Diverse near neighbor problem

Sofiane Abbar, Sihem Amer-Yahia, Piotr Indyk, Sepideh Mahabadi, Kasturi R. Varadarajan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)


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 languageEnglish
Title of host publicationProceedings of the Annual Symposium on Computational Geometry
Number of pages7
Publication statusPublished - 8 Jul 2013
Event29th Annual Symposium on Computational Geometry, SoCG 2013 - Rio de Janeiro, Brazil
Duration: 17 Jun 201320 Jun 2013


Other29th Annual Symposium on Computational Geometry, SoCG 2013
CityRio de Janeiro



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

ASJC Scopus subject areas

  • Computational Mathematics
  • Geometry and Topology
  • Theoretical Computer Science

Cite this

Abbar, S., Amer-Yahia, S., Indyk, P., Mahabadi, S., & Varadarajan, K. R. (2013). Diverse near neighbor problem. In Proceedings of the Annual Symposium on Computational Geometry (pp. 207-213)