A tradeoff between information and communication in broadcast protocols

Baruch Awerbuch; Oded Goldreich; David Peleg; Ronen Vainish

doi:10.1007/bfb0040404

A tradeoff between information and communication in broadcast protocols

Baruch Awerbuch, Oded Goldreich, David Peleg, Ronen Vainish

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. We assume the widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors, but does not know the entire network topology. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before. We show that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires Θ(|V|) messages, where V is the set of processors in the network. We prove that if one counts messages of bounded length then broadcast requires Θ(|E|) messages, where E is the set of edges in the network. Assuming an intermediate model in which each node knows the topology of the network in radius ρ ≥ 0 from itself, we prove tight upper and lower bounds of Θ(min{|E|, |V|^1+Θ(1)/ρ}) on the number of messages of bounded length required for broadcast. Both the upper and the lower bounds hold for both synchronous and asynchronous network models. The same results hold for the construction of spanning trees, and various other global tasks.

Original language	English
Title of host publication	VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings
Editors	John H. Reif
Publisher	Springer Verlag
Pages	369-379
Number of pages	11
ISBN (Print)	9780387968186
DOIs	https://doi.org/10.1007/bfb0040404
State	Published - 1988
Externally published	Yes
Event	3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1988 - Corfu, Greece Duration: 28 Jun 1988 → 1 Jul 1988

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	319 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1988
Country/Territory	Greece
City	Corfu
Period	28/06/88 → 1/07/88

Bibliographical note

Publisher Copyright:
© 1988, Springer-Verlag.

Funding

1Dept. of Math., MIT, Cambridge, MA 02139, [email protected] artially supported by Air Force contract TNDGAFOSR-86-0078, ARO contract DAAL03-86-K-0171 and NSF contract CCR8611442. 2Dept. of Computer Science, Technion, Haifa, 32000, Israel. Partially supported by the New York Metropolitan Research Fund. 3Dept. of Computer Science, Stanford University, Stanford CA 94305. Partially supported by ONR contract N00014-85-C-0731.

Funders	Funder number
New York Metropolitan Research Fund
National Science Foundation	CCR8611442
Office of Naval Research	N00014-85-C-0731
Army Research Office	DAAL03-86-K-0171
Massachusetts Institute of Technology
Air Force Institute of Technology	TNDGAFOSR-86-0078

Access to Document

10.1007/bfb0040404

Cite this

Awerbuch, B., Goldreich, O., Peleg, D., & Vainish, R. (1988). A tradeoff between information and communication in broadcast protocols. In J. H. Reif (Ed.), VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings (pp. 369-379). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 319 LNCS). Springer Verlag. https://doi.org/10.1007/bfb0040404

Awerbuch, Baruch ; Goldreich, Oded ; Peleg, David et al. / A tradeoff between information and communication in broadcast protocols. VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings. editor / John H. Reif. Springer Verlag, 1988. pp. 369-379 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "A tradeoff between information and communication in broadcast protocols",

abstract = "This paper concerns the message complexity of broadcast in arbitrary point-to-point communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. We assume the widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors, but does not know the entire network topology. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before. We show that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires Θ(|V|) messages, where V is the set of processors in the network. We prove that if one counts messages of bounded length then broadcast requires Θ(|E|) messages, where E is the set of edges in the network. Assuming an intermediate model in which each node knows the topology of the network in radius ρ ≥ 0 from itself, we prove tight upper and lower bounds of Θ(min{|E|, |V|1+Θ(1)/ρ}) on the number of messages of bounded length required for broadcast. Both the upper and the lower bounds hold for both synchronous and asynchronous network models. The same results hold for the construction of spanning trees, and various other global tasks.",

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Awerbuch, B, Goldreich, O, Peleg, D & Vainish, R 1988, A tradeoff between information and communication in broadcast protocols. in JH Reif (ed.), VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 319 LNCS, Springer Verlag, pp. 369-379, 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures, AWOC 1988, Corfu, Greece, 28/06/88. https://doi.org/10.1007/bfb0040404

A tradeoff between information and communication in broadcast protocols. / Awerbuch, Baruch; Goldreich, Oded; Peleg, David et al.
VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings. ed. / John H. Reif. Springer Verlag, 1988. p. 369-379 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 319 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Awerbuch B, Goldreich O, Peleg D, Vainish R. A tradeoff between information and communication in broadcast protocols. In Reif JH, editor, VLSI Algorithms and Architectures - 3rd Aegean Workshop on Computing, AWOC 1988, Proceedings. Springer Verlag. 1988. p. 369-379. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/bfb0040404

A tradeoff between information and communication in broadcast protocols

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