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Volume 8 (2012) Article 8 pp. 197-208
The Communication Complexity of Gap Hamming Distance
Received: August 8, 2011
Published: May 17, 2012
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Keywords: communication complexity, gap Hamming distance, Talagrand's concentration inequality
ACM Classification: F.1.3
AMS Classification: 68Q17, 68Q25

Abstract: [Plain Text Version]

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 (2010) proved the long-conjectured $\Omega(n)$ bound on the randomized communication complexity of this problem. In follow-up work, Vidick (2010) discovered a simpler proof. We contribute a new proof, which is simpler yet and a page-and-a-half long.