Permutation Groups in NC

We show that the basic problems of permutation group manipulation admit e cient parallel solutions. Given a permutation group G by a list of generators, we nd a set of NC-e cient strong generators in NC. Using this, we show, that the following problems are in NC: membership in G; determining the order of G; nding the center of G; nding a composition series of G along with permutation representations of each composition factor. Moreover, given G, we are able to nd the pointwise stabilizer of a set in NC. One consequence is that isomorphismofgraphs with bounded multiplicityof eigenvalues is in NC. The analysis of the algorithms depends, in several ways, on consequences of the classi cation of nite simple groups.

• Type: Conference
• Year: 1987
• Where: STOC
• Authors: László Babai, Eugene M. Luks, Ákos Seress
• Keywords: Algorithms, Cient Strong Generators, Permutation Group, Permutation Group Manipulation, STOC 1987