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A Dyadic Simulation Approach to Efficient Range-Summability

Authors Jingfan Meng, Huayi Wang, Jun Xu, Mitsunori Ogihara



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Author Details

Jingfan Meng
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Huayi Wang
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Jun Xu
  • School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA
Mitsunori Ogihara
  • Department of Computer Science, University of Miami, Coral Gables, FL, USA

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Jingfan Meng, Huayi Wang, Jun Xu, and Mitsunori Ogihara. A Dyadic Simulation Approach to Efficient Range-Summability. In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 17:1-17:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ICDT.2022.17

Abstract

Efficient range-summability (ERS) of a long list of random variables is a fundamental algorithmic problem that has applications to three important database applications, namely, data stream processing, space-efficient histogram maintenance (SEHM), and approximate nearest neighbor searches (ANNS). In this work, we propose a novel dyadic simulation framework and develop three novel ERS solutions, namely Gaussian-dyadic simulation tree (DST), Cauchy-DST and Random Walk-DST, using it. We also propose novel rejection sampling techniques to make these solutions computationally efficient. Furthermore, we develop a novel k-wise independence theory that allows our ERS solutions to have both high computational efficiencies and strong provable independence guarantees.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Mathematics of computing → Random number generation
Keywords
  • fast range-summation
  • locality-sensitive hashing
  • rejection sampling

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