Relations between MDDs and Tuples and Dynamic Modifications of MDDs based constraints

TL;DR

This paper explores the relationship between Multi-valued Decision Diagrams (MDDs) and tuples, improving transformation methods, proposing dynamic modification algorithms, and demonstrating the competitiveness of MDD constraints in constraint programming.

Contribution

It introduces enhanced methods for transforming tuples into MDDs and presents algorithms for dynamic updates, adapting MDD-4R for persistent modifications during search.

Findings

Improved methods for transforming tuples into MDDs.

Algorithms for in-place addition and deletion of tuples in MDDs.

MDD constraints are competitive with Table constraints.

Abstract

We study the relations between Multi-valued Decision Diagrams (MDD) and tuples (i.e. elements of the Cartesian Product of variables). First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds, sequences of tuples into MDDs. Then, we present some in-place algorithms for adding and deleting tuples from an MDD. Next, we consider an MDD constraint which is modified during the search by deleting some tuples. We give an algorithm which adapts MDD-4R to these dynamic and persistent modifications. Some experiments show that MDD constraints are competitive with Table constraints.