Abstract
Abstract In this paper, we consider the problems of computing the strongly connected components and the biconnected components of the complement of a given graph. In particular, for a directed graph G on n vertices and m edges, we present a simple algorithm for computing the strongly connected components of G ¯ which runs in optimal O ( n + m ) time. The algorithm can be parallelized to yield an O ( log 2 n ) -time and O ( m 1.188 / log n ) -processor solution. As a byproduct, we obtain a very simple optimal parallel co-connectivity algorithm. Additionally, we establish properties which, for an undirected graph on n vertices and m edges, enable us to describe an O ( n + m ) -time algorithm for computing the biconnected components of G ¯ , which can be parallelized resulting in an algorithm that runs in O ( log n ) time using O ( ( n + m ) / log n ) processors.
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