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Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem

Authors Mélanie Cambus , Fabian Kuhn , Shreyas Pai , Jara Uitto



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Author Details

Mélanie Cambus
  • Aalto University, Finland
Fabian Kuhn
  • University of Freiburg, Germany
Shreyas Pai
  • Aalto University, Finland
Jara Uitto
  • Aalto University, Finland

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Mélanie Cambus, Fabian Kuhn, Shreyas Pai, and Jara Uitto. Time and Space Optimal Massively Parallel Algorithm for the 2-Ruling Set Problem. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 11:1-11:12, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DISC.2023.11

Abstract

In this work, we present a constant-round algorithm for the 2-ruling set problem in the Congested Clique model. As a direct consequence, we obtain a constant round algorithm in the MPC model with linear space-per-machine and optimal total space. Our results improve on the O(log log log n)-round algorithm by [HPS, DISC'14] and the O(log log Δ)-round algorithm by [GGKMR, PODC'18]. Our techniques can also be applied to the semi-streaming model to obtain an O(1)-pass algorithm. Our main technical contribution is a novel sampling procedure that returns a small subgraph such that almost all nodes in the input graph are adjacent to the sampled subgraph. An MIS on the sampled subgraph provides a 2-ruling set for a large fraction of the input graph. As a technical challenge, we must handle the remaining part of the graph, which might still be relatively large. We overcome this challenge by showing useful structural properties of the remaining graph and show that running our process twice yields a 2-ruling set of the original input graph with high probability.

Subject Classification

ACM Subject Classification
  • Theory of computation → Massively parallel algorithms
  • Theory of computation → Streaming models
Keywords
  • Ruling Sets
  • Parallel Algorithms
  • Congested Clique
  • Massively Parallel Computing
  • Semi-Streaming

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