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Universal schemes for parallel communication

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G. J. BrebnerAuthors Info & Claims

STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

Pages 263 - 277

https://doi.org/10.1145/800076.802479

Published: 11 May 1981 Publication History

Abstract

In this paper we isolate a combinatorial problem that, we believe, lies at the heart of this question and provide some encouragingly positive solutions to it. We show that there exists an N-processor realistic computer that can simulate arbitrary idealistic N-processor parallel computations with only a factor of O(log N) loss of runtime efficiency. The main innovation is an O(log N) time randomized routing algorithm. Previous approaches were based on sorting or permutation networks, and implied loss factors of order at least (log N)².

References

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D. Angluin and L.G. Valiant. Fast probabilistic algorithms for Hamiltonian circuits and matchings. J. of Comp. and Syst. Sci. (1979) 155-193.

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K. Batcher. Sorting networks and their applications. AFIPS Spring Joint Comp. Conf. 32 (1968) 307-314.

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V.E. Benes. Mathematical Theory of Connecting Networks and Telephone Traffic. Academic Press, New York (1965).

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H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. of Math. Stat. 23 (1952) 493-507.

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Z. Galil and W.J. Paul. A practical general purpose parallel computer, (this volume).

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W. Hoeffding. On the distribution of the number of successes in independent trials. Ann. of Math. Stat. 27 (1956) 713-721.

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G. Lev, N. Pippenger and L.G. Valiant. A fast parallel algorithm for routing in permutation networks. IEEE Trans. on Computers (1981).

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D. Nassimi and S Sahni Parallel algorithms to set-up the Benes permutation networks. Manuscript, University of Minnesota.

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Cited By

Amir DSaran NWilson TKleinberg RShrivastav VWeatherspoon HSekar VYu MSeneviratne AVeitch D(2024)Shale: A Practical, Scalable Oblivious Reconfigurable NetworkProceedings of the ACM SIGCOMM 2024 Conference10.1145/3651890.3672248(449-464)Online publication date: 4-Aug-2024
https://dl.acm.org/doi/10.1145/3651890.3672248
Wilson TAmir DSaran NKleinberg RShrivastav VWeatherspoon HMohar BShinkar IO'Donnell R(2024)Breaking the VLB Barrier for Oblivious Reconfigurable NetworksProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649608(1865-1876)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649608
Dillencourt MGoodrich MMitzenmacher M(2024)Leveraging Parameterized Chernoff Bounds for Simplified Algorithm AnalysesInformation Processing Letters10.1016/j.ipl.2024.106516(106516)Online publication date: Jun-2024
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Index Terms

Universal schemes for parallel communication
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Permutations and combinations
  2. Probability and statistics
    1. Probabilistic algorithms
    2. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods
      2. Sequential Monte Carlo methods
2. Theory of computation
  1. Design and analysis of algorithms
    1. Data structures design and analysis
      1. Sorting and searching
  2. Models of computation
    1. Concurrency
      1. Parallel computing models

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cover image ACM Conferences

STOC '81: Proceedings of the thirteenth annual ACM symposium on Theory of computing

May 1981

390 pages

ISBN:9781450373920

DOI:10.1145/800076

Copyright © 1981 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 11 May 1981

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Cited By

Amir DSaran NWilson TKleinberg RShrivastav VWeatherspoon HSekar VYu MSeneviratne AVeitch D(2024)Shale: A Practical, Scalable Oblivious Reconfigurable NetworkProceedings of the ACM SIGCOMM 2024 Conference10.1145/3651890.3672248(449-464)Online publication date: 4-Aug-2024
https://dl.acm.org/doi/10.1145/3651890.3672248
Wilson TAmir DSaran NKleinberg RShrivastav VWeatherspoon HMohar BShinkar IO'Donnell R(2024)Breaking the VLB Barrier for Oblivious Reconfigurable NetworksProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649608(1865-1876)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649608
Dillencourt MGoodrich MMitzenmacher M(2024)Leveraging Parameterized Chernoff Bounds for Simplified Algorithm AnalysesInformation Processing Letters10.1016/j.ipl.2024.106516(106516)Online publication date: Jun-2024
https://doi.org/10.1016/j.ipl.2024.106516
Camarero CMartínez CBeivide R(2024)Ant Mill: an adversarial traffic pattern for low-diameter direct networksThe Journal of Supercomputing10.1007/s11227-024-06146-180:12(18062-18080)Online publication date: 10-May-2024
https://doi.org/10.1007/s11227-024-06146-1
Gajjar KJha AKumar MLahiri A(2024)Reconfiguring Shortest Paths in GraphsAlgorithmica10.1007/s00453-024-01263-y86:10(3309-3338)Online publication date: 27-Aug-2024
https://doi.org/10.1007/s00453-024-01263-y
Mehak Mahato D(2024)Hop-Constrained Oblivious Routing Using Prim’s-Sollin’s AlgorithmAdvanced Information Networking and Applications10.1007/978-3-031-57942-4_43(444-452)Online publication date: 10-Apr-2024
https://doi.org/10.1007/978-3-031-57942-4_43
Arabas PJóźwik TNiewiadomska-Szynkiewicz E(2023)Router Activation Heuristics for Energy-Saving ECMP and Valiant Routing in Data Center NetworksEnergies10.3390/en1610413616:10(4136)Online publication date: 17-May-2023
https://doi.org/10.3390/en16104136
Zuzic GHaeupler BRoeyskoe AOshman RNolin AHalldorsson MBalliu A(2023)Sparse Semi-Oblivious Routing: Few Random Paths SufficeProceedings of the 2023 ACM Symposium on Principles of Distributed Computing10.1145/3583668.3594585(222-232)Online publication date: 19-Jun-2023
https://dl.acm.org/doi/10.1145/3583668.3594585
Addanki VAvin CSchmid S(2023)Mars: Near-Optimal Throughput with Shallow Buffers in Reconfigurable Datacenter NetworksProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/35793127:1(1-43)Online publication date: 2-Mar-2023
https://dl.acm.org/doi/10.1145/3579312
Chitavisutthivong KSupittayapornpong SNamyar PZhang MYu MGovindan R(2023)Optimal Oblivious Routing With Concave Objectives for Structured NetworksIEEE/ACM Transactions on Networking10.1109/TNET.2023.326463231:6(2669-2681)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1109/TNET.2023.3264632
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