Diverse Near Neighbor Problem

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.
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https://hal.archives-ouvertes.fr/hal-00923544
Contributor : Valérie Samper <>
Submitted on : Monday, January 6, 2014 - 5:59:27 PM
Last modification on : Thursday, October 11, 2018 - 8:48:03 AM

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Sofiane Abbar, Sihem Amer-Yahia, Piotr Indyk, Sepideh Mahabadi, Kasturi Varadarajan. Diverse Near Neighbor Problem. SoCG 2013 - Symposium on Computational Geometry, Jun 2013, Rio de Janeiro, Brazil. pp.207-214, ⟨10.1145/2462356.2462401⟩. ⟨hal-00923544⟩

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