A Dyadic Simulation Approach to Efficient Range-Summability

TL;DR

This paper introduces a new dyadic simulation framework for efficient range-summability, enabling improved algorithms for data stream processing, histogram maintenance, and nearest neighbor searches with strong independence guarantees.

Contribution

It presents a novel dyadic simulation approach and three ERS solutions, along with efficient rejection sampling and a new k-wise independence theory.

Findings

Developed Gaussian-dyadic simulation tree (DST)

Created Cauchy-DST and Random Walk-DST solutions

Achieved high computational efficiency with strong independence guarantees

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.