Computing the smallest k-enclosing circle and related problems

Alon Efrat, Micha Sharir, Alon Ziv

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


We present an efficient algorithm for solving the "smallest k-enclosing circle" (kSC) problem: Given a set of n points in the plane and an integer k ≤ n, find the smallest disk containing k of the points. We present two solutions. When using O(nk) storage, the problem can be solved in time O(nk log2 n). When only O(n log n) storage is allowed, the running time is O(nk log2 n log n/k). We also extend our technique to obtain efficient solutions of several related problems (with similar time and storage bounds). These related problems include: finding the smallest homothetic copy of a given convex polygon P which contains k points from a given planar set, and finding the smallest disk intersecting k segments from a given planar set of non-intersecting segments.

Original languageEnglish (US)
Pages (from-to)119-136
Number of pages18
JournalComputational Geometry: Theory and Applications
Issue number3
StatePublished - Jul 1994
Externally publishedYes


  • Geometric optimization
  • Smallest enclosing circle

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics


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