Physical Sciences and Mathematics Commons^™

An Optimal Lower Bound On The Communication Complexity Of Gap-Hamming-Distance, Amit Chakrabarti, Oded Regev

Dartmouth Scholarship

We prove an optimal Ω(n) lower bound on the randomized communication complex- ity of the much-studied gap-hamming-distance problem. As a consequence, we obtain essentially optimal multipass space lower bounds in the data stream model for a number of fundamental prob- lems, including the estimation of frequency moments. The gap-hamming-distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively. They are promised that the Hamming distance between x and y is either at least n/2 + √n or at most n, and their goal is to decide which of these is the case. Since …