On the Geometric Dilation of Finite Point Sets

Let G be an embedded planar graph whose edges may be curves. For two arbitrary points of G, we can compare the length of the shortest path in G connecting them against their Euclidean distance. The maximum of all these ratios is called the geometric dilation of G. Given a finite point set, we would like to know the smallest possible dilation of any graph that contains the given points. In this paper we

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Annette Ebbers-Baumann, Ansgar Grüne, Rolf Klein
• Keywords: Arbitrary Points, ISAAC 2003, Planar Graph, Smallest Possible Dilation