An improved communication-randomness tradeoff

    Research output: Chapter in Book/Report/Conference proceedingChapter

    Abstract

    Two processors receive inputs X and Y respectively. The communication complexity of the function f is the number of bits (as a function of the input size) that the processors have to exchange to compute f(X, Y) for worst case inputs X and Y. The List-Non-Disjointness problem (X = (x1, . . . ,xn), Y = (y1, . . . , yn), xi, yj ∈ Z2n, to decide whether ∃j xj = yj) exhibits maximal discrepancy between deterministic n2 and Las Vegas (Θ(n)) communication complexity. Fleischer, Jung, Mehlhorn (1995) have shown that if a Las Vegas algorithm expects to communicate Ω(n log n) bits, then this can be done with a small number of coin tosses. Even with an improved randomness efficiency, this result is extended to the (much more interesting) case of efficient algorithms (i.e. with linear communication complexity). For any R ∈ ℕ, R coin tosses are sufficient for O(n + n2/2R) transmitted bits.

    Original languageEnglish (US)
    Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    EditorsMartin Farach-Colton
    PublisherSpringer Verlag
    Pages444-454
    Number of pages11
    ISBN (Print)3540212582, 9783540212584
    DOIs
    StatePublished - Jan 1 2004

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume2976
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

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