On the parallel computation of the biconnected and strongly connected co-components of graphs

In this paper, we consider the problems of co-biconnectivity and strong co-connectivity, i.e., computing the biconnected components and the strongly connected components of the complement of a given graph. We describe simple sequential algorithms for these problems, which work on the input graph and not on its complement, and which for a graph on n vertices and m edges both run in optimal O(n + m) time. Our algorithms are not data structure-based and they employ neither breadth-first-search nor