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

Richard Cole, Uzi Vishkin

Research output: Contribution to journalArticle

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 - 1991

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Graph Algorithms
Parallel algorithms
Parallel Algorithms
Logarithmic
Scheduling
Optimal Algorithm
Denote
Graph in graph theory
Iterate
Connected Components
Undirected Graph
Euler
Ranking
Connectivity
Union
Imply
Computing

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Approximate parallel scheduling. II. Applications to logarithmic-time optimal parallel graph algorithms. / Cole, Richard; Vishkin, Uzi.

In: Information and Computation, Vol. 92, No. 1, 1991, p. 1-47.

Research output: Contribution to journalArticle

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