Universal sketches for the frequency negative moments and other decreasing streaming sums
Vladimir Braverman, Stephen R. Chestnut

TL;DR
This paper characterizes the space complexity for streaming algorithms approximating negative frequency moments and general decreasing sums, providing a universal approach with solutions to a nonlinear optimization problem.
Contribution
It introduces a universal framework for approximating decreasing streaming sums, including negative moments, with space complexity characterized by a nonlinear optimization problem.
Findings
Provides space bounds for negative moments in streaming
Characterizes space for sums of general decreasing functions
Offers a universal approximation algorithm for such sums
Abstract
Given a stream with frequencies , for , we characterize the space necessary for approximating the frequency negative moments , where and the sum is taken over all items with nonzero frequency, in terms of , , and . To accomplish this, we actually prove a much more general result. Given any nonnegative and nonincreasing function , we characterize the space necessary for any streaming algorithm that outputs a -approximation to , where again the sum is over items with nonzero frequency. The storage required is expressed in the form of the solution to a relatively simple nonlinear optimization problem, and the algorithm is universal for -approximations to any such sum where the applied function is nonnegative, nonincreasing, and has the same or smaller space…
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Taxonomy
TopicsComputer Graphics and Visualization Techniques · Computational Geometry and Mesh Generation · Music Technology and Sound Studies
