• Corpus ID: 16163450

Reducing Symmetry in a Combinatorial Design Problem

@inproceedings{Smith2001ReducingSI,
  title={Reducing Symmetry in a Combinatorial Design Problem},
  author={Barbara M. Smith and Hd Dh Huddersfield},
  year={2001}
}
A combinatorial design problem is considered which can be modelled as a constraint satisfaction problem in several diierent ways. The models all have a large number of symmetries which cause diiculties when searching for solutions. Diierent approaches to reducing the symmetry are discussed: remodelling the problem ; adding constraints to the model at the outset; and adding constraints during search to prevent symmetric assignments being explored on backtracking. The most successful strategy for… 

Partial symmetry breaking by local search in the group

TLDR
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 in a Rack Configuration Problem

TLDR
The issue of reducing symmetry in a rack configuration problem, which can be modelled as a constraint satisfaction problem, is addressed, with the best result obtained by integrating a primal model of the problem with its corresponding dual model.

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.

Automated static symmetry breaking in constraint satisfaction problems

TLDR
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.

Efficient structural symmetry breaking for constraint satisfaction problems

TLDR
This work identifies several classes of CSPs that encompass many practical problems and for which symmetry breaking for various forms of value and variable interchangeability is tractable using dedicated search procedures or symmetry-breaking constraints that allow nogoods and their symmetrically equivalent solutions to be stored and checked efficiently.

Structural symmetry breaking for constraint satisfaction problems

TLDR
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 structural symmetry breaking for constraint satisfaction problems

TLDR
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.

Breaking Local Symmetries in Quasigroup Completion Problems

TLDR
An experimental study on breaking local symmetries in quasigroup completion problems, a well-studied problem among combinatorial problems, concludes that additional constraints have a puzzling effect on state of theart SAT solvers, mainly due to the heuristics being used by these solvers.

Symmetry Breaking Revisited

TLDR
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.

Partial Symmetry Breaking

TLDR
This paper is the first systematic study of partial symmetry breaking in constraint programming, and shows experimentally that performing symmetry breaking with only a subset of all symmetries can result in greatly reduced run-times.
...

References

SHOWING 1-6 OF 6 REFERENCES

Symmetry breaking during search in constraint programming

TLDR
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.

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.

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.

Mathematical Recreations and Essays

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some

Mathematical Recreations and Essays. Macmillan

  • Mathematical Recreations and Essays. Macmillan
  • 1938