Symmetry Breaking in Graceful Graphs

@inproceedings{Petrie2003SymmetryBI,
  title={Symmetry Breaking in Graceful Graphs},
  author={Karen E. Petrie and Barbara M. Smith},
  booktitle={CP},
  year={2003}
}
Symmetry occurs frequently in Constraint Satisfaction Problems (CSPs). For instance, in 3-colouring the nodes of a graph, a CSP model that assigns a specific colour to each node has sets of equivalent solutions in which the three colours are permuted. Symmetry in CSPs can cause wasted search, because the search for solutions may repeatedly visit partial assignments symmetric to ones already considered. If a partial assignment does not lead to a solution, neither will any symmetrically… 

Automatic Generation of Constraints for Partial Symmetry Breaking

TLDR
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.

Constraint Programming Models for Graceful Graphs

TLDR
A new and much faster CSP model of the problem is presented, with several new results for graphs whose gracefulness was previously unknown, and several classes of graph that are conjectured to be graceful only for small instances are investigated.

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.

Breaking Symmetry in Injective Problems

TLDR
It is shown how this partial ordering of the variables can be automatically computed using computational group theory (CGT) and further shown that partial orders can be safely used together with the GE-tree method.

Value Ordering for Finding All Solutions

TLDR
It is shown that if the values of a variable are assigned instead via a sequence of binary choice points, and the removal of the value just tried from the domain of the variable is propagated before another value is selected, the value ordering can affect the search effort.

Symmetry Definitions for Constraint Satisfaction Problems

TLDR
The many different definitions of symmetry for constraint satisfaction problems (CSPs) are reviewed, and it is shown that a symmetry can be defined in two fundamentally different ways: as an operation preserving the solutions of a CSP instance, or else as anoperation preserving the constraints.

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 by Local Search ⋆

TLDR
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.

Breaking symmetries in all different problems

TLDR
It is shown how this partial ordering of the variables can be automatically computed using computational group theory (CGT) and that partial orders can be safely used together with the GE-tree method of [Roney-Dougal et al., 2004].

Sets of Symmetry Breaking Constraints

[Puget, 2004] has shown that if the symmetry in a constraint satisfaction problem acts only on the variables and there is also an allDifferent constraint on the variables, the symmetry can be
...

References

SHOWING 1-10 OF 23 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 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.

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

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.

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.

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.

Generic SBDD Using Computational Group Theory

We introduce a novel approach for symmetry breaking by dominance detection (SBDD). The essence of SBDD is to perform 'dominance checks' at each node in a search tree to ensure that no symmetrically

A Constraint Programming Approach to the Stable Marriage Problem

TLDR
Two encodings of an instance I of SM as an instance J of a Constraint Satisfaction Problem are presented and it is proved that, in a precise sense, establishing arc consistency in J is equivalent to the action of the established Extended Gale/Shapley algorithm for SM on I.

Breaking Row and Column Symmetries in Matrix Models

TLDR
This work identifies an important class of symmetries in constraint programming, arising from matrices of decision variables where rows and columns can be swapped, and identifies special cases where all compositions of the row and column asymmetries can be eliminated by the addition of only a linear number of symmetry-breaking constraints.

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.