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

STOC '18: Symposium on Theory of Computing Los Angeles CA USA June, 2018, pp. 587-597, 2018.

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Keywords:
Discrepancyrandom walksrounding techniques

Abstract:

An important result in discrepancy due to Banaszczyk states that for any set of n vectors in ℝm of ℓ2 norm at most 1 and any convex body K in ℝm of Gaussian measure at least half, there exists a ± 1 combination of these vectors which lies in 5K. This result implies the best known bounds for several problems in discrepancy. Banaszczyk’s pr...More

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