Permutation group algorithms based on directed graphs

Random Remarks on Permutation Group Algorithms

NC Coloring Algorithms for Permutation Graphs

We show that the problem of coloring a permutation graph of size n can be solved in O(logn logk) time using O(kn2 / logk log2n) processors on the CREW PRAM model of computation, where 1 < k < n. We estimate the parameter k on random permutation graphs and show that the coloring problem can be solved in O(logn loglogn) time in the average-case on the CREW PRAM model of computation with O(n2) pro...

Permutation Group Algorithms via Black Box

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. This is used to upgrade all nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimen...

Permutation group algorithms via black box recognition algorithms

If a black box simple group is known to be isomorphic to a classical group over a eld of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. This is used to upgrade all nearly linear time Monte Carlo permutation group algorithms to Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3{dimensi...

Coset Enumeration, Permutation Group Algorithms, and Applications to Graphs and Geometries

In these notes we discuss coset enumeration and basic permutation group algorithms. To illustrate some applications to graphs and nite geometries, we classify and study some graphs which are locally the incidence graph of the 2 ? (11; 5; 2) design.