Abstract
Parallel algorithms for finding the minimum spanning tree of a weighted undirected graph and the bridge-connected and biconnected components of an undirected graph on a linear array of processors are presented. On an n-vertex graph, our algorithms perform in O(n2/p) time on an array of size p, for all p, 1 ≤ p ≤ n, thus providing optimal speedup for dense graphs. The paper describes two approaches to limit the communication requirements for solving the problems. The first is a divide-and-conquer strategy applied to Sollin's algorithm for finding the minimum spanning tree of a graph. The second uses a novel data-reduction technique that constructs an auxiliary graph with no more than 2n-2 edges, whose bridges and articulation points are the bridges and articulation points of the original graph.
This research was supported in part by an IBM Faculty Development Award.
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© 1987 Springer-Verlag Berlin Heidelberg
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Doshi, K., Varman, P. (1987). Efficient graph algorithms using limited communication on a fixed-size array of processors. In: Brandenburg, F.J., Vidal-Naquet, G., Wirsing, M. (eds) STACS 87. STACS 1987. Lecture Notes in Computer Science, vol 247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0039596
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DOI: https://doi.org/10.1007/BFb0039596
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