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14
Generic SBDD using computational group theory
 In Proceedings of CP’03
, 2003
"... 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 wit ..."
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Cited by 33 (9 self)
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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. 1
Order computations in generic groups
 PHD THESIS MIT, SUBMITTED JUNE 2007. RESOURCES
, 2007
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Polyhedral representation conversion up to symmetries
, 2009
"... We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfu ..."
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Cited by 4 (2 self)
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We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfully used by different authors in special contexts. Moreover, we sketch an incremental method, which is a generalization of Fourier–Motzkin elimination, and we give some ideas how symmetry can be exploited using pivots.
Finding central decompositions of pgroups
 J. Group Theory
"... Abstract. Polynomialtime algorithms are given to find a central decomposition of maximum size for a finite pgroup of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite ∗rings and also the Las Vegas CMeatAxe. Whe ..."
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Cited by 3 (1 self)
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Abstract. Polynomialtime algorithms are given to find a central decomposition of maximum size for a finite pgroup of class 2 and for a nilpotent Lie ring of class 2. The algorithms use Las Vegas probabilistic routines to compute the structure of finite ∗rings and also the Las Vegas CMeatAxe. When p is small, the probabilistic methods can be replaced by deterministic polynomialtime algorithms. The methods introduce new group isomorphism invariants including new characteristic subgroups. 1.
Algorithmic problems in twisted groups of Lie type
"... This thesis contains a collection of algorithms for working with the twisted groups of Lie type known as Suzuki groups, and small and large Ree groups. The two main problems under consideration are constructive recognition and constructive membership testing. We also consider problems of generatin ..."
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Cited by 1 (0 self)
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This thesis contains a collection of algorithms for working with the twisted groups of Lie type known as Suzuki groups, and small and large Ree groups. The two main problems under consideration are constructive recognition and constructive membership testing. We also consider problems of generating and conjugating Sylow and maximal subgroups. The algorithms are motivated by, and form a part of, the Matrix Group Recognition Project. Obtaining both theoretically and practically efficient algorithms has been a central goal. The algorithms have been developed with, and implemented
ADDENDUM TO AN ELEMENTARY INTRODUCTION TO COSET TABLE METHODS IN COMPUTATIONAL GROUP THEORY
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1 Efficient recovering of operation tables of black box groups and rings
, 805
"... www.math.unizh.ch/aa ..."
Polynomialtime normalizers
"... For an integer constant d>0, let Γd denote the class of finite groups all of whose nonabelian composition factors lie in Sd; in particular, Γd includes all solvable groups. Motivated by applications to graphisomorphism testing, there has been extensive study of the complexity of computation for per ..."
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For an integer constant d>0, let Γd denote the class of finite groups all of whose nonabelian composition factors lie in Sd; in particular, Γd includes all solvable groups. Motivated by applications to graphisomorphism testing, there has been extensive study of the complexity of computation for permutation groups in this class. In particular, the problems of finding set stabilizers, intersections and centralizers have all been shown to be polynomialtime computable. A notable open issue for the class Γd has been the question of whether normalizers can be found in polynomial time. We resolve this question in the affirmative. We prove that, given permutation groups G, H ≤ Sym(Ω) such that G ∈ Γd, the normalizer of H in G can be found in polynomial time. Among other new procedures, our method includes a key subroutine to solve the problem of finding stabilizers of subspaces in linear representations of permutation groups in Γd.