License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2016.137
URN: urn:nbn:de:0030-drops-62812
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2016/6281/
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Charron-Bost, Bernadette ; Függer, Matthias ; Nowak, Thomas

Fast, Robust, Quantizable Approximate Consensus

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LIPIcs-ICALP-2016-137.pdf (0.5 MB)

Abstract

We introduce a new class of distributed algorithms for the approximate consensus problem in dynamic rooted networks, which we call amortized averaging algorithms. They are deduced from ordinary averaging algorithms by adding a value-gathering phase before each value update. This results in a drastic drop in decision times, from being exponential in the number n of processes to being polynomial under the assumption that each process knows n. In particular, the amortized midpoint algorithm is the first algorithm that achieves a linear decision time in dynamic rooted networks with an optimal contraction rate of 1/2 at each update step.

We then show robustness of the amortized midpoint algorithm under violation of network assumptions: it gracefully degrades if communication graphs from time to time are non rooted, or under a wrong estimate of the number of processes. Finally, we prove that the amortized midpoint algorithm behaves well if processes can store and send only quantized values, rendering it well-suited for the design of dynamic networked systems. As a corollary we obtain that the 2-set consensus problem is solvable in linear time in any dynamic rooted network model.

BibTeX - Entry

@InProceedings{charronbost_et_al:LIPIcs:2016:6281,
  author =	{Bernadette Charron-Bost and Matthias F{\"u}gger and Thomas Nowak},
  title =	{{Fast, Robust, Quantizable Approximate Consensus}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{137:1--137:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Ioannis Chatzigiannakis and Michael Mitzenmacher and Yuval Rabani and Davide Sangiorgi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6281},
  URN =		{urn:nbn:de:0030-drops-62812},
  doi =		{10.4230/LIPIcs.ICALP.2016.137},
  annote =	{Keywords: approximate consensus, dynamic networks, averaging algorithms}
}

Keywords: approximate consensus, dynamic networks, averaging algorithms
Collection: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
Issue Date: 2016
Date of publication: 23.08.2016

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