Upper bounds for minimum dilation triangulation in two special cases

Sattari, S ; Sharif University of Technology | 2018

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ipl.2018.01.001
  3. Publisher: Elsevier B.V , 2018
  4. Abstract:
  5. Give a triangulation of a set of points on the plane, dilation of any two points is defined as the ratio between the length of the shortest path of these points and their Euclidean distance. Minimum dilation triangulation is a triangulation in which the maximum dilation between any pair of the points is minimized. We give upper bounds on the dilation of the minimum dilation triangulation for two kinds of point sets: An upper bound of nsin⁡(π/n)/2 for a centrally symmetric convex point set containing n points, and an upper bound of 1.19098 for a set of points on the boundary of a semicircle. © 2018 Elsevier B.V
  6. Keywords:
  7. Computational geometry ; Dilation ; Point set ; Triangulation ; Geometry ; Euclidean distance ; Point set ; Shortest path ; Two-point ; Upper Bound ; Surveying
  8. Source: Information Processing Letters ; Volume 133 , 2018 , Pages 33-38 ; 00200190 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0020019018300103