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2009
Springer

A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences

8 years 11 months ago
A Multi-Round Communication Lower Bound for Gap Hamming and Some Consequences
—The Gap-Hamming-Distance problem arose in the context of proving space lower bounds for a number of key problems in the data stream model. In this problem, Alice and Bob have to decide whether the Hamming distance between their n-bit input strings is large (i.e., at least n/2 + √ n) or small (i.e., at most n/2 − √ n); they do not care if it is neither large nor small. This Θ( √ n) gap in the problem specification is crucial for capturing the approximation allowed to a data stream algorithm. Thus far, for randomized communication, an Ω(n) lower bound on this problem was known only in the one-way setting. We prove an Ω(n) lower bound for randomized protocols that use any constant number of rounds. As a consequence we conclude, for instance, that εapproximately counting the number of distinct elements in a data stream requires Ω(1/ε2 ) space, even with multiple (a constant number of) passes over the input stream. This extends earlier one-pass lower bounds, answering a...
Joshua Brody, Amit Chakrabarti
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where COCO
Authors Joshua Brody, Amit Chakrabarti
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