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Massively Parallel Ruling Set Made Deterministic

Authors Jeff Giliberti , Zahra Parsaeian

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Author Details

Jeff Giliberti
  • University of Maryland, College Park, MD, USA
Zahra Parsaeian
  • University of Freiburg, Germany

Funding

  • Giliberti, Jeff: Financial support in part by the Fulbright U.S. Graduate Student Program, sponsored by the U.S. Department of State and the Italian-American Fulbright Commission. The content does not necessarily represent the views of the Program.

Acknowledgements

We are grateful to Christoph Grunau and Manuela Fischer for valuable discussions. We would also like to thank the anonymous reviewers for their helpful feedback, and Yannic Maus for his shepherding of the paper.

Cite AsGet BibTex

Jeff Giliberti and Zahra Parsaeian. Massively Parallel Ruling Set Made Deterministic. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.29

Abstract

We study the deterministic complexity of the 2-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. - Linear MPC: We present a constant-round deterministic algorithm for the 2-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic O(log log n)-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU’s algorithm based solely on bounded independence, which makes its efficient derandomization possible. - Sublinear MPC: We present a deterministic algorithm that computes a 2-Ruling Set in Õ(√{log n}) rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the O(log Δ + log log^* n)-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized Õ(√{log n})-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12].

Subject Classification

ACM Subject Classification
  • Theory of computation → MapReduce algorithms
Keywords
  • deterministic algorithms
  • distributed computing
  • massively parallel computation
  • graph algorithms
  • derandomization

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