Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms

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Abstract

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.

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This research was supported in part by NSF Grants DCR-84-01633, CCR-8702271, CCR-8902221 and CCR-8906949 by ORN Grant N00014-85-K-0046, by an IBM faculty development award, and by a John Simon Guggenheim Memorial Foundation Fellowship.