Local Routing in Sparse and Lightweight Geometric Graphs
Online routing in a planar embedded graph is central to a number of fields and has been studied extensively in the literature. For most planar graphs no O(1)-competitive online routing algorithm exists. A notable exception is the Delaunay triangulation for which Bose and Morin [Bose and Morin, 2004] showed that there exists an online routing algorithm that is O(1)-competitive. However, a Delaunay triangulation can have Omega(n) vertex degree and a total weight that is a linear factor greater than the weight of a minimum spanning tree.
We show a simple construction, given a set V of n points in the Euclidean plane, of a planar geometric graph on V that has small weight (within a constant factor of the weight of a minimum spanning tree on V), constant degree, and that admits a local routing strategy that is O(1)-competitive. Moreover, the technique used to bound the weight works generally for any planar geometric graph whilst preserving the admission of an O(1)-competitive routing strategy.
Computational geometry
Spanners
Routing
Theory of computation~Design and analysis of algorithms
30:1-30:13
Regular Paper
A full version of the paper is available at https://arxiv.org/abs/1909.10215.
Vikrant
Ashvinkumar
Vikrant Ashvinkumar
University of Sydney, Australia
Joachim
Gudmundsson
Joachim Gudmundsson
University of Sydney, Australia
Funded by the Australian Government through the Australian Research Council DP150101134 and DP180102870.
Christos
Levcopoulos
Christos Levcopoulos
Lund University, Sweden
Swedish Research Council grants 2017-03750 and 2018-04001.
Bengt J.
Nilsson
Bengt J. Nilsson
Malmö University, Sweden
André
van Renssen
André van Renssen
University of Sydney, Australia
10.4230/LIPIcs.ISAAC.2019.30
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Vikrant Ashvinkumar, Joachim Gudmundsson, Christos Levcopoulos, Bengt J. Nilsson, and André van Renssen
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