Parallel algorithms for permutation groups and graph isomorphism

Abstract

We develop parallel techniques for dealing with permutation group problems. These are most effective on the class of groups with bounded non-abelian composition factors. For this class, we place in NC problems such as membership testing, finding the center and composition factors, and, of particular significance, finding pointwise-set-stabilisers. The last has applications to instances of graph-isomorphism and we show that NC contains isomorphism-testing for vertex-colored graphs with bounded color multiplicity, a problem not long known to be in polynomial time.