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The Complexity of SymmetryBreaking Formulas
 Annals of Mathematics and Artificial Intelligence
, 2002
"... Symmetrybreaking formulas for a constraintsatisfaction problem are satisifed by exactly one member (e.g., the lexicographic leader) from each set of \symmetrical points" in the search space. Thus, the incorporation of such formulas can accelerate the search for a solution without sacrificing satis ..."
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Cited by 6 (0 self)
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Symmetrybreaking formulas for a constraintsatisfaction problem are satisifed by exactly one member (e.g., the lexicographic leader) from each set of \symmetrical points" in the search space. Thus, the incorporation of such formulas can accelerate the search for a solution without sacrificing satisfiability.
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.
Construction of Combinatorial Objects
, 1995
"... Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, u ..."
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Cited by 1 (1 self)
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Isomorphism problems often can be solved by determining orbits of a group acting on the set of all objects to be classified. The paper centers around algorithms for this topic and shows how to base them on the same idea, the homomorphism principle. Especially it is shown that forming Sims chains, using an algorithmic version of Burnside's table of marks, computing double coset representatives, and computing Sylow subgroups of automorphism groups can be explained in this way. The exposition is based on graph theoretic concepts to give an easy explanation of data structures for group actions.
Classification of simple 2(11,3,3) designs
"... We present an orderly algorithm for classifying triple systems. Subsequently, we show that there exist exactly 7,038,699,746 nonisomorphic simple 2(11, 3, 3) designs. The method is also used to confirm the previously accomplished classifications of 2(8,3,6), 2(12, 3, 2) and 2(19, 3, 1) designs. ..."
Abstract
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We present an orderly algorithm for classifying triple systems. Subsequently, we show that there exist exactly 7,038,699,746 nonisomorphic simple 2(11, 3, 3) designs. The method is also used to confirm the previously accomplished classifications of 2(8,3,6), 2(12, 3, 2) and 2(19, 3, 1) designs.