Papers › Discrepancy Minimization via a Self-Balancing Walk
Discrepancy Minimization via a Self-Balancing Walk
Ryan Alweiss, Yang P. Liu, Mehtaab Sawhney
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We study discrepancy minimization for vectors in ℝⁿ 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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