APPROXIMATE PARALLEL SCHEDULING .2. APPLICATIONS TO LOGARITHMIC-TIME OPTIMAL PARALLEL GRAPH ALGORITHMS

Part I of this paper presented a novel technique for approximate parallel scheduling and a new logarithmic time optimal parallel algorithm for the list ranking problem. In this part, we give a new logarithmic time parallel (PRAM) algorithm for computing the connected components of undirected graphs which uses this scheduling technique. The connectivity algorithm is optimal unless m = o(n log* n) in graphs of n vertices and m edges. (log(k) denotes the kth iterate of the log function and log* n denotes the least i such that log(i) n ≤ 2). Using known results, this new algorithm implies logarithmic time optimal parallel algorithms for a number of other graph problems, including biconnectivity, Euler tours, strong orientation and st-numbering. Another contribution of the present paper is a parallel union/find algorithm. © 1991.