduced property of the MDD dynamically and provides domain entailment detection. Finally we also show how to adapt the approach to constraint types that are closely related to MDDs, such as AOMDDs and Case DAGs.