An Optimal Parallel Co-Connectivity Algorithm

Authors:
Ka Wong Chong;Stavros D. Nikolopoulos;Leonidas Palios
Affiliations:
Department of Computer Science, The University of Hong Kong, Porfulam Road, Hong Kong;Department of Computer Science, University of Ioannina, GR-45110 Ioannina, Greece;Department of Computer Science, University of Ioannina, GR-45110 Ioannina, Greece
Venue:
Theory of Computing Systems
Year:
2004

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Abstract

In this paper we consider the problem of computing the connected components of the complement of a given graph. We describe a simple sequential algorithm for this problem, which works on the input graph and not on its complement, and which for a graph on n vertices and m edges runs in optimal O(n+m) time. Moreover, unlike previous linear co-connectivity algorithms, this algorithm admits efficient parallelization, leading to an optimal O(log n)-time and O((n+m)log n)-processor algorithm on the EREW PRAM model of computation. It is worth noting that, for the related problem of computing the connected components of a graph, no optimal deterministic parallel algorithm is currently available. The co-connectivity algorithms find applications in a number of problems. In fact, we also include a parallel recognition algorithm for weakly triangulated graphs, which takes advantage of the parallel co-connectivity algorithm and achieves an O(log2 n) time complexity using O((n+m2) log n) processors on the EREW PRAM model of computation.