Enclosing k points in the smallest axis parallel rectangle

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30 Scopus citations

Abstract

We consider the following clustering problem. Given a set S of n points in the plane, and given an integer k, n/2 < k ≤ n, we want to find the smallest axis parallel rectangle (smallest perimeter or area) that encloses exactly k points of S. We present an algorithm which runs in time O(n + k(n - k)2) improving previous algorithms which run in time O(k2n) and do not perform well for larger k values. We present an algorithm to enclose k of n given points in an axis parallel box in d-dimensional space which runs in time O(dn + dk(n - k)2(d-1)) and occupies O(dn) space. We slightly improve algorithms for other problems whose runtimes depend on k.

Original languageEnglish
Pages (from-to)95-99
Number of pages5
JournalInformation Processing Letters
Volume65
Issue number2
DOIs
StatePublished - 1 Jan 1998

Keywords

  • Algorithms
  • Axis parallel
  • Computational geometry
  • Optimization

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