### Abstract

Motivated by the recent research on diversity-aware search, we investigate the k-diverse near neighbor reporting problem. The problem is defined as follows: given a query point q, report the maximum diversity set S of k points in the ball of radius r around q. The diversity of a set S is measured by the minimum distance between any pair of points in S (the higher, the better). We present two approximation algorithms for the case where the points live in a d-dimensional Hamming space. Our algorithms guarantee query times that are sub-linear in n and only polynomial in the diversity parameter k, as well as the dimension d. For low values of k, our algorithms achieve sub-linear query times even if the number of points within distance r from a query q is linear in n. To the best of our knowledge, these are the first known algorithms of this type that offer provable guarantees.

Original language | English |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Pages | 207-213 |

Number of pages | 7 |

Publication status | Published - 8 Jul 2013 |

Event | 29th Annual Symposium on Computational Geometry, SoCG 2013 - Rio de Janeiro, Brazil Duration: 17 Jun 2013 → 20 Jun 2013 |

### Other

Other | 29th Annual Symposium on Computational Geometry, SoCG 2013 |
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Country | Brazil |

City | Rio de Janeiro |

Period | 17/6/13 → 20/6/13 |

### Fingerprint

### Keywords

- Core-set
- Diversity
- Near neighbor
- Sub-linear

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology
- Theoretical Computer Science

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 207-213)

**Diverse near neighbor problem.** / Abbar, Sofiane; Amer-Yahia, Sihem; Indyk, Piotr; Mahabadi, Sepideh; Varadarajan, Kasturi R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*pp. 207-213, 29th Annual Symposium on Computational Geometry, SoCG 2013, Rio de Janeiro, Brazil, 17/6/13.

}

TY - GEN

T1 - Diverse near neighbor problem

AU - Abbar, Sofiane

AU - Amer-Yahia, Sihem

AU - Indyk, Piotr

AU - Mahabadi, Sepideh

AU - Varadarajan, Kasturi R.

PY - 2013/7/8

Y1 - 2013/7/8

N2 - Motivated by the recent research on diversity-aware search, we investigate the k-diverse near neighbor reporting problem. The problem is defined as follows: given a query point q, report the maximum diversity set S of k points in the ball of radius r around q. The diversity of a set S is measured by the minimum distance between any pair of points in S (the higher, the better). We present two approximation algorithms for the case where the points live in a d-dimensional Hamming space. Our algorithms guarantee query times that are sub-linear in n and only polynomial in the diversity parameter k, as well as the dimension d. For low values of k, our algorithms achieve sub-linear query times even if the number of points within distance r from a query q is linear in n. To the best of our knowledge, these are the first known algorithms of this type that offer provable guarantees.

AB - Motivated by the recent research on diversity-aware search, we investigate the k-diverse near neighbor reporting problem. The problem is defined as follows: given a query point q, report the maximum diversity set S of k points in the ball of radius r around q. The diversity of a set S is measured by the minimum distance between any pair of points in S (the higher, the better). We present two approximation algorithms for the case where the points live in a d-dimensional Hamming space. Our algorithms guarantee query times that are sub-linear in n and only polynomial in the diversity parameter k, as well as the dimension d. For low values of k, our algorithms achieve sub-linear query times even if the number of points within distance r from a query q is linear in n. To the best of our knowledge, these are the first known algorithms of this type that offer provable guarantees.

KW - Core-set

KW - Diversity

KW - Near neighbor

KW - Sub-linear

UR - http://www.scopus.com/inward/record.url?scp=84879673771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879673771&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84879673771

SN - 9781450320313

SP - 207

EP - 213

BT - Proceedings of the Annual Symposium on Computational Geometry

ER -