Faster Symmetry Breaking Constraints for Abstract Structures

TL;DR

This paper introduces a faster, incomplete symmetry-breaking method for abstract structures in constraint programming, improving efficiency when handling symmetries from indistinguishable objects.

Contribution

The paper proposes a novel incomplete symmetry-breaking technique that leverages representations of abstract structures, outperforming previous methods in speed.

Findings

Faster symmetry-breaking for abstract structures.

Effective in handling symmetries from indistinguishable objects.

Outperforms previous methods in computational speed.

Abstract

In constraint programming and related paradigms, a modeller specifies their problem in a modelling language for a solver to search and return its solution(s). Using high-level modelling languages such as Essence, a modeller may express their problems in terms of abstract structures. These are structures not natively supported by the solvers, and so they have to be transformed into or represented as other structures before solving. For example, nested sets are abstract structures, and they can be represented as matrices in constraint solvers. Many problems contain symmetries and one very common and highly successful technique used in constraint programming is to "break" symmetries, to avoid searching for symmetric solutions. This can speed up the solving process by many orders of magnitude. Most of these symmetry-breaking techniques involve placing some kind of ordering for the variables of the problem, and picking a particular member under the symmetries, usually the smallest. Unfortunately, applying this technique to abstract variables produces a very large number of complex constraints that perform poorly in practice. In this paper, we demonstrate a new incomplete method of breaking the symmetries of abstract structures by better exploiting their representations. We apply the method in breaking the symmetries arising from indistinguishable objects, a commonly occurring type of symmetry, and show that our method is faster than the previous methods proposed in (Akg\"un et al. 2025).