eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-11-28
30:1
30:13
10.4230/LIPIcs.ISAAC.2019.30
article
Local Routing in Sparse and Lightweight Geometric Graphs
Ashvinkumar, Vikrant
1
Gudmundsson, Joachim
1
Levcopoulos, Christos
2
Nilsson, Bengt J.
3
van Renssen, André
1
University of Sydney, Australia
Lund University, Sweden
Malmö University, Sweden
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol149-isaac2019/LIPIcs.ISAAC.2019.30/LIPIcs.ISAAC.2019.30.pdf
Computational geometry
Spanners
Routing