Upper bound on dilation of triangulations of cyclic polygons

Authors:
Narayanasetty Amarnadh;Pinaki Mitra
Affiliations:
Department of Computer Science & Engineering, Indian Institute of Technology, Guwahati, India;Department of Computer Science & Engineering, Indian Institute of Technology, Guwahati, India
Venue:
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Year:
2006

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Abstract

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.