# A Commentary on "Breaking Row and Column Symmetries in Matrix Models"

arXiv: https://arxiv.org/abs/1910.01423 · HTML: https://mlsanity.com/paper/1910.01423/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Pairwise Symmetry Reasoning for Multi-Agent Path Finding Search](https://mlsanity.com/paper/2103.07116/) (2021)
- [Incomplete MaxSAT Approaches for Combinatorial Testing](https://mlsanity.com/paper/2105.12552/) (2021)
- [The Complexity of Symmetry Breaking Beyond Lex-Leader](https://mlsanity.com/paper/2407.04419/) (2024)
- [Exploiting Symmetries in MUS Computation (Extended version)](https://mlsanity.com/paper/2412.13606/) (2024)
- [Breaking the Symmetries of Indistinguishable Objects](https://mlsanity.com/paper/2503.17251/) (2025)
- [Faster Symmetry Breaking Constraints for Abstract Structures](https://mlsanity.com/paper/2511.11029/) (2025)
- [Orbitopal Fixing in SAT](https://mlsanity.com/paper/2601.16855/) (2026)
- [Streamlined Constraint Reasoning via CNN Pattern Recognition on Enumerated Solutions](https://mlsanity.com/paper/2605.19895/) (2026)
- [LLM-Guided Evolutionary Search for Constraint Model Reformulation to Improve Solver Efficiency](https://mlsanity.com/paper/2607.28268/) (2026)

## Abstract (arXiv)

The CP 2002 paper entitled "Breaking Row and Column Symmetries in Matrix Models" by Flener et al. (https://link.springer.com/chapter/10.1007%2F3-540-46135-3_31) describes some of the first work for identifying and analyzing row and column symmetry in matrix models and for efficiently and effectively dealing with such symmetry using static symmetry-breaking ordering constraints. This commentary provides a retrospective on that work and highlights some of the subsequent work on the topic.