PARALLEL GRAPH ALGORITHMS FOR HYPERCUBE COMPUTERS

This paper presents several parallel algorithms on unweighted graphs for hypercube computers. The algorithms are for checking bipartiteness and for finding a spanning forest, the connected components, a fundamental cycle set, and the bridges of a graph. The algorithm for finding spanning forest is based on a strategy of successive elimination of non-forest edges. The input graph is partitioned equally among processors, which repeatedly eliminate non-forest edges and merge their results to finally construct the desired forest of the entire graph. In all the algorithms, low communication overhead is achieved by restricting the message-flow to only between the neighboring processors. The spanning-forest algorithm is used as a subroutine to design the remaining algortihms. Except for the bridge-finding algorithm, all others achieve optimal speedups for dense as well as sparse graphs, and each algorithm is optimally scalable up to a large number of processors depending upon the density of the input graph. For a graph of n vertices and m edges, the time complexity of the spanning-forest algorithm, using p processors, is O(m/p + n log p), which corresponds to an optimal speedup for p ≤(m/n)/(1+log(m/n)). © 1990.