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An Ω(√ log log n) lower bound for routing in optical networks

Authors:

Leslie Ann Goldberg,

Philip D. MacKenzieAuthors Info & Claims

SPAA '94: Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures

Pages 147 - 156

https://doi.org/10.1145/181014.181093

Published: 01 August 1994 Publication History

Abstract

Optical communication is likely to significantly speed up parallel computation because the vast bandwidth of the optical medium can be divided to produce communication networks of very high degree. However, the problem of contention in high-degree networks makes the routing problem in these networks theoretically (and practically) difficult. In this paper we examine Valiant's h-relation routing problem, which is a fundamental problem in the theory of parallel computing. The h-relation routing problem arises both in the direct implementation of specific parallel algorithms on distributed-memory machines and in the general simulation of shared memory models such as the PRAM on distributed-memory machines. In an h

-relation routing problem each processor has up to h messages that it wishes to send to other processors and each processor is the destination of at most h messages. We present a lower bound for routing an h-relation (for any h> 1) on a complete optical network of size n. Our lower bound applies to any randomized distributed algorithm for this task. Specifically. we show that the expected number of communication steps required to route an arbitrary h-relation is W(h+√loglogn). This is the first

known lower bound for this problem which does not restrict the class of algorithms under consideration.

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Cited By

Berthomé PDuboux THagerup TNewman ISchuster A(2005)Self-simulation for the Passive Optical Star modelAlgorithms — ESA '9510.1007/3-540-60313-1_156(369-380)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-60313-1_156
Adler MByers JKarp R(2005)Scheduling parallel communication: The h-relation problemMathematical Foundations of Computer Science 199510.1007/3-540-60246-1_109(1-20)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-60246-1_109
Durand DJain RTseytlin D(2003)Parallel I/O scheduling using randomized, distributed edge coloring algorithmsJournal of Parallel and Distributed Computing10.1016/S0743-7315(03)00015-763:6(611-618)Online publication date: 1-Jun-2003
https://dl.acm.org/doi/10.1016/S0743-7315%2803%2900015-7
Show More Cited By

Index Terms

An Ω(√ log log n) lower bound for routing in optical networks
1. Theory of computation
  1. Computational complexity and cryptography
    1. Complexity classes
  2. Design and analysis of algorithms
    1. Approximation algorithms analysis
      1. Routing and network design problems

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cover image ACM Conferences

SPAA '94: Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures

August 1994

374 pages

ISBN:0897916719

DOI:10.1145/181014

Chairmen:
Lawrence Snyder
Univ. of Washington, Seattle
,
Charles E. Leiserson
Massachusetts Institute of Technology, Cambridge

Copyright © 1994 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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European Comp Soc: European Computer Society
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGARCH: ACM Special Interest Group on Computer Architecture

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1994

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6SPAA94

Sponsor:

European Comp Soc
SIGACT
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6SPAA94: 6th Annual ACM Symposium on Parallel Algorithms and Architectures

June 27 - 29, 1994

New Jersey, Cape May, USA

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Overall Acceptance Rate 447 of 1,461 submissions, 31%

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Cited By

Berthomé PDuboux THagerup TNewman ISchuster A(2005)Self-simulation for the Passive Optical Star modelAlgorithms — ESA '9510.1007/3-540-60313-1_156(369-380)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-60313-1_156
Adler MByers JKarp R(2005)Scheduling parallel communication: The h-relation problemMathematical Foundations of Computer Science 199510.1007/3-540-60246-1_109(1-20)Online publication date: 2-Jun-2005
https://doi.org/10.1007/3-540-60246-1_109
Durand DJain RTseytlin D(2003)Parallel I/O scheduling using randomized, distributed edge coloring algorithmsJournal of Parallel and Distributed Computing10.1016/S0743-7315(03)00015-763:6(611-618)Online publication date: 1-Jun-2003
https://dl.acm.org/doi/10.1016/S0743-7315%2803%2900015-7
Berthomé PHagerup TNewman ISchuster A(2000)Self-Simulation for the Passive Optical StarJournal of Algorithms10.1006/jagm.1999.103634:1(128-147)Online publication date: 1-Jan-2000
https://dl.acm.org/doi/10.1006/jagm.1999.1036
Agbaria ABen-Asher YNewman IMiller GRamachandran V(1999)Communication-processor tradeoffs in limited resources PRAMProceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures10.1145/305619.305628(74-82)Online publication date: 1-Jun-1999
https://dl.acm.org/doi/10.1145/305619.305628
Mackenzie P(1997)Lower Bounds for Randomized Exclusive Write PRAMsTheory of Computing Systems10.1007/s00224000007030:6(599-626)Online publication date: 1-Dec-1997
https://dl.acm.org/doi/10.1007/s002240000070
Deng XDymond PBlelloch G(1996)On multiprocessor system schedulingProceedings of the eighth annual ACM symposium on Parallel Algorithms and Architectures10.1145/237502.237510(82-88)Online publication date: 24-Jun-1996
https://dl.acm.org/doi/10.1145/237502.237510
Durand DJain RTseytlin DLeiserson C(1995)Applying randomized edge coloring algorithms to distributed communicationProceedings of the seventh annual ACM symposium on Parallel algorithms and architectures10.1145/215399.215456(264-274)Online publication date: 20-Jul-1995
https://dl.acm.org/doi/10.1145/215399.215456
MacKenzie PLeiserson C(1995)Lower bounds for randomized exclusive write PRAMsProceedings of the seventh annual ACM symposium on Parallel algorithms and architectures10.1145/215399.215454(254-263)Online publication date: 20-Jul-1995
https://dl.acm.org/doi/10.1145/215399.215454

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