English

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 Rn\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.

Keywords

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

R2 v1 2026-06-23T16:36:15.655Z