Parallel algorithms for permutation groups and graph isomorphism

  • Authors:
  • Eugene M. Luks

  • Affiliations:
  • -

  • Venue:
  • SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
  • Year:
  • 1986

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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.