On Efficient Range-Summability of IID Random Variables in Two or Higher Dimensions
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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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