# Symmetry Breaking in Constraint Programming

@inproceedings{Gent2000SymmetryBI, title={Symmetry Breaking in Constraint Programming}, author={Ian P. Gent and Barbara M. Smith}, booktitle={ECAI}, year={2000} }

We describe a method for symmetry breaking during search (SBDS) in constraint programming. It has the great advantage of not interfering with heuristic choices. It guarantees to return a unique solution from each set of symmetrically equivalent ones, which is the one found first by the variable and value ordering heuristics. We describe an implementation of SBDS in ILOG Solver, and applications to low autocorrelation binary sequences and the n-queens problem. We discuss how SBDS can be applied…

## 232 Citations

### 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 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.

### 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.

### 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.

### 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.

### Symmetry Breaking in Graceful Graphs

- MathematicsCP
- 2003

Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs) and can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered.

### 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.

### Exploiting symmetries within constraint satisfaction search

- Computer ScienceArtif. Intell.
- 2001

### Symmetry Breaking by Metaheuristic Search

- Computer Science
- 2008

A new partial symmetry breaking method that can be applied to arbitrary variable/value symmetries is described, which models dominance detection as a nonstationary optimisation problem, and solves it by resource-bounded metaheuristic search in the symmetry group.

### 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.

## References

SHOWING 1-10 OF 10 REFERENCES

### Symmetry breaking during search in constraint programming

- Computer Science
- 1999

A method for symmetry breaking during search (SBDS) in constraint programming that guarantees to return a unique solution from each set of symmetrically equivalent ones, which is the one found by the variable and value ordering heuristics.

### Symmetry-Breaking Predicates for Search Problems

- Computer ScienceKR
- 1996

This work presents a general scheme whereby symmetries are exploited by adding \symmetry-breaking" predicates to the theory, and discusses methods for generating partial symmetry-breaking predicates, and shows that in several speciic cases asymmetries can be broken either fully or partially using a polynomial number of predicates.

### Backtrack Searching in the Presence of Symmetry

- Computer ScienceNord. J. Comput.
- 1996

This paper gives the first algorithm that combines search rearrangement with an arbitrary symmetry group, and it is confirmed that the algorithms save a considerable amount of time on symmetric search problems.

### On the Satisfiability of Symmetrical Constrained Satisfaction Problems

- Computer ScienceISMIS
- 1993

A general solution for symmetrical constraint satisfaction problems is described and both a theoretical study and experimental results using the constraint-based library PECOS are provided.

### Using Symmetry of Global Constraints to Speed up the Resolution of Constraint Satisfaction Problems

- Computer Science
- 2002

This paper addresses the problem of detecting and exploiting a particular class of symmetry called intensional permutability, which is based on the notion of interchangeability between variables and can be detected with a very small overhead, and proposes a simple method to exploit it.

### Principles and Practice of Constraint Programming – CP’99

- Computer ScienceLecture Notes in Computer Science
- 1999

A simple, yet very general framework is provided that allows us to explain several constraint propagation algorithms in a systematic way using the notions commutativity and semi-commutativity.

### Constraint Techniques for Solving the Protein Structure Prediction Problem

- Computer ScienceCP
- 1998

A constraint formulation of the HP-model structure prediction problem is described, a novel, general technique for excluding geometrical symmetries in constraint programming is introduced and a new lower bound on the energy of an HP-protein is described.

### Exhaustive search for low-autocorrelation binary sequences

- Computer Science
- 1996

An exhaustive search algorithm with run-time characteristic is discussed and applied to compile a table of exact ground states of the Bernasconi model up to N = 48, suggesting F > 9 for the optimal merit factor in the limit.

### Solving Strategies for Highly Symmetric CSPs

- MathematicsIJCAI
- 1999

A rationale for exploiting symmetry within depth-first search is proposed, leading to an heuristic for variable selection and a domain pruning procedure, which are then applied to a highly symmetric combinatorial problem, namely the generation of balanced incomplete block designs.