### Abstract

The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay (Voronoi) triangulation (DT). It is shown that the RNG is a superset of the MST and a subset of the DT. Two algorithms for obtaining the RNG of n points on the plane are presented. One algorithm runs in 0(n^{2}) time and the other runs in 0(n^{3}) time but works also for the d-dimensional case. Finally, several open problems concerning the RNG in several areas such as geometric complexity, computational perception, and geometric probability, are outlined.

Original language | English (US) |
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Pages (from-to) | 261-268 |

Number of pages | 8 |

Journal | Pattern Recognition |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - 1980 |

### Keywords

- Algorithms
- Computational perception
- Delaunay triangulation
- Dot patterns
- Geometric complexity Geometric probability
- Minimal spanning tree
- Pattern recognition
- Relative neighbourhood graph
- Triangulations

### ASJC Scopus subject areas

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