Fast, Small-Space Algorithms for Approximate Histogram Maintenance

Martin J. Strauss, AT&T Shannon Labs, Florham Park

April 23, 4:30 PM, Rutgers Univ. CORE 431

Abstract.

Consider an array, A, of N values, defined implicitly by a stream of updates of the form

"add/subtract 3 to/from A[5]".

Our goal is to produce, on demand, a nearly optimal B-bucket histogram for A (piecewise-constant approximation to A), by making good choices for bucket boundaries and heights. We give a data structure that produces a histogram H such that, with high probability,
||A-H|| <= (1+epsilon)||A-Hopt||,
where Hopt is the best possible B-bucket histogram under L1 or L2 norm ||*||. For each of three costs: total space, time to process an update, and time to produce a histogram on demand, our data structure uses resources polynomial in (B*log(N)/epsilon).

Joint work with Anna C. Gilbert, Sudipto Guha, Piotr Indyk, Yannis Kotidis, and S. Muthukrishnan.



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