Fast, small-space algorithms for approximate histogram maintenance

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Fast, small-space algorithms for approximate histogram maintenance

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Annual ACM Symposium on Theory of Computing archive
Proceedings of the thiry-fourth annual ACM symposium on Theory of computing table of contents

Montreal, Quebec, Canada

SESSION: Session 7A table of contents

Pages: 389 - 398

Year of Publication: 2002

ISBN:1-58113-495-9

Authors

Anna C. Gilbert	AT&T Labs---Research
Sudipto Guha	University of Pennsylvania
Piotr Indyk	MIT
Yannis Kotidis	AT&T Labs---Research
S. Muthukrishnan	AT&T Labs---Research
Martin J. Strauss	AT&T Labs---Research

Sponsor

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 17, Downloads (12 Months): 83, Citation Count: 55

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ABSTRACT

(MATH) A vector A of length N is defined implicitly, via a stream of updates of the form "add 5 to A₃." We give a sketching algorithm, that constructs a small sketch from the stream of updates, and a reconstruction algorithm, that produces a B-bucket piecewise-constant representation (histogram) H for A from the sketch, such that ||A—H||&xie;(1+&egr;)||A—H_opt||, where the error ||A—H|| is either $\ell_1$ (absolute) or $\ell_2$ (root-mean-square) error. The time to process a single update, time to reconstruct the histogram, and size of the sketch are each bounded by poly(B,log(N),log||A,1/&egr;. Our result is obtained in two steps. First we obtain what we call a robust histogram approximation for A, a histogram such that adding a small number of buckets does not help improve the representation quality significantly. From the robust histogram, we cull a histogram of desired accruacy and B buckets in the second step. This technique also provides similar results for Haar wavelet representations, under $\ell_2$ error. Our results have applications in summarizing data distributions fast and succinctly even in distributed settings.

REFERENCES

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