NDLI: On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

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On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

Content Provider	MDPI
Author	Connor, Matthew Michail, Othon Spirakis, Paul
Copyright Year	2021
Abstract	We study the class of networks, which can be created in polylogarithmic parallel time by network constructors: groups of anonymous agents that interact randomly under a uniform random scheduler with the ability to form connections between each other. Starting from an empty network, the goal is to construct a stable network that belongs to a given family. We prove that the class of trees where each node has any $k \geq 2$ children can be constructed in $O (log n)$ parallel time with high probability. We show that constructing networks that are k-regular is $Ω (n)$ time, but a minimal relaxation to $(l, k)$ -regular networks, where $l = k - 1$ , can be constructed in polylogarithmic parallel time for any fixed k, where $k > 2$ . We further demonstrate that when the finite-state assumption is relaxed and k is allowed to grow with n, then $k = log log n$ acts as a threshold above which network construction is, again, polynomial time. We use this to provide a partial characterisation of the class of polylogarithmic time network constructors.
Starting Page	254
e-ISSN	20782489
DOI	10.3390/info12060254
Journal	Information
Issue Number	6
Volume Number	12
Language	English
Publisher	MDPI
Publisher Date	2021-06-19
Access Restriction	Open
Subject Keyword	Information Hardware and Architecturee Population Protocol Distributed Network Construction Polylogarithmic Time Protocol Spanning Tree Regular Network Partial Characterisation
Content Type	Text
Resource Type	Article

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