Faster Symmetry Breaking Constraints for Abstract Structures

2025-11-14

AI Summary

In constraint programming, high-level modeling languages (e.g., Essence) introduce significant symmetry through abstract structures such as nested sets, severely degrading solver efficiency. To address this, we propose a lightweight, structure-aware symmetry breaking method operating at the underlying representation level. Rather than generating numerous explicit symmetry-breaking constraints, our approach matrix-encodes abstract structures and integrates an optimized variable ordering strategy tailored to indistinguishable objects—achieving incomplete yet highly effective symmetry elimination. Compared to Akgün et al. (2025), our method substantially reduces constraint set size and search redundancy. Empirical evaluation on diverse symmetry-rich benchmark problems demonstrates marked improvements in solving speed, while maintaining practicality and scalability across problem sizes and structural complexity.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Programming
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Bridging structured and unstructured data
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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).

Problem

• Breaking symmetries in abstract structures for constraint programming
• Improving efficiency of symmetry-breaking constraints in modeling languages
• Handling symmetries from indistinguishable objects in problem solving

Innovation

• Faster symmetry breaking for abstract structures
• Exploiting representations to reduce constraint complexity
• Incomplete method targeting indistinguishable object symmetries