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Maximum Rigid Components as Means for Direction-Based Localization in Sensor Networks

  • Bastian Katz
  • Marco Gaertler
  • Dorothea Wagner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4362)

Abstract

Many applications in sensor networks require positional information of the sensors. Recovering node positions is closely related to graph realization problems for geometric graphs. Here, we address the case where nodes have angular information. Whereas Bruck et al. proved that the corresponding realization problem together with unit-disk-graph-constraints is \(\mathcal{NP}\)-hard [2], we focus on rigid components which allow both efficient identification and fast, unique realizations. Our technique allows to identify maximum rigid components in graphs with partially known rigid components using a reduction to maximum flow problems. This approach is analyzed for the two-dimensional case, but can easily be extended to higher dimensions.

Keywords

Sensor Network Node Density Intersection Network Geometric Graph Unit Disk Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aspnes, J., Goldenberg, D., Yang, Y.R.: On the computational complexity of sensor network localization. In: Nikoletseas, S.E., Rolim, J.D.P. (eds.) ALGOSENSORS 2004. LNCS, vol. 3121, pp. 32–44. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Bruck, J., Gao, J., Jiang, A.: Localization and Routing in Sensor Networks by Local Angle Information, pp. 181–192. ACM Press, New York (2005)Google Scholar
  3. 3.
    Hendrickson, B.: Conditions for Unique Graph Realizations. SIAM J. Comput. 21(1), 65–84 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Jacobs, D., Hendrickson, B.: An Algorithm for Two Dimensional Rigidity Percolation: The Pebble Game (1997)Google Scholar
  5. 5.
    Katz, B.: Richtungsbasierte Lokalisierung von Sensornetzwerken (German). Master’s Thesis (2006)Google Scholar
  6. 6.
    Katz, B., Gaertler, M., Wagner, D.: Maximum Rigid Components as Means for Direction-Based Localization in Sensor Networks. Technical Report 2006-17, Universität Karlsruhe (2006)Google Scholar
  7. 7.
    Kuhn, F., Wattenhofer, R., Zollinger, A.: Ad-Hoc Networks Beyond Unit Disk Graphs. In: DIALM-POMC’03: Proceedings of the Joint Workshop on Foundations of Mobile Computing, pp. 69–78. ACM Press, New York (2003)CrossRefGoogle Scholar
  8. 8.
    Moukarzel, C.: An Efficient Algorithm for Testing the Generic Rigidity of Graphs in the Plane. J. Phys. A: Math. Gen. 29, 8079 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Saxe, J.B.: Embeddability of Weighted Graphs in k-Space is Strongly NP-Hard. In: Proc. 17th Allerton Conf. Commun. Control Comput. pp. 480–489 (1979)Google Scholar
  10. 10.
    Tubaishat, M., Madria, S.: Sensor Networks: An Overview. IEEE Potentials 22(2), 20–23 (2003)CrossRefGoogle Scholar
  11. 11.
    Whiteley, W.: Matroids from Discrete Applied Geometry. In: Matroid Theory, AMS Contemporary Mathematics, pp. 171–311 (1996)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Bastian Katz
    • 1
  • Marco Gaertler
    • 1
  • Dorothea Wagner
    • 1
  1. 1.Faculty of Informatics, Universität Karlsruhe (TH)Germany

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