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.
This research was partly supported by the ANR grant BLAN06-1-13889 (projet OPTICOMB).
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References
Alzoubi, K., Li, X., Wang, Y., Wan, P., Frieder, O.: Geometric spanners for wireless ad hoc networks. IEEE Trans. Par. Dist. Syst. 14, 408–421 (2003)
Bose, P., Devroye, L., Evans, W., Kirkpatrick, D.: On the spanning ratio of Gabriel graphs and β-skeletons. SIAM J. Discr. Math. 20, 412–427 (2006)
Bose, P., Smid, M.: On plane geometric spanners: a survey and open problems (2009) (submitted)
Chen, J., Jiang, A., Kanj, I.A., Xia, G., Zhang, F.: Separability and topology control of quasi unit disk graphs. In: INFOCOM 2007, pp. 2225–2233 (2007)
Eppstein, D.: Spanning trees and spanners. In: Sack, J.-R., Urrutia, J. (eds.) Handbook of Computational Geometry, pp. 425–461. Elsevier Science Publishers B.V., North-Holland, Amsterdam (2000)
Fürer, M., Kasiviswanathan, S.P.: Spanners for geometric intersection graphs. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 312–324. Springer, Heidelberg (2007)
Gao, J., Guibas, L.J., Hershberger, J., Zhang, L., Zhu, A.: Discrete mobile centers. Discr. Comput. Geom. 30(1), 45–63 (2003)
Gao, J., Guibas, L., Hershberger, J., Zhang, L., Zhu, A.: Geometric spanner for routing in mobile networks. In: ACM MobiHoc 2001, pp. 45–55 (2001)
Li, X., Cǎlinescu, G., Wan, P.: Distributed construction of planar spanner and routing for ad hoc wireless networks. In: INFOCOM 2002 (2002)
Narasimhan, G., Smid, M.: Geometric Spanner Networks. Cambridge University Press, Cambridge (2007)
Rührup, S.: Position-based Routing Strategies, PhD Thesis, University of Paderborn, Germany (2006)
Yan, C., Xiang, Y., Dragan, F.F.: Compact and low delay routing labeling scheme for unit disk graphs. In: WADS 2009, pp. 566–577 (2009)
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Catusse, N., Chepoi, V., Vaxès, Y. (2010). Planar Hop Spanners for Unit Disk Graphs. In: Scheideler, C. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2010. Lecture Notes in Computer Science, vol 6451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16988-5_2
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DOI: https://doi.org/10.1007/978-3-642-16988-5_2
Publisher Name: Springer, Berlin, Heidelberg
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