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Discrepancy Minimization via a Self-Balancing Walk

06/24/2020

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by Ryan Alweiss, et al.

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We study discrepancy minimization for vectors in ℝ^n under various settings. The main result is the analysis of a new simple random process in multiple dimensions through a comparison argument. As corollaries, we obtain bounds which are tight up to logarithmic factors for several problems in online vector balancing posed by Bansal, Jiang, Singla, and Sinha (STOC 2020), as well as linear time algorithms for logarithmic bounds for the Komlós conjecture.

Ryan Alweiss
3 publications
Yang P. Liu
24 publications
Mehtaab Sawhney
11 publications

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