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Streaming Quantiles Algorithms with Small Space and Update Time.

Nikita Ivkin1, Edo Liberty2, Kevin Lang3

  • 1Amazon, New York, NY 10001, USA.

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|December 23, 2022
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Summary
This summary is machine-generated.

This study presents a practical, faster algorithm for approximating quantiles and distributions in streaming data. Our improved quantile sketch reduces error and speeds up data processing.

Keywords:
quantilessketchingstreaming

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Area of Science:

  • Computer Science
  • Data Science
  • Algorithm Analysis

Background:

  • Approximating quantiles and distributions from streaming data is a significant challenge.
  • Existing methods have limitations in optimality and practical performance.
  • Recent theoretical advancements offer asymptotically optimal solutions.

Purpose of the Study:

  • To develop a practical variant of the asymptotically optimal quantile sketch algorithm.
  • To improve the accuracy and reduce the computational complexity of streaming quantile approximation.
  • To provide experimentally verified enhancements to existing theoretical results.

Main Methods:

  • Modification of the Karnin, Lang, and Liberty algorithm for quantile sketching.
  • Introduction of improved constants to reduce sketch error bounds.
  • Analysis of worst-case update time complexity for the modified algorithm.

Main Results:

  • Provable reduction of the upper bound on sketch error by a factor of two.
  • Experimental verification of accuracy improvements.
  • Reduction of worst-case update time from O(1/ε) to O(log(1/ε)).

Conclusions:

  • The modified quantile sketch offers a practical and efficient solution for streaming data analysis.
  • The enhanced algorithm achieves provable error reduction and improved latency.
  • This work bridges the gap between theoretical optimality and practical implementation in streaming algorithms.