Abstract
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. 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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This article is part of the topical collection “Future Data and Security Engineering 2019” guest edited by Tran Khanh Dang.
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Dai, H.K., Toulouse, M. Extremal Problem with Network-Diameter and -Minimum-Degree for Distributed Function Computation. SN COMPUT. SCI. 1, 236 (2020). https://doi.org/10.1007/s42979-020-00219-7
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DOI: https://doi.org/10.1007/s42979-020-00219-7