# Partial Symmetry Breaking

@inproceedings{McDonald2002PartialSB, title={Partial Symmetry Breaking}, author={Iain McDonald}, booktitle={CP}, year={2002} }

In this paper we define partial symmetry breaking, a concept that has been used in many previous papers without being the main topic of any research. This paper is the first systematic study of partial symmetry breaking in constraint programming. We show experimentally that performing symmetry breaking with only a subset of all symmetries can result in greatly reduced run-times. We also look at the consequences of using partial symmetry breaking in terms of variable and value orderingâ€¦Â

## 34 Citations

### Lightweight dynamic symmetry breaking

- Computer ScienceConstraints
- 2013

Lightweight Dynamic Symmetry Breaking is presented, an automatic symmetry breaking method that is efficient enough to be used as a default, since it never yields a major slowdown while often giving major performance improvements.

### Partial symmetry breaking by local search in the group

- Computer ScienceConstraints
- 2012

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.

### Automatic Generation of Constraints for Partial Symmetry Breaking

- Computer ScienceCP
- 2011

This paper introduces a new method of finding a small set of constraints which provide very efficient partial symmetry breaking, which works with all problem classes and modelling techniques.

### Symmetry Breaking Revisited

- Computer ScienceConstraints
- 2004

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.

### Breaking More Composition Symmetries Using Search Heuristics

- Computer ScienceAAAI
- 2016

This paper gives the first formal characterization of the pruning behavior of ParSBDS and its improved variants and introduces the notion of Dominance-Completeness (DC-ness), showing that ParSB DS and variants eliminate the symmetry group of the given subset of symmetries if the resultant search tree is DC, and giving an example scenario.

### Increasing Symmetry Breaking by Preserving Target Symmetries

- Computer ScienceCP
- 2012

Theorems and examples are given to demonstrate that it is beneficial to post symmetry breaking constraints that preserve the target symmetry and restrict the side-effects to only non-target symmetries as much as possible, resulting in a smaller solution set and search space.

### Towards breaking more composition symmetries in partial symmetry breaking

- Computer ScienceArtif. Intell.
- 2017

### Almost-Symmetry in Search

- Mathematics, Computer Science
- 2005

The approach is to relax the notion of graph symmetries (automorphisms) to account for vertices whose colors may change and whose edges may appear or disappear, and can discover a small number edge additions or removals that can make a given graph more symmetry.

### Symmetry Breaking in Soft CSPs

- Computer ScienceSGAI Conf.
- 2003

It is demonstrated that breaking symmetries in soft constraint satisfaction problems improves the efficiency of search and contributes to the state-of-the-art in symmetry breaking, as well as in reasoning about preferences.

### Symmetry in Constraint Programming

- Computer ScienceHandbook of Constraint Programming
- 2006

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