Derandomizing Local Distributed Algorithms under Bandwidth Restrictions.

TLDR: This paper provides tools for derandomizing solutions to local problems, when the n nodes can only send O(\log n)-bit messages in each round of communication, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions.

Abstract: This paper addresses the cornerstone family of local problems in distributed computing, and investigates the curious gap between randomized and deterministic solutions under bandwidth restrictions. Our main contribution is in providing tools for derandomizing solutions to local problems, when the n nodes can only send $$O(\log n)$$-bit messages in each round of communication. Our framework mostly follows by the derandomization approach of Luby (J Comput Syst Sci 47(2):250–286, 1993) combined with the power of all to all communication. Our key results are as follows: first, we show that in the congested clique model, which allows all-to-all communication, there is a deterministic maximal independent set algorithm that runs in $$O(\log ^2 {\varDelta })$$ rounds, where $${\varDelta }$$ is the maximum degree. When $${\varDelta }=O(n^{1/3})$$, the bound improves to $$O(\log {\varDelta })$$. In addition, we deterministically construct a $$(2k-1)$$-spanner with $$O(kn^{1+1/k}\log n)$$ edges in $$O(k \log n)$$ rounds in the congested clique model.