Alkida Balliu · Sebastian Brandt · Dennis Olivetti · Jukka Suomela

How much does randomness help with locally checkable problems?

PODC 2020 · 39th ACM Symposium on Principles of Distributed Computing, online, August 2020 · doi:10.1145/3382734.3405715

authors’ version publisher’s version arXiv.org

Abstract

Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are examples of LCLs.

On the one hand, it is known that some LCLs benefit exponentially from randomness—for example, any deterministic distributed algorithm that finds a sinkless orientation requires $\Theta(\log n)$ rounds in the LOCAL model, while the randomized complexity of the problem is $\Theta(\log \log n)$ rounds. On the other hand, there are also many LCLs in which randomness is useless.

Previously, it was not known if there are any LCLs that benefit from randomness, but only subexponentially. We show that such problems exist: for example, there is an LCL with deterministic complexity $\Theta(\log^2 n)$ rounds and randomized complexity $\Theta(\log n \log \log n)$ rounds.

Publication

Yuval Emek and Christian Cachin (Eds.): PODC '20: Proceedings of the 39th Symposium on Principles of Distributed Computing, pages 299–308, ACM Press, New York, 2020

ISBN 978-1-4503-7582-5

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