Computing closest and farthest points for a query segment

Michael Segal, Eli Zeitlin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper we present an improved algorithm for finding k closest (farthest) points for a given arbitrary query segment. We show how to preprocess a planar set P of n given points in O (n2 log n) expected time (or, alternatively, in O (n2 log2 n) deterministic time) and a subquadratic space, in order to report k closest points to an arbitrary given query line segment in O (k + log2 n log log n) time. Here, for the first time, the data structure that provides polylogarithmic query time and uses subquadratic space is presented. We also show an algorithm for reporting the k farthest points from an arbitrary given query line segment.

Original languageEnglish
Pages (from-to)294-300
Number of pages7
JournalTheoretical Computer Science
Issue number1-3
StatePublished - 20 Mar 2008


  • Computational geometry
  • Data structure
  • Segment dragging problem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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