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Local Routing in Sparse and Lightweight Geometric Graphs

Authors Vikrant Ashvinkumar, Joachim Gudmundsson, Christos Levcopoulos, Bengt J. Nilsson, André van Renssen

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Computational geometry
  • Spanners
  • Routing

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Abstract

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.

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Vikrant Ashvinkumar, Joachim Gudmundsson, Christos Levcopoulos, Bengt J. Nilsson, and André van Renssen. Local Routing in Sparse and Lightweight Geometric Graphs. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ISAAC.2019.30

Author Details

Vikrant Ashvinkumar
  • University of Sydney, Australia
Joachim Gudmundsson
  • University of Sydney, Australia
Christos Levcopoulos
  • Lund University, Sweden
Bengt J. Nilsson
  • Malmö University, Sweden
André van Renssen
  • University of Sydney, Australia

Funding

  • Gudmundsson, Joachim: Funded by the Australian Government through the Australian Research Council DP150101134 and DP180102870.
  • Levcopoulos, Christos: Swedish Research Council grants 2017-03750 and 2018-04001.

References

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