Optimal Graph Algorithms on a Fixed-Size Linear Array

• Published in: IEEE transactions on computers Vol. C-36; no. 4; pp. 460 - 470
• Main Authors: DOSHI, K. A, VARMAN, P. J
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.1987; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Array processors; articulation points; bridges; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Exact sciences and technology; graph algorithms; minimum spanning tree; parallel algorithms; pipelining; Software; Parallel algorithm; Minimum; Array processor; Divide-and-conquer method; Optimal algorithm; Spanning tree; Algorithm complexity; Parallel processing; Minimum spanning Trei; Graph theory; Data reduction
• ISSN: 0018-9340
• DOI: 10.1109/TC.1987.1676928

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.