### Abstract

Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthest-site Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity θ(mn
^{2}), and the algorithm runs in O(mn
^{2} log
^{2} m(logm + logn)) time.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings |

Pages | 19-29 |

Number of pages | 11 |

Volume | 1533 LNCS |

State | Published - 1998 |

Event | 9th Annual International Symposium on Algorithms and Computation, ISAAC'98 - Taejon, Korea, Republic of Duration: Dec 14 1998 → Dec 16 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1533 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 9th Annual International Symposium on Algorithms and Computation, ISAAC'98 |
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Country | Korea, Republic of |

City | Taejon |

Period | 12/14/98 → 12/16/98 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings*(Vol. 1533 LNCS, pp. 19-29). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS).

**Facility location on terrains.** / Aronov, Boris; Van Kreveld, Marc; Van Oostrum, René; Varadarajan, Kasturirangan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings.*vol. 1533 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1533 LNCS, pp. 19-29, 9th Annual International Symposium on Algorithms and Computation, ISAAC'98, Taejon, Korea, Republic of, 12/14/98.

}

TY - GEN

T1 - Facility location on terrains

AU - Aronov, Boris

AU - Van Kreveld, Marc

AU - Van Oostrum, René

AU - Varadarajan, Kasturirangan

PY - 1998

Y1 - 1998

N2 - Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthest-site Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity θ(mn 2), and the algorithm runs in O(mn 2 log 2 m(logm + logn)) time.

AB - Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the surface of) a polyhedron. To compute the optimum placement, we compute the furthest-site Voronoi diagram of the sites on the polyhedron. The diagram has maximum combinatorial complexity θ(mn 2), and the algorithm runs in O(mn 2 log 2 m(logm + logn)) time.

UR - http://www.scopus.com/inward/record.url?scp=84867478123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867478123&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84867478123

SN - 3540653856

SN - 9783540653851

VL - 1533 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 19

EP - 29

BT - Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings

ER -