# An optimal lower bound on the communication complexity of gap-hamming-distance

@inproceedings{Chakrabarti2011AnOL, title={An optimal lower bound on the communication complexity of gap-hamming-distance}, author={Amit Chakrabarti and Oded Regev}, booktitle={STOC '11}, year={2011} }

We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem. As a consequence, we obtain essentially optimal multi-pass space lower bounds in the data stream model for a number of fundamental problems, 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… CONTINUE READING

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