Partial Symmetry Breaking

  title={Partial Symmetry Breaking},
  author={Iain McDonald},
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… 

Lightweight dynamic symmetry breaking

Lightweight Dynamic Symmetry Breaking is presented, an automatic symmetry breaking method that is efficient enough to be used as a default, since it never yields a major slowdown while often giving major performance improvements.

Partial symmetry breaking by local search in the group

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.

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.

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.

Breaking More Composition Symmetries Using Search Heuristics

This paper gives the first formal characterization of the pruning behavior of ParSBDS and its improved variants and introduces the notion of Dominance-Completeness (DC-ness), showing that ParSB DS and variants eliminate the symmetry group of the given subset of symmetries if the resultant search tree is DC, and giving an example scenario.

Increasing Symmetry Breaking by Preserving Target Symmetries

Theorems and examples are given to demonstrate that it is beneficial to post symmetry breaking constraints that preserve the target symmetry and restrict the side-effects to only non-target symmetries as much as possible, resulting in a smaller solution set and search space.

Towards breaking more composition symmetries in partial symmetry breaking

Almost-Symmetry in Search

The approach is to relax the notion of graph symmetries (automorphisms) to account for vertices whose colors may change and whose edges may appear or disappear, and can discover a small number edge additions or removals that can make a given graph more symmetry.

Symmetry Breaking in Soft CSPs

It is demonstrated that breaking symmetries in soft constraint satisfaction problems improves the efficiency of search and contributes to the state-of-the-art in symmetry breaking, as well as in reasoning about preferences.

Symmetry in Constraint Programming



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.

Symmetry-Breaking Predicates for Search Problems

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

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

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

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

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

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

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

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.