# Reducing Symmetry in a Combinatorial Design Problem

@inproceedings{Smith2001ReducingSI, title={Reducing Symmetry in a Combinatorial Design Problem}, author={Barbara M. Smith and Hd Dh Huddersfield}, year={2001} }

A combinatorial design problem is considered which can be modelled as a constraint satisfaction problem in several diierent ways. The models all have a large number of symmetries which cause diiculties when searching for solutions. Diierent approaches to reducing the symmetry are discussed: remodelling the problem ; adding constraints to the model at the outset; and adding constraints during search to prevent symmetric assignments being explored on backtracking. The most successful strategy for…

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## 72 Citations

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A new method called Symmetry Breaking by Nonstationary Optimisation is described, which interleaves local search in the symmetry group with backtrack search on the constraint problem, which can be tuned to break each symmetry with an arbitrarily high probability with high runtime overhead.

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### Symmetry Breaking

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Through the utilisation of graph automorphism tools and the groups and permutations software GAP, a method of defining variable symmetries in a problem as a group is provided, which can construct a minimal set of ordering constraints for that problem automatically.

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This work identifies several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value and variable interchangeability is tractable using dedicated search procedures or symmetry-breaking constraints that allow nogoods and their symmetrically equivalent solutions to be stored and checked efficiently.

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Several classes of CSPs are identified that encompass many practical problems and for which symmetry breaking for various forms of value or variable interchangeability is tractable using dedicated search procedures, and the limits of efficient symmetry breaking are shown.

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Several classes of CSPs are identified that encompass many practical problems and for which symmetry breaking for various forms of value or variable interchangeability is tractable using dedicated search procedures, and the limits of efficient symmetry breaking are shown.

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An experimental study on breaking local symmetries in quasigroup completion problems, a well-studied problem among combinatorial problems, concludes that additional constraints have a puzzling effect on state of theart SAT solvers, mainly due to the heuristics being used by these solvers.

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This paper presents a new method based on the symmetries of decisions taken from the root of the search tree that is theoretically more efficient as the size of each no-good is smaller and can be seen as an improvement of the SBDD method.

### Partial Symmetry Breaking

- Computer ScienceCP
- 2002

This paper is the first systematic study of partial symmetry breaking in constraint programming, and shows experimentally that performing symmetry breaking with only a subset of all symmetries can result in greatly reduced run-times.

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