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Improved Routing on the Delaunay Triangulation

Abstract : A geometric graph G = (P,E) is a set of points in the plane and edges between pairs of points, where the weight of the edge is equal to the Euclidean distance between the points. In k-local routing we find a path through G from a source vertex s to a destination vertex t, using only knowledge of the present location, the locations of s and t, and the k-neighbourhood of the current vertex. We present an algorithm for 1-local routing on the Delaunay triangulation, and show that it finds a path between a source vertex s and a target vertex t that is not longer than 3.56|st|, improving the previous bound of 5.9.
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https://hal.archives-ouvertes.fr/hal-01881280
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Submitted on : Friday, October 12, 2018 - 10:53:48 AM
Last modification on : Friday, January 21, 2022 - 3:10:53 AM
Long-term archiving on: : Sunday, January 13, 2019 - 4:41:12 PM

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Nicolas Bonichon, Prosenjit Bose, Jean-Lou de Carufel, Vincent Despré, Darryl Hill, et al.. Improved Routing on the Delaunay Triangulation. ESA 2018 - 26th Annual European Symposium on Algorithms, Aug 2018, Helsinki, Finland. ⟨10.4230/LIPIcs.ESA.2018.22⟩. ⟨hal-01881280⟩

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