Discrepancy Minimization via a Self-Balancing Walk
Data Structures and Algorithms
2020-08-07 v2 Discrete Mathematics
Probability
Abstract
We study discrepancy minimization for vectors in 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.
Cite
@article{arxiv.2006.14009,
title = {Discrepancy Minimization via a Self-Balancing Walk},
author = {Ryan Alweiss and Yang P. Liu and Mehtaab Sawhney},
journal= {arXiv preprint arXiv:2006.14009},
year = {2020}
}
Comments
v2, 10 pages