• Corpus ID: 244773062

# A note on spherical discrepancy

@inproceedings{Lonke2021ANO,
title={A note on spherical discrepancy},
author={Y. Lonke},
year={2021}
}
• Y. Lonke
• Published 30 October 2021
• Mathematics
A non-algorithmic, generalized version of a recent result, asserting that a natural relaxation of the Komlós conjecture from boolean discrepancy to spherical discrepancy is true, is proved by a very short argument using convex geometry.

## References

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### The Komlos Conjecture Holds for Vector Colorings

Here it is proved that if the columns of A are assigned unit real vectors rather than +/- 1 then the Komlos conjecture holds with K=1, which opens the way to proving tighter efficient (polynomial-time computable) upper bounds for the conjecture using semidefinite programming techniques.

### Spherical Discrepancy Minimization and Algorithmic Lower Bounds for Covering the Sphere

• Computer Science, Mathematics
SODA
• 2020
The algorithm is used to give the first non-trivial lower bounds for the problem of covering a hypersphere by hyperspherical caps of uniform volume at least $2^{-o(\sqrt{n})}$.

### Six standard deviations suffice

Given n sets on n elements it is shown that there exists a two-coloring such that all sets have discrepancy at most Knl/2, K an absolute constant. This improves the basic probabilistic method with