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.
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© 2006 Springer-Verlag Berlin Heidelberg
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Amarnadh, N., Mitra, P. (2006). Upper Bound on Dilation of Triangulations of Cyclic Polygons. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_1
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DOI: https://doi.org/10.1007/11751540_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34070-6
Online ISBN: 978-3-540-34071-3
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