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Block Heavy Hitters

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dc.contributor.advisor Piotr Indyk en_US Andoni, Alexandr en_US Ba, Khanh Do en_US Indyk, Piotr en_US
dc.contributor.other Theory of Computation en_US 2008-05-05T15:45:27Z 2008-05-05T15:45:27Z 2008-05-02 en_US
dc.identifier.other MIT-CSAIL-TR-2008-024 en_US
dc.description.abstract e study a natural generalization of the heavy hitters problem in thestreaming context. We term this generalization *block heavy hitters* and define it as follows. We are to stream over a matrix$A$, and report all *rows* that are heavy, where a row is heavy ifits ell_1-norm is at least phi fraction of the ell_1 norm ofthe entire matrix $A$. In comparison, in the standard heavy hittersproblem, we are required to report the matrix *entries* that areheavy. As is common in streaming, we solve the problem approximately:we return all rows with weight at least phi, but also possibly someother rows that have weight no less than (1-eps)phi. To solve theblock heavy hitters problem, we show how to construct a linear sketchof A from which we can recover the heavy rows of A.The block heavy hitters problem has already found applications forother streaming problems. In particular, it is a crucial buildingblock in a streaming algorithm that constructs asmall-size sketch for the Ulam metric, a metric on non-repetitivestrings under the edit (Levenshtein) distance. en_US
dc.format.extent 3 p. en_US
dc.relation Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory en_US
dc.relation en_US
dc.title Block Heavy Hitters en_US

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