The Gram-Schmidt Walk: A Cure for the Banaszczyk Blues

3 Aug 2017Nikhil BansalDaniel DadushShashwat GargShachar Lovett

An important result in discrepancy due to Banaszczyk states that for any set of $n$ vectors in $\mathbb{R}^m$ of $\ell_2$ norm at most $1$ and any convex body $K$ in $\mathbb{R}^m$ of Gaussian measure at least half, there exists a $\pm 1$ combination of these vectors which lies in $5K$. This result implies the best known bounds for several problems in discrepancy... (read more)

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