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An improved upper bound on dilation of regular polygons

Sattari, S ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.comgeo.2019.01.009
  3. Publisher: Elsevier B.V , 2019
  4. Abstract:
  5. Dilation of a set of points on the plane is the lowest possible dilation of a plane spanner on the point set. We show that dilation of vertices of any regular polygon is less than 1.4482. We introduce a method for constructing a triangulation of a regular polygon and prove this bound on its dilation. The upper bound on dilation is shown using mathematical proofs and experimental results. The new upper bound improves the previously known bound of 1.48454. © 2019 Elsevier B.V
  6. Keywords:
  7. Dilation ; Plane spanner ; Regular polygon ; Triangulation ; A-plane ; Mathematical proof ; Point set ; Upper Bound ; Geometry
  8. Source: Computational Geometry: Theory and Applications ; Volume 80 , 2019 , Pages 53-68 ; 09257721 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0925772118300622