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Improved Separations between Nondeterministic and Randomized Multiparty Communication

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Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques (APPROX 2008, RANDOM 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5171))

Abstract

We exhibit an explicit function f : {0, 1}n →{0,1} that can be computed by a nondeterministic number-on-forehead protocol communicating O(logn) bits, but that requires n Ω(1) bits of communication for randomized number-on-forehead protocols with k = δ·logn players, for any fixed δ< 1. Recent breakthrough results for the Set-Disjointness function (Sherstov, STOC ’08; Lee Shraibman, CCC ’08; Chattopadhyay Ada, ECCC ’08) imply such a separation but only when the number of players is k < loglogn.

We also show that for any k = A loglogn the above function f is computable by a small circuit whose depth is constant whenever A is a (possibly large) constant. Recent results again give such functions but only when the number of players is k < loglogn.

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Authors and Affiliations

  1. Department of Computer Science, University of Toronto,  

    Matei David & Toniann Pitassi

  2. Computer Science Department, Columbia University,  

    Emanuele Viola

Authors
  1. Matei David
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  2. Toniann Pitassi
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  3. Emanuele Viola
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Ashish Goel Klaus Jansen José D. P. Rolim Ronitt Rubinfeld

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© 2008 Springer-Verlag Berlin Heidelberg

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David, M., Pitassi, T., Viola, E. (2008). Improved Separations between Nondeterministic and Randomized Multiparty Communication. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_30

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  • DOI: https://doi.org/10.1007/978-3-540-85363-3_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85362-6

  • Online ISBN: 978-3-540-85363-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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