Given a planar graph G, the dilation between two points of a Euclidean graph is defined as the ratio of the length of the shortest path between the points to the Euclidean distance between the points. The dilation of a graph is defined as the maximum over all vertex pairs (u,v) of the dilation between u and v. In this paper we consider the upper bound on the dilation of triangulation over the set of vertices of a cyclic polygon. We have shown that if the triangulation is a fan (i.e. every edge of the triangulation starts from the same vertex), the dilation will be at most approximately 1.48454. We also show that if the triangulation is a star the dilation will be at most 1.18839. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Amarnadh, N., & Mitra, P. (2006). Upper bound on dilation of triangulations of cyclic polygons. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3980 LNCS, pp. 1–9). Springer Verlag. https://doi.org/10.1007/11751540_1
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