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Relating Network-Diameter and Network-Minimum-Degree for Distributed Function Computation

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Future Data and Security Engineering (FDSE 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12466))

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Abstract

Distributed computing network-systems are modeled as directed/undirected graphs with vertices representing compute elements and adjacency-edges capturing their uni- or bi-directional communication. To quantify an intuitive tradeoff between two graph-parameters: minimum vertex-degree and diameter of the underlying graph, we formulate an extremal problem with the two parameters: for all positive integers n and d, the extremal value \(\nabla (n, d)\) denotes the least minimum vertex-degree among all connected order-n graphs with diameters of at most d. We prove matching upper and lower bounds on the extremal values of \(\nabla (n, d)\) for various combinations of n- and d-values.

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Authors and Affiliations

  1. Computer Science Department, Oklahoma State University, Stillwater, Oklahoma, 74078, USA

    H. K. Dai

  2. School of Information and Communication Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    M. Toulouse

Authors
  1. H. K. Dai
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  2. M. Toulouse
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Corresponding author

Correspondence to H. K. Dai .

Editor information

Editors and Affiliations

  1. Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam

    Tran Khanh Dang

  2. Johannes Kepler University of Linz, Linz, Austria

    Josef Küng

  3. Hosei University, Tokyo, Japan

    Makoto Takizawa

  4. Sungkyunkwan University, Suwon, Korea (Republic of)

    Tai M. Chung

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Dai, H.K., Toulouse, M. (2020). Relating Network-Diameter and Network-Minimum-Degree for Distributed Function Computation. In: Dang, T.K., Küng, J., Takizawa, M., Chung, T.M. (eds) Future Data and Security Engineering. FDSE 2020. Lecture Notes in Computer Science(), vol 12466. Springer, Cham. https://doi.org/10.1007/978-3-030-63924-2_8

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  • DOI: https://doi.org/10.1007/978-3-030-63924-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63923-5

  • Online ISBN: 978-3-030-63924-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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