Breaking Row and Column Symmetries in Matrix Models

Flener, Pierre; Frisch, Alan M.; Hnich, Brahim; Kızıltan, Zeynep; Miguel, Ian; Pearson, Justin; Walsh, Toby

doi:10.1007/3-540-46135-3_31

Cited by 133 publications

(192 citation statements)

References 8 publications

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“…The timings obtained are comparable with those presented for the same problems in [6], where lexicographic ordering constraints were use to break the row and column symmetries. The advantage of using SBDD is that all symmetries are broken, whereas a lexicographic solution for the (6, 20, 10, 3, 4) BIBD problem returns 21 solutions.…”

Section: Example: Balanced Incomplete Block Designssupporting

confidence: 60%

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Generic SBDD Using Computational Group Theory

Gent

Harvey

Kelsey

et al. 2003

Principles and Practice of Constraint Programming – CP 2003

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Abstract. 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 equivalent node has been visited before. While a highly effective technique for dealing with symmetry in constraint programs, SBDD forces a major overhead on the programmer, of writing a dominance checker for each new problem to be solved. Our novelty here is an entirely generic dominance checker. This in itself is new, as are the algorithms to implement it. It can be used for any symmetry group arising in a constraint program. A constraint programmer using our system merely has to define a small number (typically 2-6) of generating symmetries, and our system detects and breaks all resulting symmetries. Our dominance checker also performs some propagation, again generically, so that values are removed from variables if setting them would lead to a successful dominance check. We have implemented this generic SBDD and report results on its use. Our implementation easily handles problems involving 10 36 symmetries, with only four permutations needed to direct the dominance checks during search.

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Section: Example: Balanced Incomplete Block Designssupporting

confidence: 60%

“…Compared to the use of GAP for SBDS [9], we avoid the large space overhead, meaning that -as we reported here -we are able to solve completely problems with groups many orders of magnitude larger. Some techniques, such as [6], do not guarantee to eliminate all symmetries, while we do.…”

Section: Discussionmentioning

confidence: 96%

Generic SBDD Using Computational Group Theory

Gent

Harvey

Kelsey

et al. 2003

Principles and Practice of Constraint Programming – CP 2003

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“…The orbit of the integer i + 1 in the i th subgroup, i.e., all the integers it can be mapped to by any permutation in this subgroup, thus define exactly the pairs for which we must impose an inequality. These pairs can be obtained with the Shreier-Sims algorithm which runs in O(n 2 log 3 (#Σ) + tn log(#Σ)), where t is the cardinality of the input generating set 5 . Since #Σ is at most n!…”

Section: Symmetry-breaking Constraints For Ncspsmentioning

confidence: 99%

“…Two main symmetrybreaking strategies have been pursued: 1) to devise specialized search algorithms that avoid symmetric portions of the search space [14,8]; and 2) to add symmetry-breaking constraints (SBCs) that filter out redundant subspaces [5,16]. Contrarily to this, there exists very little work on symmetry breaking for numerical problems.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Breaking in Numeric Constraint Problems

Goldsztejn

Jermann

Angulo

et al. 2011

Principles and Practice of Constraint Programming – CP 2011

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Abstract. Symmetry-breaking constraints in the form of inequalities between variables have been proposed for a few kind of solution symmetries in numeric CSPs. We show that, for the variable symmetries among those, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs. We discuss the merits of this relaxation and present experimental evidences of its practical interest.

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“…There has also been a tendency to abstract some of the techniques from particular applications to classes of CSPs (Van Hentenryck et al 2003) or models (Flener et al 2002). However, this line of research assumes that symmetries are given and ignores the tedious and error-prone task of discovering them.…”

Section: Introductionmentioning

confidence: 99%

Compositional Derivation of Symmetries for Constraint Satisfaction

Hentenryck

Flener

Pearson

et al. 2005

Lecture Notes in Computer Science

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Abstract. This paper reconsiders the problems of discovering symmetries in constraint satisfaction problems (CSPs). It proposes a compositional approach which derives symmetries of the applications from primitive constraints. Its key insight is the recognition of the special role of global constraints in symmetry detection. Once the symmetries of global constraints are available, it often becomes much easier to derive symmetries compositionally and efficiently. The paper demonstrates the potential of this approach by studying several classes of value and variable symmetries and applying the resulting techniques to two non-trivial applications. The paper also discusses the potential of reformulations and high-level modelling abstractions to strengthen symmetry discovery.

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Breaking Row and Column Symmetries in Matrix Models

Cited by 133 publications

References 8 publications

Generic SBDD Using Computational Group Theory

Generic SBDD Using Computational Group Theory

Symmetry Breaking in Numeric Constraint Problems

Compositional Derivation of Symmetries for Constraint Satisfaction

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