# Towards a Constructive Version of Banaszczyk's Vector Balancing Theorem

@article{Dadush2016TowardsAC,
title={Towards a Constructive Version of Banaszczyk's Vector Balancing Theorem},
author={D. Dadush and Shashwat Garg and Shachar Lovett and A. Nikolov},
journal={ArXiv},
year={2016},
volume={abs/1612.04304}
}
• D. Dadush, +1 author A. Nikolov
• Published 2016
• Mathematics, Computer Science
• ArXiv
• An important theorem of Banaszczyk (Random Structures & Algorithms `98) states that for any sequence of vectors of $\ell_2$ norm at most $1/5$ and any convex body $K$ of Gaussian measure $1/2$ in $\mathbb{R}^n$, there exists a signed combination of these vectors which lands inside $K$. A major open problem is to devise a constructive version of Banaszczyk's vector balancing theorem, i.e. to find an efficient algorithm which constructs the signed combination. We make progress towards this goal… CONTINUE READING
12 Citations

#### Explore Further: Topics Discussed in This Paper

The Gram-Schmidt walk: a cure for the Banaszczyk blues
• Mathematics, Computer Science
• STOC 2018
• 2018
• 25
• PDF
Balancing Vectors in Any Norm
• Mathematics, Computer Science
• 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)
• 2018
• 7
Online Discrepancy Minimization for Stochastic Arrivals
• Mathematics, Computer Science
• ArXiv
• 2020
• 1
• PDF
Vector Balancing in Lebesgue Spaces
• Computer Science, Physics
• ArXiv
• 2020
• 1
• PDF
Algorithmic discrepancy beyond partial coloring
• Mathematics, Computer Science
• STOC
• 2017
• 25
• PDF
An Algorithm for Komlós Conjecture Matching Banaszczyk's Bound
• Mathematics, Computer Science
• 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
• 2016
• 24
• PDF

#### References

SHOWING 1-10 OF 51 REFERENCES
Efficient Algorithms for Discrepancy Minimization in Convex Sets
• Mathematics, Computer Science
• Random Struct. Algorithms
• 2018
• 20
• PDF
The Gram-Schmidt walk: a cure for the Banaszczyk blues
• Mathematics, Computer Science
• STOC 2018
• 2018
• 25
• PDF
Constructive Discrepancy Minimization for Convex Sets
• T. Rothvoss
• Mathematics, Computer Science
• 2014 IEEE 55th Annual Symposium on Foundations of Computer Science
• 2014
• 47
• PDF
On the Beck-Fiala Conjecture for Random Set Systems
• Mathematics, Computer Science
• Electron. Colloquium Comput. Complex.
• 2015
• 12
• PDF
Constructive Discrepancy Minimization by Walking on the Edges
• Mathematics, Computer Science
• 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
• 2012
• 67
• PDF
Sampling and integration of near log-concave functions
• Mathematics, Computer Science
• STOC '91
• 1991
• 163
A Cubic Algorithm for Computing Gaussian Volume
• Mathematics, Computer Science
• SODA
• 2014
• 27
• PDF