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.APPROX-RANDOM.2017.49
URN: urn:nbn:de:0030-drops-75984
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7598/
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Watson, Thomas

Communication Complexity of Statistical Distance

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Abstract

We prove nearly matching upper and lower bounds on the randomized communication complexity of the following problem: Alice and Bob are each given a probability distribution over $n$ elements, and they wish to estimate within +-epsilon the statistical (total variation) distance between their distributions. For some range of parameters, there is up to a log(n) factor gap between the upper and lower bounds, and we identify a barrier to using information complexity techniques to improve the lower bound in this case. We also prove a side result that we discovered along the way: the randomized communication complexity of n-bit Majority composed with n-bit Greater-Than is Theta(n log n).

BibTeX - Entry

@InProceedings{watson:LIPIcs:2017:7598,
  author =	{Thomas Watson},
  title =	{{Communication Complexity of Statistical Distance}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{49:1--49:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Klaus Jansen and Jos{\'e} D. P. Rolim and David Williamson and Santosh S. Vempala},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7598},
  URN =		{urn:nbn:de:0030-drops-75984},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.49},
  annote =	{Keywords: Communication, complexity, statistical, distance}
}

Keywords: Communication, complexity, statistical, distance
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)
Issue Date: 2017
Date of publication: 11.08.2017

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