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On spanning properties of various Delaunay graphs

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1 Author(s)
Bose, P. ; Sch. of Comput. Sci., Carleton Univ., Ottawa, ON, Canada

A geometric graph G is a graph whose vertices are points in the plane and whose edges are line segments weighted by the Euclidean distance between their endpoints. In this setting, a t-spanner of G is a connected spanning subgraph G' with the property that for every pair of vertices x, y, the shortest path from x to y in G' has weight at most L ≥ 1 times the shortest path from x to y in G. The parameter t is commonly referred to as the spanning ratio or the stretch factor. Among the many beautiful properties that Delaunay graphs possess, a constant spanning ratio is one of them. We provide a comprehensive overview of various results concerning the spanning ratio among other properties of different types of Delaunay graphs and their subgraphs.

Published in:

Voronoi Diagrams in Science and Engineering (ISVD), 2012 Ninth International Symposium on

Date of Conference:

27-29 June 2012