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### Paper:

TR11-063 | 19th April 2011 22:31

#### The Communication Complexity of Gap Hamming Distance

TR11-063
Authors: Alexander A. Sherstov
Publication: 20th April 2011 12:14
Downloads: 4386
Keywords:

Abstract:

In the gap Hamming distance problem, two parties must
determine whether their respective strings $x,y\in\{0,1\}^n$
are at Hamming distance less than $n/2-\sqrt n$ or greater
than $n/2+\sqrt n.$ In a recent tour de force, Chakrabarti and
Regev (STOC '11) proved the long-conjectured $\Omega(n)$ bound
on the randomized communication complexity of this problem. In
follow-up work several months ago, Vidick (2010; ECCC TR11-051)
discovered a simpler proof. We contribute a new proof, which
is simpler yet and a page-and-a-half long.

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