A lower bound for radio broadcast

Noga Alon; Amotz Bar-Noy; Nathan Linial; David Pelegi

doi:10.1016/0022-0000(91)90015-W

A lower bound for radio broadcast

Noga Alon^*, Amotz Bar-Noy, Nathan Linial, David Pelegi

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

296 Scopus citations

Abstract

A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any broadcast schedule requires at least Ω(log² n) rounds of transmissions. This matches an upper bound of O(log² n) rounds for networks of radius 2 proved earlier by Bar-Yehuda, Goldreich, and Itai, in "Proceedings of the 4th ACM Symposium on Principles of Distributed Computing, 1986," pp. 98-107.

Original language	English
Pages (from-to)	290-298
Number of pages	9
Journal	Journal of Computer and System Sciences
Volume	43
Issue number	2
DOIs	https://doi.org/10.1016/0022-0000(91)90015-W
State	Published - Oct 1991

Bibliographical note

Funding Information:
* Supported in part by an Allon Fellowship, by a Bat-Sheva de Rothschild Grant, and by a Bergmann Memorial Grant. + Supported in part by a Weizmann Fellowship and by Contract ONR NOOOl4-85-C-0731. Current address: IBM, T. J. Watson Research Center, Yorktown Heights, NY 10598. : Supported in part by Contract ONR NOOOl4-85-C-0731. Current address: The Weizmann Institute, Rehovot 76100, Israel.

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title = "A lower bound for radio broadcast",

abstract = "A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any broadcast schedule requires at least Ω(log2 n) rounds of transmissions. This matches an upper bound of O(log2 n) rounds for networks of radius 2 proved earlier by Bar-Yehuda, Goldreich, and Itai, in {"}Proceedings of the 4th ACM Symposium on Principles of Distributed Computing, 1986,{"} pp. 98-107.",

author = "Noga Alon and Amotz Bar-Noy and Nathan Linial and David Pelegi",

note = "Funding Information: * Supported in part by an Allon Fellowship, by a Bat-Sheva de Rothschild Grant, and by a Bergmann Memorial Grant. + Supported in part by a Weizmann Fellowship and by Contract ONR NOOOl4-85-C-0731. Current address: IBM, T. J. Watson Research Center, Yorktown Heights, NY 10598. : Supported in part by Contract ONR NOOOl4-85-C-0731. Current address: The Weizmann Institute, Rehovot 76100, Israel.",

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doi = "10.1016/0022-0000(91)90015-W",

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AU - Pelegi, David

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AB - A radio network is a synchronous network of processors that communicate by transmitting messages to their neighbors, where a processor receives a message in a given step if and only if it is silent in this step and precisely one of its neighbors transmits. In this paper we prove the existence of a family of radius-2 networks on n vertices for which any broadcast schedule requires at least Ω(log2 n) rounds of transmissions. This matches an upper bound of O(log2 n) rounds for networks of radius 2 proved earlier by Bar-Yehuda, Goldreich, and Itai, in "Proceedings of the 4th ACM Symposium on Principles of Distributed Computing, 1986," pp. 98-107.

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A lower bound for radio broadcast

Abstract

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