License
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://drops.dagstuhl.de/opus/volltexte/2019/10673/
Go to the corresponding LIPIcs Volume Portal


Woodruff, David P. ; Yang, Guang

Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams

pdf-format:
LIPIcs-ICALP-2019-97.pdf (0.5 MB)


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
Seminar: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 08.07.2019


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI