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On the number of higher order Delaunay triangulations
dc.contributor.author | Dieter Wilhelm, Mitsche |
dc.contributor.author | Saumell Mendiola, Maria |
dc.contributor.author | Silveira, Rodrigo Ignacio |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2011-01-31T13:38:56Z |
dc.date.available | 2011-01-31T13:38:56Z |
dc.date.created | 2010 |
dc.date.issued | 2010 |
dc.identifier.citation | Dieter, M.; Saumell, M.; Silveira, R.I. On the number of higher order Delaunay triangulations. A: International Conference on Algorithms and Complexity. "7th International Conference on Algorithms and Complexity". Springer Verlag, 2010, p. 217-228. |
dc.identifier.isbn | 978-3-642-13072-4 |
dc.identifier.uri | http://hdl.handle.net/2117/11237 |
dc.description.abstract | Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is 2n−3. Next we show that uniformly distributed points have an expected number of at least 2ρ1n(1+o(1)) first order Delaunay triangulations, where ρ1 is an analytically defined constant (ρ1 ≈ 0.525785), and for k > 1, the expected number of order-k Delaunay triangulations (which are not order-i for any i < k) is at least 2ρkn(1+o(1)), where ρk can be calculated numerically. |
dc.format.extent | 12 p. |
dc.language.iso | eng |
dc.publisher | Springer Verlag |
dc.subject | Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat |
dc.subject.lcsh | Delaunay triangulations |
dc.title | On the number of higher order Delaunay triangulations |
dc.type | Conference report |
dc.subject.lemac | Triangulació |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1007/978-3-642-13073-1_20 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.springerlink.com/content/a0792196316004gu |
dc.rights.access | Restricted access - publisher's policy |
local.identifier.drac | 2867995 |
dc.description.version | Postprint (published version) |
local.citation.author | Dieter, M.; Saumell, M.; Silveira, R.I. |
local.citation.contributor | International Conference on Algorithms and Complexity |
local.citation.publicationName | 7th International Conference on Algorithms and Complexity |
local.citation.startingPage | 217 |
local.citation.endingPage | 228 |