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.2019.97
URN: urn:nbn:de:0030-drops-106733
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10673/
Woodruff, David P. ;
Yang, Guang
Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams
Abstract
In a k-party communication problem, the k players with inputs x_1, x_2, ..., x_k, respectively, want to evaluate a function f(x_1, x_2, ..., x_k) using as little communication as possible. We consider the message-passing model, in which the inputs are partitioned in an arbitrary, possibly worst-case manner, among a smaller number t of players (t<k). The t-player communication cost of computing f can only be smaller than the k-player communication cost, since the t players can trivially simulate the k-player protocol. But how much smaller can it be? We study deterministic and randomized protocols in the one-way model, and provide separations for product input distributions, which are optimal for low error probability protocols. We also provide much stronger separations when the input distribution is non-product.
A key application of our results is in proving lower bounds for data stream algorithms. In particular, we give an optimal Omega(epsilon^{-2}log(N) log log(mM)) bits of space lower bound for the fundamental problem of (1 +/-{epsilon})-approximating the number |x |_0 of non-zero entries of an n-dimensional vector x after m updates each of magnitude M, and with success probability >= 2/3, in a strict turnstile stream. Our result matches the best known upper bound when epsilon >= 1/polylog(mM). It also improves on the prior Omega({epsilon}^{-2}log(mM)) lower bound and separates the complexity of approximating L_0 from approximating the p-norm L_p for p bounded away from 0, since the latter has an O(epsilon^{-2}log(mM)) bit upper bound.
BibTeX - Entry
@InProceedings{woodruff_et_al:LIPIcs:2019:10673,
author = {David P. Woodruff and Guang Yang},
title = {{Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {97:1--97:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10673},
URN = {urn:nbn:de:0030-drops-106733},
doi = {10.4230/LIPIcs.ICALP.2019.97},
annote = {Keywords: Communication complexity, multi-player communication, one-way communication, streaming complexity}
}
|
Keywords: |
|
Communication complexity, multi-player communication, one-way communication, streaming complexity |
|
Collection: |
|
46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) |
|
Issue Date: |
|
2019 |
|
Date of publication: |
|
04.07.2019 |
