Issue No. 04 - April (1987 vol. 36)

ISSN: 0018-9340

pp: 460-470

K.A. Doshi , Department of Electrical and Computer Engineering, Rice University

ABSTRACT

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. , pp. 460-470, April 1987, doi:10.1109/TC.1987.1676928