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Simulation beats richness: new data-structure lower bounds

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10387323" target="_blank" >RIV/00216208:11320/18:10387323 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1145/3188745.3188874" target="_blank" >https://doi.org/10.1145/3188745.3188874</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1145/3188745.3188874" target="_blank" >10.1145/3188745.3188874</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Simulation beats richness: new data-structure lower bounds

  • Original language description

    We develop a new technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC&apos;94) and Miltersen, Nisan, Safra and Wigderson (STOC&apos;95). At the core of our technique is the first simulation theorem in the asymmetric setting, where Alice gets a p x n matrix x over F2 and Bob gets a vector y ELEMENT OF F2n. Alice and Bob need to evaluate f(x. y) for a Boolean function f: {0,1}p RIGHTWARDS ARROW {0,1}. Our simulation theorems show that a deterministic/randomized communication protocol exists for this problem, with cost C. n for Alice and C for Bob, if and only if there exists a deterministic/randomized *parity decision tree* of cost Θ(C) for evaluating f. As applications of this technique, we obtain the following results: 1. The first strong lower-bounds against randomized data-structure schemes for the Vector-Matrix-Vector product problem over F2. Moreover, our method yields strong lower bounds even when the data-structure scheme has tiny advantage over random guessing. 2. The first lower bounds against randomized data-structures schemes for two natural Boolean variants of Orthogonal Vector Counting. 3. We construct an asymmetric communication problem and obtain a deterministic lower-bound for it which is provably better than any lower-bound that may be obtained by the classical Richness Method of Miltersen et al. (STOC &apos;95). This seems to be the first known limitation of the Richness Method in the context of proving deterministic lower bounds.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Proceedings of the 50th Annual {ACM} {SIGACT} Symposium on Theory of Computing, {STOC} 2018, Los Angeles, CA, USA, June 25-29, 2018

  • ISBN

    978-1-4503-5559-9

  • ISSN

  • e-ISSN

    neuvedeno

  • Number of pages

    8

  • Pages from-to

    1013-1020

  • Publisher name

    ACM New York, NY, USA

  • Place of publication

    New York, NY, USA

  • Event location

    Los Angeles, CA, USA

  • Event date

    Jun 25, 2018

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article