Enclosing k points in the smallest axis parallel rectangle

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


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
Issue number2
StatePublished - 1 Jan 1998


  • Algorithms
  • Axis parallel
  • Computational geometry
  • Optimization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Information Systems
  • Computer Science Applications


Dive into the research topics of 'Enclosing k points in the smallest axis parallel rectangle'. Together they form a unique fingerprint.

Cite this