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

  • Authors:

  • Stavros D. Nikolopoulos;Leonidas Palios

  • Affiliations:

  • Department of Computer Science, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece;Department of Computer Science, University of Ioannina, P.O. Box 1186, GR-45110 Ioannina, Greece

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2007

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Abstract

In this paper, we consider the problems of co-biconnectivity andstrong co-connectivity, i.e., computing the biconnected componentsand the strongly connected components of the complement of a givengraph. We describe simple sequential algorithms for these problems,which work on the input graph and not on its complement, and whichfor a graph on n vertices and m edges both run in optimalO(n+m) time. Our algorithms are not datastructure-based and they employ neither breadth-first-search nordepth-first-search. Unlike previous linear co-biconnectivity andstrong co-connectivity sequential algorithms, both algorithms admitefficient parallelization. The co-biconnectivity algorithm can beparallelized resulting in an optimal parallel algorithm that runsin O(log2n) time usingO((n+m)/log2n) processors. Thestrong co-connectivity algorithm can also be parallelized to yieldan O(log2n)-time andO(m1.188/logn)-processor solution. As abyproduct, we obtain a simple optimal O(logn)-time parallelco-connectivity algorithm. Our results show that, in a parallelprocess environment, the problems of computing the biconnectedcomponents and the strongly connected components can be solved withbetter time-processor complexity on the complement of a graphrather than on the graph itself.