Larry Finkelstein

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We introduce new Monte Carlo methods to speed up and greatly simplify the manipulation of permutation groups. The methods are of a combinatorial character and use elementary group theory only. We achieve a nearly optimal 0(n3 loge n) running time for membership testing, an improvement of two orders of magnitude compared to known elementary algorithms and(More)
A variety of elementary combinatorial techniques for permutation groups are reviewed. It is shown how to apply these techniques to yield faster and/or more space-eecient algorithms for problems including group membership, normal closure, center, base change and Cayley graphs. Emphasis is placed on randomized techniques and new data structures. The paper(More)
ii Dedicated to my wife Linda and my c hildren Jonathan and Daniel for their encouragment and support. iii Acknowledgements I thank my advisor, Kenneth Baclawski for his support over the years that it took to complete this research. Ken was always quick t o understand my o wn eeorts, and came up with a great many useful suggestions, which I w as able to(More)
A number of researchers have proposed Cayley graphs and Schreier coset graphs as models for interconnection networks. New algorithms are presented for generating Cayley graphs in a more time-eecient manner than was previously possible. Alternatively, a second algorithm is provided for storing Cayley graphs in a space-eecient manner (log 2 (3) bits per(More)
The group membership problem for permutation groups is perhaps the most important problem of computational group theory. Solution of this problem seems to depend intrinsically on constructing a strong generating set. Until now, recognizing if a set of generators is strong has been thought to be as hard as constructing a strong generating set from an(More)
The construction of point stabilizer subgroups is a problem which has been studied intensively. [1, 4, 5, 10, 11, 12, 14] This work describes a general reduction of certain group constructions to the point stabilizer problem. Examples are given for the centralizer, the normal closure, and a restricted group intersection problem. For the normal closure(More)
A base of a permutation group G is a subset B of the permutation domain such that only the identity of G fixes B pointwise. The permutation representations of important classes of groups, including all finite simple groups other than the alternating groups, admit O(log n) size bases, where n is the size of the permutation domain. Groups with very small(More)