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, Shashwat Garg, +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
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