Improving shortest paths in the Delaunay triangulation

We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t, in the Delaunay triangulation of P ∪ {p}, improves as much as possible. We st...

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Detalles Bibliográficos
Autores: Abellanas, Manuel, Claverol Aguas, Mercè|||0000-0002-9138-8594, Hernández-Peñalver, Gregorio, Hurtado Díaz, Fernando Alfredo|||0000-0002-0108-9671, Sacristán Adinolfi, Vera|||0000-0003-0203-256X, Saumell Mendiola, Maria, Silveira, Rodrigo Ignacio|||0000-0003-0202-4543
Tipo de recurso: artículo
Fecha de publicación:2012
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/16981
Acceso en línea:https://hdl.handle.net/2117/16981
Access Level:acceso abierto
Palabra clave:Geometria integral
Triangulació
Trigonometria
Triangulation
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Descripción
Sumario:We study a problem about shortest paths in Delaunay triangulations. Given two nodes s, t in the Delaunay triangulation of a point set P, we look for a new point p that can be added, such that the shortest path from s to t, in the Delaunay triangulation of P ∪ {p}, improves as much as possible. We study several properties of the problem, and give efficient algorithms to find such point when the graph-distance used is Euclidean and for the link-distance. Several other variations of the problem are also discussed.

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