2026-07-21T14:16:25Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:10673 2024-03-06T10:46:26Z ddc:004 open_access

Separating k-Player from t-Player One-Way Communication, with Applications to Data Streams Woodruff, David P. Yang, Guang Communication complexity multi-player communication one-way communication streaming complexity 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David P. Woodruff and Guang Yang 2019 Is Part Of LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2019.97 urn:nbn:de:0030-drops-106733 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.97 eng https://creativecommons.org/licenses/by/3.0/legalcode