• Corpus ID: 116763333

Symmetry Breaking in the Alien Tiles Puzzle

@inproceedings{Gent2000SymmetryBI,
  title={Symmetry Breaking in the Alien Tiles Puzzle},
  author={Ian P. Gent and Steve Linton and Barbara M. Smith},
  year={2000}
}
We describe an application of symmetry breaking in constrai n programming to a combinatorial puzzle based on the Alien Tiles game. We obtain a 40-fold run-tim e provement over code with no symmetry breaking. We believe this is the first integration o f an algebraic system like GAP and a constraint programming system like ILOG Solver. Available from http://www.cs.strath.ac.uk/ ̃apes/apesr eports.html School of Computer Science, University of St Andrews, St And rews, Fife, KY16 9SS, UK. ipg@cs.st… 

Comparison of Symmetry Breaking Methods in Constraint Programming

GAPSBDS and GAP-SBDS are compared in finding all graceful labellings of graphs with symmetry, or prove that there are none, for several graphs whose gracefulness was not previously known.

Symmetry Breaking Revisited

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.

Reducing Symmetry in a Combinatorial Design Problem

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.

Symmetry in Constraint Programming

Combination: automated generation of puzzles with constraints

This showed that fun, immersing computer games can be created with constraint programming, and all the levels of Combination were generated, checked for correctness and rated for difficulty completely automatically through the use of constraints.

Symmetry Breaking in Graceful Graphs

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.

Partial Symmetry Breaking

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.

Optimum Symmetry Breaking in CSPs Using Group Theory

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.

Groups and Constraints: Symmetry Breaking during Search

We present an interface between the ECLiPSe constraint logic programming system and the GAP computational abstract algebra system. The interface provides a method for efficiently dealing with large

Algebraic Constraint Programming ∗

CP relies on efficient ‘propagation’ algorithms, deducing derived consequences of current facts, through the area known as Constraint Programming (CP).

References

SHOWING 1-3 OF 3 REFERENCES

Symmetry Breaking in Constraint Programming

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.

Excluding Symmetries in Constraint-Based Search

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.

GAP – Groups, Algorithms, and Programming

  • GAP – Groups, Algorithms, and Programming
  • 1998