Block Heavy Hitters

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.