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The Multiparty Communication Complexity of Exact-T: Improved Bounds and New Problems

  • Richard Beigel
  • William Gasarch
  • James Glenn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4162)

Abstract

Let x i ,...,x k be n-bit numbers and T ∈ ℕ. Assume that P 1,...,P k are players such that P i knows all of the numbers exceptx i . They want to determine if \(\sum^{k}_{j=1}{\it x}_{j}\)= T by broadcasting as few bits as possible. In [7] an upper bound of \(O(\sqrt n )\) bits was obtained for the k=3 case, and a lower bound of ω(1) for k ≥3 when T=Θ(2 n ). We obtain (1) for k ≥3 an upper bound of \(k+O((n+\log k)^{1/(\lfloor{\rm lg(2k-2)}\rfloor)})\), (2) for k=3, T=Θ(2 n ), a lower bound of Ω(loglogn), (3) a generalization of the protocol to abelian groups, (4) lower bounds on the multiparty communication complexity of some regular languages, and (5) empirical results for k = 3.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Richard Beigel
    • 1
  • William Gasarch
    • 2
  • James Glenn
    • 3
  1. 1.Dept. of Computer and Information SciencesTemple UniversityPhiladelphia
  2. 2.Dept. of Computer Science and Institute for Advanced Computer StudiesUniversity of MarylandCollege Park
  3. 3.Dept. of Computer ScienceLoyola College in MarylandBaltimore

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