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

Richard Cole, Uzi Vishkin

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1-47
Number of pages47
JournalInformation and Computation
Volume92
Issue number1
DOIs
StatePublished - May 1991

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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