Two absolute bounds for distributed bit complexity

Yefim Dinitz; Noam Solomon

doi:10.1007/11429647_11

Two absolute bounds for distributed bit complexity

Yefim Dinitz, Noam Solomon

Department of Computer Science

Research output: Contribution to journal › Conference article › peer-review

2 Scopus citations

Abstract

The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained open. The first is to close the gap between the known upper and lower bounds, for electing a leader by two linked processors. The second is whether the known algorithm, sending 1.5n bits while electing a leader in a chain of even length n, is optimal, in the case when n is known to the processors. For both problems, absolutely exact bounds are found. Moreover, the lower bound proofs show that there is no optimal algorithm other than the suggested one(s).

Original language	English
Pages (from-to)	115-126
Number of pages	12
Journal	Lecture Notes in Computer Science
Volume	3499
DOIs	https://doi.org/10.1007/11429647_11
State	Published - 1 Jan 2005
Event	12 International Colloquium on Structural Information and Communication Complexity, SIROCCO 2005 - Mont Saint-Michel, France Duration: 24 May 2005 → 26 May 2005

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/11429647_11

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abstract = "The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained open. The first is to close the gap between the known upper and lower bounds, for electing a leader by two linked processors. The second is whether the known algorithm, sending 1.5n bits while electing a leader in a chain of even length n, is optimal, in the case when n is known to the processors. For both problems, absolutely exact bounds are found. Moreover, the lower bound proofs show that there is no optimal algorithm other than the suggested one(s).",

author = "Yefim Dinitz and Noam Solomon",

note = "Funding Information: IPartially supported by the Lynn and William Frankel Center for Computer Science. ∗Corresponding author. Tel.: +972 8 647 7867; fax: +972 8 647 7650. E-mail addresses: [email protected] (Y. Dinitz), [email protected] (N. Solomon).; 12 International Colloquium on Structural Information and Communication Complexity, SIROCCO 2005 ; Conference date: 24-05-2005 Through 26-05-2005",

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N1 - Funding Information: IPartially supported by the Lynn and William Frankel Center for Computer Science. ∗Corresponding author. Tel.: +972 8 647 7867; fax: +972 8 647 7650. E-mail addresses: [email protected] (Y. Dinitz), [email protected] (N. Solomon).

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AB - The concept of distributed communication bit complexity was introduced by Dinitz, Rajsbaum, and Moran. They studied bit complexity of Consensus and Leader Election, arriving at more or less exact bounds. This paper answers two questions on Leader Election, which remained open. The first is to close the gap between the known upper and lower bounds, for electing a leader by two linked processors. The second is whether the known algorithm, sending 1.5n bits while electing a leader in a chain of even length n, is optimal, in the case when n is known to the processors. For both problems, absolutely exact bounds are found. Moreover, the lower bound proofs show that there is no optimal algorithm other than the suggested one(s).

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Two absolute bounds for distributed bit complexity

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