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Lower bounds on communication complexity in distributed computer networks

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Prasoon TiwariAuthors Info & Claims

Journal of the ACM (JACM), Volume 34, Issue 4

Pages 921 - 938

https://doi.org/10.1145/31846.32978

Published: 01 October 1987 Publication History

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Abstract

The main result of this paper is a general technique for determining lower bounds on the communication complexity of problems on various distributed computer networks. This general technique is derived by simulating the general network by a linear array and then using a lower bound on the communication complexity of the problem on the linear array. Applications of this technique yield optimal bounds on the communication complexity of merging, ranking, uniqueness, and triangle-detection problems on a ring of processors. Nontrivial near-optimal lower bounds on the communication complexity of distinctness, merging, and ranking on meshes and complete binary trees are also derived.

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Lower bounds on communication complexity in distributed computer networks

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Reviews

Reviewer: Thomas Rainer Michael Fischer

This paper describes a general technique for determining lower bounds on the communication complexity of computational problems on distributed computer networks. The communication complexity is a common measure of the number of bits that must be exchanged among the processors in the worst case by any distributed algorithm computing a specified function on a given type of processor array. The main idea of the presented method is to simulate a general network by a linear array and then use the lower bound on the communication complexity of the problem on the linear array. From a mathematical viewpoint the most fundamental result states that the communication complexity of a function f: {0,1, . . . ,2 n?1} 2 :2WZ {0,1} given by its result matrix R on a linear ( p + 1)-processor array is at least pn if R is nonsingular over any field. The general technique is applied to derive optimal lower bounds on a ring of processors for some elementary problems on sets of integers such as distinctness and ranking and for the triangle-detection problem in graphs. Furthermore, near-optimal lower bounds on the communication complexity on meshes and complete binary trees are also obtained. The presented method is interesting and seems to be powerful at least for computation problems that can be easily formulated by predicates as required here. Unfortunately, however, the text is difficult to read because it is far from being self-contained; in parts it requires intimate knowledge of results and proofs obtained in various papers by other authors cited in the reference list.

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Published In

Journal of the ACM Volume 34, Issue 4

Oct. 1987

254 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/31846

Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1987

Published in JACM Volume 34, Issue 4

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Pandurangan GPeleg DScquizzato M(2018)Message lower bounds via efficient network synchronizationTheoretical Computer Science10.1016/j.tcs.2018.11.017Online publication date: Nov-2018
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Beame PKoutris PSuciu D(2017)Communication Steps for Parallel Query ProcessingJournal of the ACM10.1145/312564464:6(1-58)Online publication date: 14-Oct-2017
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