On Efficient Range-Summability of IID Random Variables in Two or Higher Dimensions
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by
Jingfan Meng, Huayi Wang, Jun Xu, Mitsunori Ogihara
2021
Abstract
d-dimensional efficient range-summability (dD-ERS) of a long list of
random variables (RVs) is a fundamental algorithmic problem that has
applications to two important families of database problems, namely, fast
approximate wavelet tracking (FAWT) on data streams and approximately answering
range-sum queries over a data cube. In this work, we propose a novel solution
framework to dD-ERS for d>1 on RVs that have Gaussian or Poisson
distribution. Our solutions are the first ones that compute any rectangular
range-sum of the RVs in polylogarithmic time. Furthermore, we develop a novel
k-wise independence theory that allows our dD-ERS solutions to have both
high computational efficiencies and strong provable independence guarantees.
Finally, we generalize existing DST-based solutions for 1D-ERS to 2D, and
characterize a sufficient and likely necessary condition on the target
distribution for this generalization to be feasible.
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