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URN: urn:nbn:de:0030-drops-112666
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A Lower Bound for Sampling Disjoint Sets

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Abstract

Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x subseteq[n] and Bob ends up with a set y subseteq[n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant beta<1, this requires Omega(n) communication even to get within statistical distance 1-beta^n of the target distribution. Previously, Ambainis, Schulman, Ta-Shma, Vazirani, and Wigderson (FOCS 1998) proved that Omega(sqrt{n}) communication is required to get within some constant statistical distance epsilon>0 of the uniform distribution over all pairs of disjoint sets of size sqrt{n}.

BibTeX - Entry

@InProceedings{gs_et_al:LIPIcs:2019:11266,
  author =	{Mika G{\"o}{\"o}s and Thomas Watson},
  title =	{{A Lower Bound for Sampling Disjoint Sets}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{51:1--51:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Dimitris Achlioptas and L{\'a}szl{\'o} A. V{\'e}gh},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11266},
  URN =		{urn:nbn:de:0030-drops-112666},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.51},
  annote =	{Keywords: Communication complexity, set disjointness, sampling}
}

Keywords: Communication complexity, set disjointness, sampling
Seminar: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)
Issue date: 2019
Date of publication: 17.09.2019


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