## Samenvatting

An important result in discrepancy due to Banaszczyk States that for any set of n vectors in R^{m} of 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 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-2 | Engels |
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Titel | STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing |

Uitgeverij | Association for Computing Machinery, Inc |

Pagina's | 1269-1282 |

Aantal pagina's | 14 |

ISBN van elektronische versie | 9781450355599 |

DOI's | |

Status | Gepubliceerd - 20 jun 2018 |

Evenement | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 - Los Angeles, Verenigde Staten van Amerika Duur: 25 jun 2018 → 29 jun 2018 |

### Congres

Congres | 50th Annual ACM Symposium on Theory of Computing, STOC 2018 |
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Land | Verenigde Staten van Amerika |

Stad | Los Angeles |

Periode | 25/06/18 → 29/06/18 |