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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{0,1}n are at Hamming distance less than n/2n or greater than n/2+n. In a recent tour de force, Chakrabarti and Regev (2010) proved the long-conjectured Ω(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.