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Improved MPC Algorithms for MIS, Matching, and Coloring on Trees and Beyond

Authors Mohsen Ghaffari, Christoph Grunau, Ce Jin

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Author Details

Mohsen Ghaffari
  • ETH Zürich, Switzerland
Christoph Grunau
  • ETH Zürich, Switzerland
Ce Jin
  • Tsinghua University, Beijing, China

Funding

This work was supported in part by funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 853109), and the Swiss National Foundation (project grant 200021-184735).

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Mohsen Ghaffari, Christoph Grunau, and Ce Jin. Improved MPC Algorithms for MIS, Matching, and Coloring on Trees and Beyond. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.DISC.2020.34

Abstract

We present O(log log n) round scalable Massively Parallel Computation algorithms for maximal independent set and maximal matching, in trees and more generally graphs of bounded arboricity, as well as for coloring trees with a constant number of colors. Following the standards, by a scalable MPC algorithm, we mean that these algorithms can work on machines that have capacity/memory as small as n^{δ} for any positive constant δ < 1. Our results improve over the O(log²log n) round algorithms of Behnezhad et al. [PODC'19]. Moreover, our matching algorithm is presumably optimal as its bound matches an Ω(log log n) conditional lower bound of Ghaffari, Kuhn, and Uitto [FOCS'19].

Subject Classification

ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
Keywords
  • Massively Parallel Computation
  • MIS
  • Matching
  • Coloring

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