The multiparty communication complexity of exact-T: improved bounds and new problems

  • Authors:

  • Richard Beigel;William Gasarch;James Glenn

  • Affiliations:

  • Dept. of Computer and Information Sciences, Temple University, Philadelphia, PA;Dept. of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD;Dept. of Computer Science, Loyola College in Maryland, Baltimore, MD

  • Venue:
  • MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
  • Year:
  • 2006

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Abstract

Let xi,...,xk be n-bit numbers and T∈ℕ. Assume that P1,...,Pk are players such that Pi knows all of the numbers exceptxi. 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(2n). 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(2n), 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.