A Randomized Parallel Algorithm for Planar Graph Isomorphism - Gazit, Hillel; Reif, John H (Journal of algorithms, 1998)
We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known algorithms inO(log2n) time withn1+ϵprocessors, for any ϵ>0). Ifnis the number of vertices, our algorithm takesO(log(n)) time with processors and with a probability of failure of 1/nat most. The algorithm needs 2·log(m)−log(n)+O(log(n)) random bits. The number of random bits can be decreased toO(log(n)) by increasing the number of processors ton3/2+ϵ, for any ϵ>0. Our parallel algorithm has significantly improved processor efficiency, compared to the previous logarithmic time parallel algorithm of Miller and Reif (Siam J. Comput.20(1991), 1128–1147), which requiresn4randomized processors orn5deterministic processors.