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April 1987 (vol. 36 no. 4)
pp. 460-470
K.A. Doshi, Department of Electrical and Computer Engineering, Rice University
Parallel algorithms for computing the minimum spanning tree of a weighted undirected graph, and the bridges and articulation points of an undirected graphs on a fixed-size linear array of processors are presented. For a graph of n vertices, the algorithms operate on a linear array of p processors and require O(n2/p) time for all p, 1 = p = n. In particular, using n processors the algorithms require O(n) time which is optimal on this model. 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.
Index Terms:
pipelining, Array processors, articulation points, bridges, graph algorithms, minimum spanning tree, parallel algorithms
Citation:
K.A. Doshi, P.J. Varman, "Optimal Graph Algorithms on a Fixed-Size Linear Array," IEEE Transactions on Computers, vol. 36, no. 4, pp. 460-470, April 1987, doi:10.1109/TC.1987.1676928
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