Solving Set Constraint Satisfaction Problems using ROBDDs

TL;DR

This paper introduces a novel ROBDD-based method for modeling and solving finite set constraint problems, offering enhanced flexibility and performance, with extensions to integer and multiset constraints and various consistency notions.

Contribution

The paper presents a new ROBDD-based approach for set constraints that improves modeling flexibility and performance, and extends to integer and multiset constraints with different consistency levels.

Findings

ROBDD-based solver outperforms traditional constraint solvers on set problems.

Efficient representation of set domains and constraints using ROBDDs.

Extension of the approach to integer and multiset constraints.

Abstract

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly represents many set domains and set constraints using ROBDDs. We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements. We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner. Since domain propagation is not always practical, we also show how to incorporate less strict consistency notions into the ROBDD framework, such as set bounds, cardinality bounds and lexicographic bounds consistency. Finally, we present experimental results that demonstrate the ROBDD-based solver performs better than various more conventional constraint solvers on several standard set constraint problems.