Efficient Graph Algorithm Using Limited Communication on a Fixed-Size Array of Processors

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.