## Samenvatting

We show tight upper and lower bounds for time-space trade-offs for the c-approximate Near Neighbor Search problem. For the d-dimensional Euclidean space and n- point datasets, we develop a data structure with space n1+pu+°(1) + O(dn) and query time npq +o(1) + dno(1) for every pu, pq > 0 with: c2√pq +(c2 - 1)√pU- In particular, for the approximation c = 2 we get: Space n1.77....." and query time no(1), significantly improving upon known data structures that support very fast queries [IM98, KOR00]; Space n1.14 and query time n0.14 , matching the optimal data-dependent Locality-Sensitive Hashing (LSH) from [AR15] Space n1+o(1) and query time n0.43 , making significant progress in the regime of near-linear space, which is arguably of the most interest for practice [LJW+07]. This is the first data structure that achieves sublinear query time and near-linear space for every approximation factor c > 1, improving upon [Kap15]. The data structure is a culmination of a long line of work on the problem for all space regimes; it builds on Spherical Locality-Sensitive Filtering [BDGL16] and data- dependent hashing [AINR14, AR15]. Our matching lower bounds are of two types: conditional and unconditional. First, we prove tightness of the whole trade-off (0.1) in a restricted model of computation, which captures all known hashing-based approaches. We then show unconditional cell-probe lower bounds for one and two probes that match (0.1) for pq = 0, improving upon the best known lower bounds from [PTW10]. In particular, this is the first space lower bound (for any static data structure) for two probes which is not polynomially smaller than the one-probe bound. To show the result for two probes, we establish and exploit a connection to locally-decodable codes.

Originele taal-2 | Engels |
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Titel | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |

Redacteuren | Philip N. Klein |

Plaats van productie | s.l. |

Uitgeverij | Society for Industrial and Applied Mathematics (SIAM) |

Pagina's | 47-66 |

Aantal pagina's | 20 |

ISBN van elektronische versie | 978-1-61197-478-2 |

DOI's | |

Status | Gepubliceerd - 4 jan 2017 |

Evenement | 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) - Barcelona, Spanje Duur: 16 jan 2017 → 19 jan 2017 Congresnummer: 28 |

### Congres

Congres | 28th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2017) |
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Verkorte titel | SODA 2017 |

Land | Spanje |

Stad | Barcelona |

Periode | 16/01/17 → 19/01/17 |