An Adaptive Prefix-Assignment Technique for Symmetry Reduction

  title={An Adaptive Prefix-Assignment Technique for Symmetry Reduction},
  author={Tommi A. Junttila and Matti Karppa and Petteri Kaski and Jukka Kohonen},
  journal={J. Symb. Comput.},
This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKay's canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with… 

A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms

A new equivalence on graphs is introduced, defined by its symmetry-breaking capability, in which the equivalence is used to prune the search tree and an optimization problem with the goal of finding an equivalence partition with the highest pruning potential is defined.



Dynamic Symmetry Breaking by Simulating Zykov Contraction

A new method to break symmetry in graph coloring problems by developing a learning scheme that translates each encountered conflict into one conflict clause which covers equivalent conflicts arising from any permutation of the colors.

Graph Isomorphism in Quasipolynomial Time

The algorithm builds on Luks’s SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic “local certificates” and combinatorial canonical partitioning techniques and shows that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioned.

An Improved Isomorphism Test for Bounded-tree-width Graphs

A new fpt algorithm testing isomorphism of n-vertex graphs of tree width in time is given, which avoids the use of Babai's algorithm and has the additional benefit that it can also used as a canonization algorithm.

Dynamic symmetry breaking in the satisfiability problem

A new method for local symmetry breaking is presented that consists in detecting dynamically local symmetries by reducing the remaining partial SAT instance at each node of the search tree to a graph that has an equivalent automorphism group than the symmetry group of thepartial SAT instance.

SymChaff: exploiting symmetry in a structure-aware satisfiability solver

This article presents a new low-overhead framework for representing and utilizing problem symmetry in propositional satisfiability algorithms by using high level problem description to pass on symmetry information to the SAT solver in a simple and concise form.

Symmetry and Satisfiability

  • K. Sakallah
  • Computer Science
    Handbook of Satisfiability
  • 2009
This chapter explores the symmetry of Boolean functions, particularly the symmetries of their conjunctive normal form (CNF) representations, and examines how to model them using the mathematical language of group theory, how to derive them from a CNF formula, and how to utilize them to speed up CNF SAT solvers.

Efficient symmetry breaking for Boolean satisfiability

A more systematic and efficient construction of symmetry-breaking predicates is described, which uses the cycle structure of symmetry generators, which typically involve very few variables, to drastically reduce the size of SBPs.

Automatic Generation of Constraints for Partial Symmetry Breaking

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.

Minimal ordering constraints for some families of variable symmetries

This paper examines some commonly-occurring families of groups and derives a minimal set of ordering constraints sufficient to break the symmetry each group describes, and uses these minimal sets as building blocks to generate minimal sets ofordering constraints for groups constructed via direct and imprimitive wreath products.

Classification Algorithms for Codes and Designs

A new starting-point and a new method are requisite, to insure a complete [classi?cation of the Steiner triple systems of order 15]. This method was furnished, and its tedious and di?cult execution