### Abstract

Until recently no algorithm existed for computing the relative neighbourhood graph of n points on the plane in less than O(n^{2}) worst-case time. Urquhart recently presented an O(n log n) algorithm for solving this problem. In this letter it is shown that Urquhart's algorithm does not always work and hence finding an O(n log n) algorithm remains an open problem.

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

Number of pages | 1 |

Journal | Electronics Letters |

Volume | 16 |

Issue number | 22 |

DOIs | |

State | Published - Oct 23 1980 |

### Keywords

- Algorithms
- Graph theory
- Pattern recognition

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

**Comment : Algorithms for computing relative neighbourhood graph.** / Toussaint, Godfried.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Comment

T2 - Algorithms for computing relative neighbourhood graph

AU - Toussaint, Godfried

PY - 1980/10/23

Y1 - 1980/10/23

N2 - Until recently no algorithm existed for computing the relative neighbourhood graph of n points on the plane in less than O(n2) worst-case time. Urquhart recently presented an O(n log n) algorithm for solving this problem. In this letter it is shown that Urquhart's algorithm does not always work and hence finding an O(n log n) algorithm remains an open problem.

AB - Until recently no algorithm existed for computing the relative neighbourhood graph of n points on the plane in less than O(n2) worst-case time. Urquhart recently presented an O(n log n) algorithm for solving this problem. In this letter it is shown that Urquhart's algorithm does not always work and hence finding an O(n log n) algorithm remains an open problem.

KW - Algorithms

KW - Graph theory

KW - Pattern recognition

UR - http://www.scopus.com/inward/record.url?scp=85012591507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85012591507&partnerID=8YFLogxK

U2 - 10.1049/el:19800611

DO - 10.1049/el:19800611

M3 - Article

VL - 16

JO - Electronics Letters

JF - Electronics Letters

SN - 0013-5194

IS - 22

ER -