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Communication Complexity under Product and Nonproduct Distributions

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1 Author(s)
Sherstov, A.A. ; Dept. of Comput. Sci., Univ. of Texas at Austin, Austin, TX

We solve an open problem in communication complexity posed by Kushilevitz and Nisan (1997). Let Repsiv(f) and Dmu epsiv(f) denote the randomized and mu-distributional communication complexities off, respectively (e a small constant). Yao's well-known minimax principle states that Repsiv(f) = maxmu{Dmu epsiv(f)}. Kushilevitz and Nisan (1997) ask whether this equality is approximately preserved if the maximization is taken over product distributions only, rather than all distributions mu. We give a strong negative answer to this question. Specifically, we prove the existence of a function f : {0,1}n X {0,1}n rarr {0, 1}for which Repsiv(f) = Omega(n) but maxmuproduct {Dmu epsiv(f)} = 0(1).

Published in:

Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on

Date of Conference:

23-26 June 2008

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