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

A Dyadic Simulation Approach to Efficient Range-Summability