Abstract

. We present a parallel algorithm for finding triconnected components on a CRCW PRAM. The time complexity of our algorithm is O(log n) and the processor-time product is O((m + n) log log n) where n is the number of vertices, and m is the number of edges of the input graph. Our algorithm, like other parallel algorithms for this problem, is based on open ear decomposition but it employs a new technique, local replacement, to improve the complexity. Only the need to use the subroutines for connected components and integer sorting, for which no optimal parallel algorithm that runs in O(log n) time is known, prevents our algorithm from achieving optimality. 1. Introduction. A connected graph G = (V; E) is k-vertex connected if it has at least (k + 1) vertices and removal of any (k \Gamma 1) vertices leaves the graph connected. Designing efficient algorithms for determining the connectivity of graphs has been a subject of great interest in the last two decades. Applications of graph connect...

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