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Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2009, RANDOM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5687))

Abstract

The \({\textsc{And}}\) problem on t bits is a promise decision problem where either at most one bit of the input is set to 1 (No instance) or all t bits are set to 1 (\({\textsc{Yes}}\) instance). In this note, I will give a new proof of an Ω(1/t) lower bound on the information complexity of \({\textsc{And}}\) in the number-in-hand model of communication. This was recently established by Gronemeier, STACS 2009. The proof exploits the information geometry of communication protocols via Hellinger distance in a novel manner and avoids the analytic approach inherent in previous work. As previously known, this bound implies an Ω(n/t) lower bound on the communication complexity of multiparty disjointness and consequently a Ω(n 1 − 2/k) space lower bound on estimating the k-th frequency moment F k .

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Author information

Authors and Affiliations

  1. IBM Almaden Research Center, 650 Harry Rd, San Jose, CA, 95120, USA

    T. S. Jayram

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  1. T. S. Jayram
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Editors and Affiliations

  1. Dept. of Applied Math and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Irit Dinur

  2. Institute for Computer Science and Applied Mathematics, University of Kiel, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Technion, Computer Science Department, 32000, Haifa, Israel

    Joseph Naor

  4. University of Geneva, Centre Universitaire d’Informatique, Battelle Bat. A, 7 rte de Drize, 1227, Carouge, Switzerland

    José Rolim

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© 2009 Springer-Verlag Berlin Heidelberg

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Jayram, T.S. (2009). Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND. In: Dinur, I., Jansen, K., Naor, J., Rolim, J. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2009 2009. Lecture Notes in Computer Science, vol 5687. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03685-9_42

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  • DOI: https://doi.org/10.1007/978-3-642-03685-9_42

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03684-2

  • Online ISBN: 978-3-642-03685-9

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