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In this paper we present a deterministic $O(\log\log n)$-round algorithm forthe 2-ruling set problem in the Massively Parallel Computation model with$\tilde{O}(n)$ memory; this algorithm also runs in $O(\log\log n)$ rounds inthe Congested Clique model. This is exponentially faster than the fastest knowndeterministic 2-ruling set algorithm for these models, which is simply the$O(\log \Delta)$-round deterministic Maximal Independent Set algorithm due toCzumaj, Davies, and Parter (SPAA 2020). Our result is obtained by derandomizingthe 2-ruling set algorithm of Kothapalli and Pemmaraju (FSTTCS 2012).

Deterministic Massively Parallel Algorithms for Ruling Sets