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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2017.35
URN: urn:nbn:de:0030-drops-79930
URL: http://drops.dagstuhl.de/opus/volltexte/2017/7993/
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Mendes, Hammurabi ; Herlihy, Maurice

Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems

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Abstract

In this paper, we show that the protocol complex of a Byzantine synchronous system can remain (k-1)-connected for up to ceil(t/k) rounds, where t is the maximum number of Byzantine processes, and t >= k >= 1. This topological property implies that ceil(t/k) + 1 rounds are necessary to solve k-set agreement in Byzantine synchronous systems, compared to floor(t/k) + 1 rounds in synchronous crash-failure systems. We also show that our connectivity bound is tight as we indicate solutions to Byzantine k-set agreement in exactly ceil(t/k) + 1 synchronous rounds, at least when n is suitably large compared to t. In conclusion, we see how Byzantine failures can potentially require one extra round to solve k-set agreement, and, for n suitably large compared to t, at most that.

BibTeX - Entry

@InProceedings{mendes_et_al:LIPIcs:2017:7993,
  author =	{Hammurabi Mendes and Maurice Herlihy},
  title =	{{Tight Bounds for Connectivity and Set Agreement in Byzantine Synchronous Systems}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Andr{\'e}a W. Richa},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7993},
  URN =		{urn:nbn:de:0030-drops-79930},
  doi =		{10.4230/LIPIcs.DISC.2017.35},
  annote =	{Keywords: Byzantine, synchronous, k-set agreement, topology, connectivity}
}

Keywords: Byzantine, synchronous, k-set agreement, topology, connectivity
Seminar: 31st International Symposium on Distributed Computing (DISC 2017)
Issue Date: 2017
Date of publication: 05.10.2017


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