# An Algorithm for Koml'os Conjecture Matching Banaszczyk's bound

arXiv: https://arxiv.org/abs/1605.02882 · HTML: https://mlsanity.com/paper/1605.02882/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2016.

## Built on by (most cited first, 2 of 2)

- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [Algorithms for Discrepancy, Matchings, and Approximations: Fast, Simple, and Practical](https://mlsanity.com/paper/2209.01147/) (2022)

## Abstract (arXiv)

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(t1/2 log n) bound. The result also extends to the more general Koml'os setting and gives an algorithmic O(log1/2 n) bound.