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  Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm

Brönnimann, H., Kettner, L., Pocchiola, M., & Snoeyink, J. (2006). Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm. SIAM Journal on Computing, 36(3), 721-739.

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Kettner2006PseudoTEnum.pdf (Verlagsversion), 5KB
 
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 Urheber:
Brönnimann, Hervé, Autor
Kettner, Lutz1, Autor           
Pocchiola, Michel, Autor
Snoeyink, Jack, Autor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Zusammenfassung: This paper studies pseudo-triangulations for a given point set in the plane. Pseudo-triangulations have many properties of triangulations, and have more freedom since polygons with more than three vertices are allowed as long as they have exactly three inner angles less than $\pi$. In particular, there is a natural flip operation on every internal edge. We present an algorithm to enumerate the pseudo-triangulations of a given point set, based on the greedy flip algorithm of Pocchiola and Vegter [Topologically sweeping visibility complexes via pseudo-triangulations; \emph{Discrete Comput.\ Geom.}\ 16:419 453, 1996]. Our two independent implementations agree, and allow us to experimentally verify or disprove conjectures on the numbers of pseudo-triangulations and triangulations of a given point set. (For example, we establish that the number of triangulations is bounded by than the number of pseudo-triangulations for all sets of up to 10 points.)

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Sprache(n): eng - English
 Datum: 2008-02-282006
 Publikationsstatus: Erschienen
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 Ort, Verlag, Ausgabe: -
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 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: eDoc: 356755
Anderer: Local-ID: C12573CC004A8E26-512A66D02FF267B9C1257263006F7D0D-Kettner2006PseudoTEnum
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Titel: SIAM Journal on Computing
Genre der Quelle: Zeitschrift
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Seiten: - Band / Heft: 36 (3) Artikelnummer: - Start- / Endseite: 721 - 739 Identifikator: ISSN: 0097-5397