Planar hop spanners for unit disk graphs

Authors:
Nicolas Catusse;Victor Chepoi;Yann Vaxès
Affiliations:
Laboratoire d'Informatique Fondamentale, Université d'Aix-Marseille, Faculté des Sciences de Luminy, Marseille Cedex 9, France;Laboratoire d'Informatique Fondamentale, Université d'Aix-Marseille, Faculté des Sciences de Luminy, Marseille Cedex 9, France;Laboratoire d'Informatique Fondamentale, Université d'Aix-Marseille, Faculté des Sciences de Luminy, Marseille Cedex 9, France
Venue:
ALGOSENSORS'10 Proceedings of the 6th international conference on Algorithms for sensor systems, wireless adhoc networks, and autonomous mobile entities
Year:
2010

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Abstract

The simplest model of a wireless network graph is the Unit Disk Graph (UDG): an edge exists in UDG if the Euclidean distance between its endpoints is ≤ 1. The problem of constructing planar spanners of Unit Disk Graphs with respect to the Euclidean distance has received considerable attention from researchers in computational geometry and ad-hoc wireless networks. In this paper, we present an algorithm that, given a set X of terminals in the plane, constructs a planar hop spanner with constant stretch factor for the Unit Disk Graph defined by X. Our algorithm improves on previous constructions in the sense that (i) it ensures the planarity of the whole spanner while previous algorithms ensure only the planarity of a backbone subgraph; (ii) the hop stretch factor of our spanner is significantly smaller.