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Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity

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Abstract

Distributed computing network-systems are modeled as graphs with vertices representing compute elements and adjacency-edges capturing their uni- or bi-directional communication. Distributed function computation has a wide spectrum of major applications in distributed systems. Distributed computation over a network-system proceeds in a sequence of time-steps in which vertices update and/or exchange their values based on the underlying algorithm constrained by the time-(in)variant network-topology. For finite convergence of distributed information dissemination and function computation in the model, we present a lower bound on the number of time-steps for vertices to receive (initial) vertex-values of all vertices regardless of underlying protocol or algorithmics in time-invariant networks via the notion of vertex-eccentricity in a graph-theoretic framework. We also address lower bounds on vertex-eccentricity and its maximum version in terms of common graph-parameters such as maximum degree, and order and size.

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This study was not supported by any funding.

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Authors and Affiliations

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

    H. K. Dai

  2. Computer Science Department, Vietnamese-German University, Binh Duong New City, Vietnam

    M. Toulouse

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  1. H. K. Dai
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  2. M. Toulouse
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Correspondence to H. K. Dai.

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This article is part of the topical collection “Future Data and Security Engineering” guest edited by Tran Khanh Dang.

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Dai, H.K., Toulouse, M. Lower-Bound Study for Function Computation in Distributed Networks via Vertex-Eccentricity. SN COMPUT. SCI. 1, 10 (2020). https://doi.org/10.1007/s42979-019-0002-3

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