An Algorithm for Koml\'os Conjecture Matching Banaszczyk's bound
Data Structures and Algorithms
2016-09-13 v3 Discrete Mathematics
Abstract
We consider the problem of finding a low discrepancy coloring for sparse set systems where each element lies in at most t sets. We give an efficient algorithm that finds a coloring with discrepancy O((t log n)^{1/2}), matching the best known non-constructive bound for the problem due to Banaszczyk. The previous algorithms only achieved an O(t^{1/2} log n) bound. The result also extends to the more general Koml\'{o}s setting and gives an algorithmic O(log^{1/2} n) bound.
Cite
@article{arxiv.1605.02882,
title = {An Algorithm for Koml\'os Conjecture Matching Banaszczyk's bound},
author = {Nikhil Bansal and Daniel Dadush and Shashwat Garg},
journal= {arXiv preprint arXiv:1605.02882},
year = {2016}
}