On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

Connor, Matthew, Michail, Othon ORCID: 0000-0002-6234-3960 and Spirakis, Paul
(2021) On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time. Information, 12 (6). 254 - 254.

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<jats:p>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≥2 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=k−1, can be constructed in polylogarithmic parallel time for any fixed k, where k&gt;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.</jats:p>

Item Type: Article
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 22 Jun 2021 14:28
Last Modified: 05 Sep 2021 02:10
DOI: 10.3390/info12060254
Open Access URL: https://www.mdpi.com/2078-2489/12/6/254/htm
URI: https://livrepository.liverpool.ac.uk/id/eprint/3127305