Decomposition of the NVALUE constraint

TL;DR

This paper investigates how to decompose the NVALUE global constraint to preserve its propagation strength, enabling more effective integration with advanced solving techniques like nogood learning and impact-based heuristics.

Contribution

The paper identifies a specific decomposition of NVALUE that maintains bound consistency, facilitating better solver performance and broader applicability.

Findings

A decomposition that maintains bound consistency for NVALUE

Enhanced solver techniques leveraging the decomposition

Potential improvements in SAT and IP solver performance

Abstract

We study decompositions of NVALUE, a global constraint that can be used to model a wide range of problems where values need to be counted. Whilst decomposition typically hinders propagation, we identify one decomposition that maintains a global view as enforcing bound consistency on the decomposition achieves bound consistency on the original global NVALUE constraint. Such decompositions offer the prospect for advanced solving techniques like nogood learning and impact based branching heuristics. They may also help SAT and IP solvers take advantage of the propagation of global constraints.