Theory of Computing
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Title : The One-Way Communication Complexity of Hamming Distance
Authors : T. S. Jayram, Ravi Kumar, and D. Sivakumar
Volume : 4
Number : 6
Pages : 129-135
URL : https://theoryofcomputing.org/articles/v004a006
Abstract
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Consider the following version of the Hamming distance problem for
{1,-1}-vectors of length n: the promise is that the distance is
either at least (n/2)+sqrt{n} or at most (n/2)-sqrt{n}, and
the goal is to find out which of these two cases occurs.
Woodruff (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2004)
gave a linear lower bound for the randomized one-way communication
complexity of this problem. In this note we give a simple proof
of this result. Our proof uses a simple reduction from the indexing
problem and avoids the VC-dimension arguments used in the previous
paper. As shown by Woodruff (loc. cit.), this implies an
Omega(1/epsilon^2)-space lower bound for approximating frequency
moments within a factor 1+epsilon in the data stream model.