The gram-Schmidt walk: a cure for the banaszczyk blues

Nikhil Bansal, Shashwat Garg, Daniel Dadush, Shachar Lovett

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

5 Citaten (Scopus)


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 proof of this result is non-constructive and a major open problem has been to give an efficient algorithm to find such a ±1 combination of the vectors. In this paper, we resolve this question and give an efficient randomized algorithm to find a ±1 combination of the vectors which lies in cK for c > 0 an absolute constant. This leads to new efficient algorithms for several problems in discrepancy theory.

Originele taal-2Engels
TitelSTOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing
UitgeverijAssociation for Computing Machinery, Inc
Aantal pagina's14
ISBN van elektronische versie9781450355599
StatusGepubliceerd - 20 jun 2018
Evenement50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, Verenigde Staten van Amerika
Duur: 25 jun 201829 jun 2018


Congres50th Annual ACM Symposium on Theory of Computing, STOC 2018
LandVerenigde Staten van Amerika
StadLos Angeles

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