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}
}
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Keywords: |
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Communication complexity, set disjointness, sampling |
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Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019) |
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Issue Date: |
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2019 |
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Date of publication: |
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17.09.2019 |
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)