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DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.26
The String of Diamonds Is Tight for Rumor Spreading

Authors: Omer Angel, Abbas Mehrabian, and Yuval Peres

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
For a rumor spreading protocol, the spread time is defined as the first time that everyone learns the rumor. We compare the synchronous push&pull rumor spreading protocol with its asynchronous variant, and show that for any n-vertex graph and any starting vertex, the ratio between their expected spread times is bounded by O(n^{1/3} log^{2/3} n). This improves the O(sqrt n) upper bound of Giakkoupis, Nazari, and Woelfel (in Proceedings of ACM Symposium on Principles of Distributed Computing, 2016). Our bound is tight up to a factor of O(log n), as illustrated by the string of diamonds graph.
Cite as

Omer Angel, Abbas Mehrabian, and Yuval Peres. The String of Diamonds Is Tight for Rumor Spreading. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 26:1-26:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{angel_et_al:LIPIcs.APPROX-RANDOM.2017.26,
  author =	{Angel, Omer and Mehrabian, Abbas and Peres, Yuval},
  title =	{{The String of Diamonds Is Tight for Rumor Spreading}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{26:1--26:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.26},
  URN =		{urn:nbn:de:0030-drops-75754},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.26},
  annote =	{Keywords: randomized rumor spreading, push\&pull protocol, asynchronous time model, string of diamonds}
}
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