Deterministic Massively Parallel Algorithms for Ruling Sets

TL;DR

This paper introduces a deterministic algorithm that computes 2-ruling sets in logarithmic double-exponential time, significantly faster than previous methods, applicable in parallel and clique models.

Contribution

It derandomizes a previous randomized algorithm, achieving an exponentially faster deterministic solution for 2-ruling sets in parallel computing models.

Findings

Deterministic 2-ruling set algorithm runs in O(log log n) rounds.

Algorithm applies to Massively Parallel Computation and Congested Clique models.

Achieves exponential speedup over previous deterministic algorithms.

Abstract

In this paper we present a deterministic $O(\log\log n)$-round algorithm for the 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 in the Congested Clique model. This is exponentially faster than the fastest known deterministic 2-ruling set algorithm for these models, which is simply the $O(\log \Delta)$-round deterministic Maximal Independent Set algorithm due to Czumaj, Davies, and Parter (SPAA 2020). Our result is obtained by derandomizing the 2-ruling set algorithm of Kothapalli and Pemmaraju (FSTTCS 2012).