# Symmetry Breaking in Graceful Graphs

@inproceedings{Petrie2003SymmetryBI, title={Symmetry Breaking in Graceful Graphs}, author={Karen E. Petrie and Barbara M. Smith}, booktitle={CP}, year={2003} }

Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has sets of equivalent solutions in which the three colours are permuted. Symmetry in CSPs can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered. If a partial assignment does not lead to a solution, neither will any symmetrically…

## 73 Citations

### 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.

### Constraint Programming Models for Graceful Graphs

- Mathematics, Computer ScienceCP
- 2006

A new and much faster CSP model of the problem is presented, with several new results for graphs whose gracefulness was previously unknown, and several classes of graph that are conjectured to be graceful only for small instances are investigated.

### Automated static symmetry breaking in constraint satisfaction problems

- Computer Science
- 2011

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.

### 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.

### Value Ordering for Finding All Solutions

- BusinessIJCAI
- 2005

It is shown that if the values of a variable are assigned instead via a sequence of binary choice points, and the removal of the value just tried from the domain of the variable is propagated before another value is selected, the value ordering can affect the search effort.

### Symmetry Definitions for Constraint Satisfaction Problems

- Computer ScienceConstraints
- 2006

The many different definitions of symmetry for constraint satisfaction problems (CSPs) are reviewed, and it is shown that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as anoperation preserving the constraints.

### 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.

### 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.

### Breaking symmetries in all different problems

- Computer ScienceIJCAI
- 2005

It is shown how this partial ordering of the variables can be automatically computed using computational group theory (CGT) and that partial orders can be safely used together with the GE-tree method of [Roney-Dougal et al., 2004].

### Sets of Symmetry Breaking Constraints

- Physics
- 2005

[Puget, 2004] has shown that if the symmetry in a constraint satisfaction problem acts only on the variables and there is also an allDifferent constraint on the variables, the symmetry can be…

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