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Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set

Authors Mohsen Ghaffari, Fabian Kuhn

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LIPIcs.DISC.2018.29.pdf
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Mohsen Ghaffari
  • ETH Zurich, Switzerland
Fabian Kuhn
  • University of Freiburg, Germany

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Mohsen Ghaffari and Fabian Kuhn. Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set. In 32nd International Symposium on Distributed Computing (DISC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 121, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.DISC.2018.29

Abstract

This paper presents improved deterministic distributed algorithms, with O(log n)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set, which can replace the random part of a number of standard randomized distributed algorithms. This deterministic hitting set algorithm itself is derived using a simple method of conditional expectations. As one main end-result of this derandomized hitting set, we get a deterministic distributed algorithm with round complexity 2^O(sqrt{log n * log log n}) for computing a (2k-1)-spanner of size O~(n^{1+1/k}). This improves considerably on a recent algorithm of Grossman and Parter [DISC'17] which needs O(n^{1/2-1/k} * 2^k) rounds. We also get a 2^O(sqrt{log n * log log n})-round deterministic distributed algorithm for computing an O(log^2 n)-approximation of minimum dominating set; all prior algorithms for this problem were either randomized or required large messages.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Distributed Algorithms
  • Derandomization
  • Spanners
  • Dominating Set

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