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

THEORY OF COMPUTING, pp. 1-27, 2019.

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Abstract:

A classic result of Banaszczyk (Random Str. & Algor. 1997) states that given any n vectors in R-m with l(2)-norm at most 1 and any convex body K in R-m of Gaussian measure at least half, there exists a +/- 1 combination of these vectors that lies in 5K. Banaszczyk's proof of this result was non-constructive and it was open how to find suc...More

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