Triangulations intersect nicely

Oswin Aichholzer, Franz Aurenhammer, Siu-Wing Cheng, N. Katoh, G. Rote, M. Taschwer, Yin-Feng Xu

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)339-359
JournalDiscrete & computational geometry
Volume16
Issue number4
Publication statusPublished - 1996

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Triangulation
Intersect
Independence System
Network Flow
Point Sets
Set of points
Triangle
Polynomial time
Polynomials
Lower bound
Theorem

Treatment code (Nähere Zuordnung)

  • Theoretical

Cite this

Aichholzer, O., Aurenhammer, F., Cheng, S-W., Katoh, N., Rote, G., Taschwer, M., & Xu, Y-F. (1996). Triangulations intersect nicely. 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.

In: Discrete & computational geometry, Vol. 16, No. 4, 1996, p. 339-359.

Research output: Contribution to journalArticleResearchpeer-review

Aichholzer, O, Aurenhammer, F, Cheng, S-W, Katoh, N, Rote, G, Taschwer, M & Xu, Y-F 1996, 'Triangulations intersect nicely' Discrete & computational geometry, vol. 16, no. 4, pp. 339-359.
Aichholzer O, Aurenhammer F, Cheng S-W, Katoh N, Rote G, Taschwer M et al. Triangulations intersect nicely. Discrete & computational geometry. 1996;16(4):339-359.
Aichholzer, Oswin ; Aurenhammer, Franz ; Cheng, Siu-Wing ; Katoh, N. ; Rote, G. ; Taschwer, M. ; Xu, Yin-Feng. / Triangulations intersect nicely. In: Discrete & computational geometry. 1996 ; Vol. 16, No. 4. pp. 339-359.
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AU - Xu, Yin-Feng

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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.

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