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Article

On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

1
Department of Computer Science, University of Liverpool, Liverpool L69 3BX, UK
2
Computer Engineering and Informatics Department, University of Patras, 265 04 Patras, Greece
*
Author to whom correspondence should be addressed.
Academic Editor: Giovanni Viglietta
Information 2021, 12(6), 254; https://doi.org/10.3390/info12060254
Received: 1 May 2021 / Revised: 14 June 2021 / Accepted: 15 June 2021 / Published: 19 June 2021
(This article belongs to the Special Issue Distributed Systems and Mobile Computing)
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 k2 children can be constructed in O(logn) 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=k1, 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=loglogn 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. View Full-Text
Keywords: population protocol; distributed network construction; polylogarithmic time protocol; spanning tree; regular network; partial characterisation population protocol; distributed network construction; polylogarithmic time protocol; spanning tree; regular network; partial characterisation
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MDPI and ACS Style

Connor, M.; Michail, O.; Spirakis, P. On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time. Information 2021, 12, 254. https://doi.org/10.3390/info12060254

AMA Style

Connor M, Michail O, Spirakis P. On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time. Information. 2021; 12(6):254. https://doi.org/10.3390/info12060254

Chicago/Turabian Style

Connor, Matthew, Othon Michail, and Paul Spirakis. 2021. "On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time" Information 12, no. 6: 254. https://doi.org/10.3390/info12060254

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