, Volume 80, Issue 1, pp 279–299 | Cite as

Robust Proximity Search for Balls Using Sublinear Space

  • Sariel Har-Peled
  • Nirman KumarEmail author


Given a set of n disjoint balls \(b_1, \dots , b_n\) in \(\mathrm{I\! R}^d\), we provide a data structure of near linear size that can answer \((1\pm {\varepsilon })\)-approximate kth-nearest neighbor queries on the balls in \(O(\log n + 1/{\varepsilon }^d)\) time, where k and \({\varepsilon }\) may be provided at query time. If k and \({\varepsilon }\) are provided in advance, we provide a data structure to answer such queries requiring O(n / k) space; that is, the data structure requires sublinear space if k is sufficiently large.


Data structures Approximation algorithms Proximity search 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of IllinoisUrbanaUSA
  2. 2.Department of Computer ScienceUniversity of MemphisMemphisUSA

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