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Randomized parallel list ranking for distributed memory multiprocessors

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Abstract

We present a randomized parallel list ranking algorithm for distributed memory multiprocessors, using a BSP type model. We first describe a simple version which requires, with high probability, log(3p)+log ln(n)=Õ(logp+log logn) communication rounds (h-relations withh=Õ(n/p)) andÕ(n/p)) local computation. We then outline an improved version that requires high probability, onlyr⩽(4k+6) log(2/3p)+8=Õ(k logp) communication rounds wherek=min{i⩾0 |ln(i+1)n⩽(2/3p)2i+1}. Notek<ln*(n) is an extremely small number. Forn andp⩾4, the value ofk is at most 2. Hence, for a given number of processors,p, the number of communication rounds required is, for all practical purposes, independent ofn. Forn⩽1, 500,000 and 4⩽p⩽2048, the number of communication rounds in our algorithm is bounded, with high probability, by 78, but the actual number of communication rounds observed so far is 25 in the worst case. Forn⩽10010100 and 4⩽p⩽2048, the number of communication rounds in our algorithm is bounded, with high probability, by 118; and we conjecture that the actual number of communication rounds required will not exceed 50. Our algorithm has a considerably smaller member of communication rounds than the list ranking algorithm used in Reid-Miller’s empirical study of parallel list ranking on the Cray C-90.(1) To our knowledge, Reid-Miller’s algorithm(1) was the fastest list ranking implementation so far. Therefore, we expect that our result will have considerable practical relevance.

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Authors and Affiliations

  1. School of Computer Science, Carleton University, K1S 5B6, Ottawa, Canada

    Frank Dehne

  2. Department of Computer Science - IME, University of São Paulo, 05508-900, São Paulo, SP, Brazil

    Siang W. Song

Authors
  1. Frank Dehne
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  2. Siang W. Song
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Additional information

Research partially supported by Natural Sciences and Engineering Research Council of Canada (NSERC), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Proc. No. 95/0767-0, 95/1367-5, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Proc. No. 523112/94-7 and PROTEM II, and the Commission of the European Community (Project ITDC-207).

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Dehne, F., Song, S.W. Randomized parallel list ranking for distributed memory multiprocessors. Int J Parallel Prog 25, 1–16 (1997). https://doi.org/10.1007/BF02700044

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