The Stretch Factor of $L_1$- and $L_\infty$-Delaunay Triangulations
BONICHON, Nicolas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
GAVOILLE, Cyril
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Institut universitaire de France [IUF]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Institut universitaire de France [IUF]
HANUSSE, Nicolas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Leer más >
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
BONICHON, Nicolas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
GAVOILLE, Cyril
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Institut universitaire de France [IUF]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Institut universitaire de France [IUF]
HANUSSE, Nicolas
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
Laboratoire Bordelais de Recherche en Informatique [LaBRI]
Algorithmics for computationally intensive applications over wide scale distributed platforms [CEPAGE]
PERKOVIC, Ljubomir
School of Computer Science, Telecommunications, and Information Systems [DePaul] [CTI]
School of Computing [DePaul] [SOC]
< Leer menos
School of Computer Science, Telecommunications, and Information Systems [DePaul] [CTI]
School of Computing [DePaul] [SOC]
Idioma
en
Rapport
Resumen en inglés
In this paper we determine the stretch factor of the $L_1$-Delaunay and $L_\infty$-Delaunay triangulations, and we show that this stretch is $\sqrt{4+2\sqrt{2}} \approx 2.61$. Between any two points $x,y$ of such triangulations, ...Leer más >
In this paper we determine the stretch factor of the $L_1$-Delaunay and $L_\infty$-Delaunay triangulations, and we show that this stretch is $\sqrt{4+2\sqrt{2}} \approx 2.61$. Between any two points $x,y$ of such triangulations, we construct a path whose length is no more than $\sqrt{4+2\sqrt{2}}$ times the Euclidean distance between $x$ and $y$, and this bound is best possible. This definitively improves the 25-year old bound of $\sqrt{10}$ by Chew (SoCG~'86). To the best of our knowledge, this is the first time the stretch factor of the well-studied $L_p$-Delaunay triangulations, for any real $p\ge 1$, is determined exactly.< Leer menos
Palabras clave en inglés
Delaunay triangulations
$L_1$-metric
$L_\infty$-metric
stretch factor
Orígen
Importado de HalCentros de investigación