# Excluding Symmetries in Constraint-Based Search

@article{Backofen2004ExcludingSI, title={Excluding Symmetries in Constraint-Based Search}, author={Rolf Backofen and Sebastian A. Will}, journal={Constraints}, year={2004}, volume={7}, pages={333-349} }

We introduce a new method, called symmetry excluding search (SES), for excluding symmetries in constraint based search. To our knowledge, it is the first declarative method that can be applied to arbitrary symmetries. The SES-method is based on the notion of symmetric constraints, which are used in our modification of a general constraint based search algorithm. The method does not influence the search strategy. Furthermore, it can be used with either the full set of symmetries, or a subset of…

## 85 Citations

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This approach inherits good properties of both dynamic and static symmetry breaking methods: it can have fast propagation on the posted symmetry breaking constraints without conflicting with the branching heuristic, and it proves that its method is correct and only eliminates symmetric solutions.

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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.

### Symmetry Breaking in Constraint Satisfaction Problems

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### Symmetry Definitions for Constraint Satisfaction Problems

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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.

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A compositional approach which derives symmetries of the applications from primitive constraints is proposed, recognition of the special role of global constraints in symmetry detection.

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- Computer Science
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This work describes a novel algorithm that statically breaks symmetry in CSPs by using computational group theory during search, and believes this to be the first method that successfully combines the posting of symmetry breaking constraints before search, with symmetry breaking by analysis of search states.

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- Computer ScienceConstraints
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This paper introduces value precedence, a notion which can be used to break a common class of value symmetries, namely asymmetries of indistinguishable values, and proposes efficient propagation algorithms for implementing global value precedence constraints.

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This paper shows how to successfully combine Symmetry Breaking During Search and Lazy Clause Generation to create a new symmetry breaking method which is called SBDS-1UIP, which can be modified to exploit almost symmetries very effectively.

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