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 ordering… 

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References

SHOWING 1-10 OF 15 REFERENCES

Symmetry Breaking in Constraint Programming

TLDR
This work describes 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 first by the variable and value ordering heuristics.

Symmetry-Breaking Predicates for Search Problems

TLDR
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.

Reducing Symmetry in a Combinatorial Design Problem

TLDR
The most successful strategy for the problem of this paper employs a complex model with less inherent symmetry than the others, combined with symmetry breaking during search.

Optimum Symmetry Breaking in CSPs Using Group Theory

TLDR
The research carried out has detailed how to exploit the symmetries in CSPs so that it will take less time to find unique solutions i.e. the authors will count two symmetrically equivalent solutions as one solution.

Excluding Symmetries in Constraint-Based Search

TLDR
This work introduces a new method, called symmetry excluding search (SES), for excluding symmetries in constraint based search, which is the first declarative method that can be applied to arbitrary asymmetries, and proves correctness, completeness and symmetry exclusion properties.

Backtrack Searching in the Presence of Symmetry

TLDR
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.

Symmetry Breaking

TLDR
This work presents an approach that detects symmetric choice points during the search and enables the user to find solutions for complex problems with minimal effort spent on modeling.

Exploiting symmetries within constraint satisfaction search

Global Cut Framework for Removing Symmetries

TLDR
A general technique for removing symmetries in CSPs during search to record no-goods, during the exploration of the search tree, whose symmetric counterpart should be removed, and presents a general, correct and complete filtering algorithm for SRCs.

Symmetry Breaking in the Alien Tiles Puzzle

TLDR
This is the first integration of an algebraic system like GAP and a constraint programming system like ILOG Solver, based on the Alien Tiles game, and a 40-fold run-time provement over code with no symmetry breaking is obtained.