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Communication Lower Bounds Using Directional Derivatives

Published: 17 December 2014 Publication History

Abstract

We study the set disjointness problem in the most powerful model of bounded-error communication, the k-party randomized number-on-the-forehead model. We show that set disjointness requires Ω(√n/2kk) bits of communication, where n is the size of the universe. Our lower bound generalizes to quantum communication, where it is essentially optimal. Proving this bound was a longstanding open problem even in restricted settings, such as one-way classical protocols with k=4 parties [Wigderson 1997]. The proof contributes a novel technique for lower bounds on multiparty communication, based on directional derivatives of protocols over the reals.

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  1. Communication Lower Bounds Using Directional Derivatives

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    cover image Journal of the ACM
    Journal of the ACM  Volume 61, Issue 6
    November 2014
    285 pages
    ISSN:0004-5411
    EISSN:1557-735X
    DOI:10.1145/2700084
    Issue’s Table of Contents
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 17 December 2014
    Accepted: 01 June 2014
    Revised: 01 May 2014
    Received: 01 March 2013
    Published in JACM Volume 61, Issue 6

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    Author Tags

    1. Set disjointness problem
    2. directional derivatives
    3. multiparty communication complexity
    4. polynomial approximation
    5. quantum communication complexity

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