### Abstract

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 log^{2} n). When only O(n log n) storage is allowed, the running time is O(nk log^{2} 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 language | English (US) |
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Pages (from-to) | 119-136 |

Number of pages | 18 |

Journal | Computational Geometry: Theory and Applications |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1994 |

Externally published | Yes |

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### Keywords

- Geometric optimization
- Smallest enclosing circle

### ASJC Scopus subject areas

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

### Cite this

*Computational Geometry: Theory and Applications*,

*4*(3), 119-136. https://doi.org/10.1016/0925-7721(94)90003-5