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Robust Proximity Search for Balls Using Sublinear Space

Authors Sariel Har-Peled, Nirman Kumar

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Sariel Har-Peled
Nirman Kumar

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Sariel Har-Peled and Nirman Kumar. Robust Proximity Search for Balls Using Sublinear Space. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 315-326, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.FSTTCS.2014.315

Abstract

Given a set of n disjoint balls b_1, ..., b_n in R^d, we provide a data structure, of near linear size, that can answer (1 +- epsilon)-approximate k-th-nearest neighbor queries in O(log(n) + 1/epsilon^d) time, where k and epsilon are provided at query time. If k and epsilon are provided in advance, we provide a data structure to answer such queries, that requires (roughly) O(n/k) space; that is, the data structure has sublinear space requirement if k is sufficiently large.
Keywords
  • Approximate Nearest neighbors
  • algorithms
  • data structures

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