Discrepancy Minimization via a Self-Balancing Walk

Ryan Alweiss; Yang P. Liu; Mehtaab Sawhney

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arXiv · 2006.14009

Discrepancy Minimization via a Self-Balancing Walk

Ryan Alweiss·Yang P. Liu·Mehtaab Sawhney

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Abstract

We study discrepancy minimization for vectors in $\mathbb{R}^n$ 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 Koml\'{o}s conjecture.

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Ryan Alweiss, Yang P. Liu, Mehtaab Sawhney. 2020-06-24. Discrepancy Minimization via a Self-Balancing Walk. https://arxiv.org/abs/2006.14009

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