### Abstract

Given a simple polygon P of n vertices, we present an algorithm that finds the pair of points on the boundary of P that maximizes the external shortest path between them. This path is defined as the external geodesic diameter of P. The algorithm takes 0(n^{2}) time and requires 0(n) space. Surprisingly, this problem is quite different from that of computing the internal geodesic diameter of P. While the internal diameter is determined by a pair of vertices of P, this is not the case for the external diameter. Finally, we show how this algorithm can be extended to solve the all external geodesic furthest neighbours problem.

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

Pages (from-to) | 1-19 |

Number of pages | 19 |

Journal | Computing |

Volume | 44 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 1990 |

### Fingerprint

### Keywords

- algorithm
- AMS Subject Classifications: 68U05, 68C25
- complexity
- computational geometry
- diameter
- furthest neighbour
- geodesics
- Polygon

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computing*,

*44*(1), 1-19. https://doi.org/10.1007/BF02247961

**Computing the external geodesic diameter of a simple polygon.** / Samuel, D.; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Computing*, vol. 44, no. 1, pp. 1-19. https://doi.org/10.1007/BF02247961

}

TY - JOUR

T1 - Computing the external geodesic diameter of a simple polygon

AU - Samuel, D.

AU - Toussaint, Godfried

PY - 1990/3/1

Y1 - 1990/3/1

N2 - Given a simple polygon P of n vertices, we present an algorithm that finds the pair of points on the boundary of P that maximizes the external shortest path between them. This path is defined as the external geodesic diameter of P. The algorithm takes 0(n2) time and requires 0(n) space. Surprisingly, this problem is quite different from that of computing the internal geodesic diameter of P. While the internal diameter is determined by a pair of vertices of P, this is not the case for the external diameter. Finally, we show how this algorithm can be extended to solve the all external geodesic furthest neighbours problem.

AB - Given a simple polygon P of n vertices, we present an algorithm that finds the pair of points on the boundary of P that maximizes the external shortest path between them. This path is defined as the external geodesic diameter of P. The algorithm takes 0(n2) time and requires 0(n) space. Surprisingly, this problem is quite different from that of computing the internal geodesic diameter of P. While the internal diameter is determined by a pair of vertices of P, this is not the case for the external diameter. Finally, we show how this algorithm can be extended to solve the all external geodesic furthest neighbours problem.

KW - algorithm

KW - AMS Subject Classifications: 68U05, 68C25

KW - complexity

KW - computational geometry

KW - diameter

KW - furthest neighbour

KW - geodesics

KW - Polygon

UR - http://www.scopus.com/inward/record.url?scp=0025249046&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025249046&partnerID=8YFLogxK

U2 - 10.1007/BF02247961

DO - 10.1007/BF02247961

M3 - Article

AN - SCOPUS:0025249046

VL - 44

SP - 1

EP - 19

JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

SN - 0010-485X

IS - 1

ER -