Breaking Value Symmetry

TL;DR

This paper investigates methods for breaking value symmetry in constraint satisfaction problems, revealing computational limits while demonstrating practical effectiveness in reducing symmetry.

Contribution

It provides new insights into the computational complexity of breaking value symmetry and shows that practical symmetry breaking is often feasible despite NP-hardness.

Findings

Pruning all symmetric values is NP-hard in general.

Significant value symmetry can be broken effectively in practice.

Results are applicable across planning, scheduling, and other domains.

Abstract

Symmetry is an important factor in solving many constraint satisfaction problems. One common type of symmetry is when we have symmetric values. In a recent series of papers, we have studied methods to break value symmetries. Our results identify computational limits on eliminating value symmetry. For instance, we prove that pruning all symmetric values is NP-hard in general. Nevertheless, experiments show that much value symmetry can be broken in practice. These results may be useful to researchers in planning, scheduling and other areas as value symmetry occurs in many different domains.