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Upper Bound on Dilation of Triangulations of Cyclic Polygons

  • Narayanasetty Amarnadh
  • Pinaki Mitra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3980)

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.

Keywords

Short Path Planar Graph Delaunay Triangulation Convex Polygon Arbitrary Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Narayanasetty Amarnadh
    • 1
  • Pinaki Mitra
    • 1
  1. 1.Department of Computer Science & EngineeringIndian Institute of TechnologyGuwahatiIndia

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