### Abstract

Original language | English |
---|---|

Pages (from-to) | 339-359 |

Journal | Discrete & computational geometry |

Volume | 16 |

Issue number | 4 |

Publication status | Published - 1996 |

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### Treatment code (Nähere Zuordnung)

- Theoretical

### Cite this

*Discrete & computational geometry*,

*16*(4), 339-359.

**Triangulations intersect nicely.** / Aichholzer, Oswin; Aurenhammer, Franz; Cheng, Siu-Wing; Katoh, N. ; Rote, G. ; Taschwer, M.; Xu, Yin-Feng.

Research output: Contribution to journal › Article › Research › peer-review

*Discrete & computational geometry*, vol. 16, no. 4, pp. 339-359.

}

TY - JOUR

T1 - Triangulations intersect nicely

AU - Aichholzer, Oswin

AU - Aurenhammer, Franz

AU - Cheng, Siu-Wing

AU - Katoh, N.

AU - Rote, G.

AU - Taschwer, M.

AU - Xu, Yin-Feng

N1 - Special Issue. [SFB Report F003-030, TU Graz, Austria, 1995]

PY - 1996

Y1 - 1996

N2 - We show that there is a matching between the edges of any two triangulations of a planar point set such that an edge of one triangulation is matched either to the identical edge in the other triangulation or to an edge that crosses it. This theorem also holds for the triangles of the triangulations and in general independence systems. As an application, we give some lower bounds for the minimum-weight triangulation which can be computed in polynomial time by matching and network-flow techniques. We exhibit an easy-to-recognize class of point sets for which the minimum-weight triangulation coincides with the greedy triangulation.

AB - We show that there is a matching between the edges of any two triangulations of a planar point set such that an edge of one triangulation is matched either to the identical edge in the other triangulation or to an edge that crosses it. This theorem also holds for the triangles of the triangulations and in general independence systems. As an application, we give some lower bounds for the minimum-weight triangulation which can be computed in polynomial time by matching and network-flow techniques. We exhibit an easy-to-recognize class of point sets for which the minimum-weight triangulation coincides with the greedy triangulation.

M3 - Article

VL - 16

SP - 339

EP - 359

JO - Discrete & computational geometry

JF - Discrete & computational geometry

SN - 0179-5376

IS - 4

ER -