# Symmetry Breaking Revisited

@article{Puget2004SymmetryBR, title={Symmetry Breaking Revisited}, author={Jean-François Puget}, journal={Constraints}, year={2004}, volume={10}, pages={23-46} }

Symmetries in constraint satisfaction problems (CSPs) are one of the difficulties that practitioners have to deal with. We present in this paper a new method based on the symmetries of decisions taken from the root of the search tree. This method can be seen as an improvement of the SBDD method presented by Focacci and Milano [7] and Fahle, Schamberger and Sellmann [5]. We present a simple formalization of our method for which we prove correctness and completeness results. We show that our…

## 117 Citations

### Local Symmetry Breaking During Search in CSPs

- Computer ScienceCP
- 2007

A general principle of semantic symmetry is studied and a syntactic symmetry is defined which is a sufficient condition for semantic symmetry, and it is shown how to detect and how to eliminate it locally to increase CSP tree search methods efficiency.

### Breaking Symmetry in Injective Problems

- Computer Science
- 2007

It is shown how this partial ordering of the variables can be automatically computed using computational group theory (CGT) and further shown that partial orders can be safely used together with the GE-tree method.

### Symmetry Breaking Using Stabilizers

- Computer ScienceCP
- 2003

STAB is a method that adds some symmetry breaking constraints during the search for solution to matrix problems where rows and columns can be permuted and is more than one order of magnitude more efficient than best published techniques so far.

### 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.

### Structural symmetry breaking for constraint satisfaction problems

- Mathematics
- 2007

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.

### Combining Branch&Bound and SBDD to solve Soft CSPs

- Computer Science
- 2004

Soft-SBDD, a generalization of Symmetry Breaking via Dominance Detection, is presented, and theoretical results demonstrating that symmetry breaking in soft constraint satisfaction problems improves the efficiency of search are presented.

### 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.

### Dynamic structural symmetry breaking for constraint satisfaction problems

- MathematicsConstraints
- 2008

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.

### Dynamic Detection and Elimination of Local Symmetry in CSPs

- Computer Science
- 2007

A general principle of semantic symmetry is studied and a weakened form of this syntactic symmetry is defined which is a sufficient condition for semantic symmetry, and three local symmetry detection and elimination strategies are studied and compared to global symmetry elimination.

### Symmetry Breaking by Local Search ⋆

- Computer Science
- 2009

A new approach to symmetry breaking is described: using local search in the symmetry group to detect violated lex-leader constraints, which opens up a fruitful new connection between the fields of symme try breaking and metaheuristics.

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