Efficient parallel graph algorithms based on open ear decomposition

Abstract

We present a parallel algorithm for a novel problem in a graph's open ear decomposition. The algorithm runs in O(log n) time with n processors on a CREW PRAM, where n is the number of vertices and m is the number of edges in the graph. We apply this result in parallel algorithms to solve the two vertex disjoint s- t paths problem in O( log n ) time with n + m processors and the maximal path problem in planar graphs in O(log 2 n) time with O( n) processors. Both of these algorithms run on the CRCW PRAM.