| Autor: |
Matthew Connor, Othon Michail, Paul Spirakis |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Information, Vol 12, Iss 6, p 254 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2078-2489 |
| DOI: |
10.3390/info12060254 |
| Popis: |
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>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. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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