### Abstract

It is shown in this paper that the minimum distance between two finite planar sets of n points can be computer in O(n log n) worst-case running time and that this is optimal to within a constant factor. Furthermore, when the sets form a convex polygon this complexity can be reduced O(n).

Original language | English (US) |
---|---|

Pages (from-to) | 79-82 |

Number of pages | 4 |

Journal | Pattern Recognition Letters |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1983 |

### Keywords

- algorithms
- cluster analysis
- coloring problems
- complexity
- computational geometry
- convex polygons
- Minimum distance between sets
- pattern recognition

### ASJC Scopus subject areas

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Artificial Intelligence

### Cite this

*Pattern Recognition Letters*,

*2*(2), 79-82. https://doi.org/10.1016/0167-8655(83)90041-7

**Optimal algorithms for computing the minimum distance between two finite planar sets.** / Toussaint, Godfried; Bhattacharya, Binay K.

Research output: Contribution to journal › Article

*Pattern Recognition Letters*, vol. 2, no. 2, pp. 79-82. https://doi.org/10.1016/0167-8655(83)90041-7

}

TY - JOUR

T1 - Optimal algorithms for computing the minimum distance between two finite planar sets

AU - Toussaint, Godfried

AU - Bhattacharya, Binay K.

PY - 1983/1/1

Y1 - 1983/1/1

N2 - It is shown in this paper that the minimum distance between two finite planar sets of n points can be computer in O(n log n) worst-case running time and that this is optimal to within a constant factor. Furthermore, when the sets form a convex polygon this complexity can be reduced O(n).

AB - It is shown in this paper that the minimum distance between two finite planar sets of n points can be computer in O(n log n) worst-case running time and that this is optimal to within a constant factor. Furthermore, when the sets form a convex polygon this complexity can be reduced O(n).

KW - algorithms

KW - cluster analysis

KW - coloring problems

KW - complexity

KW - computational geometry

KW - convex polygons

KW - Minimum distance between sets

KW - pattern recognition

UR - http://www.scopus.com/inward/record.url?scp=0021058680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021058680&partnerID=8YFLogxK

U2 - 10.1016/0167-8655(83)90041-7

DO - 10.1016/0167-8655(83)90041-7

M3 - Article

AN - SCOPUS:0021058680

VL - 2

SP - 79

EP - 82

JO - Pattern Recognition Letters

JF - Pattern Recognition Letters

SN - 0167-8655

IS - 2

ER -