The simultaneous communication of disjointness with applications to data streams

Omri Weinstein*, David P. Woodruff

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations


We study k-party number-in-hand set disjointness in the simultaneous message-passing model, and show that even if each element i ∈ [n] is guaranteed to either belong to all k parties or to at most O(1) parties in expectation (and to at most O(log n) parties with high probability), then Ω(n min(log 1/δ, log k)/k) communication is required by any δ-error communication protocol for this problem (assuming k = Ω(log n)). We use the strong promise of our lower bound, together with a recent characterization of turnstile streaming algorithms as linear sketches, to obtain new lower bounds for the well-studied problem in data streams of approximating the frequency moments. We obtain a space lower bound of Ω(n1−2/pε−2 logM log 1/δ) bits for any algorithm giving a (1 + ε)-approximation to the p-th moment (Formula Presented.) of an n-dimensional vector x ∈ {±M}n with probability 1 − δ, for any (Formula Presented.). Our lower bound improves upon a prior Ω(n1−2/pε−2 log M) lower bound which did not capture the dependence on δ, and our bound is optimal whenever ε ≤ 1/poly(log n). This is the first example of a lower bound in data streams which uses a characterization in terms of linear sketches to obtain stronger lower bounds than obtainable via the one-way communication model; indeed, our set disjointness lower bound provably cannot hold in the one-way model.

Original languageAmerican English
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
EditorsMagnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783662476710
StatePublished - 2015
Externally publishedYes
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Bibliographical note

Funding Information:
O. Weinstein and D.P. Woodruff—Research supported by a Simons Fellowship in Theoretical Computer Science and NSF Award CCF-1215990.

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.


  • Frequency moments
  • Information complexity
  • Information theory
  • Multiparty communication complexity


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