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.
This work was partially supported by the German Research Foundation (DFG) within the Research Training Group GRK 1194 ”Self-organizing Sensor-Actuator Networks”, and under grant WA 654/14-3 and by EU under grant DELIS (contract no. 001907).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Bruck, J., Gao, J., Jiang, A.: Localization and Routing in Sensor Networks by Local Angle Information, pp. 181–192. ACM Press, New York (2005)
Hendrickson, B.: Conditions for Unique Graph Realizations. SIAM J. Comput. 21(1), 65–84 (1992)
Jacobs, D., Hendrickson, B.: An Algorithm for Two Dimensional Rigidity Percolation: The Pebble Game (1997)
Katz, B.: Richtungsbasierte Lokalisierung von Sensornetzwerken (German). Master’s Thesis (2006)
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)
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)
Moukarzel, C.: An Efficient Algorithm for Testing the Generic Rigidity of Graphs in the Plane. J. Phys. A: Math. Gen. 29, 8079 (1996)
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)
Tubaishat, M., Madria, S.: Sensor Networks: An Overview. IEEE Potentials 22(2), 20–23 (2003)
Whiteley, W.: Matroids from Discrete Applied Geometry. In: Matroid Theory, AMS Contemporary Mathematics, pp. 171–311 (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Katz, B., Gaertler, M., Wagner, D. (2007). Maximum Rigid Components as Means for Direction-Based Localization in Sensor Networks. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds) SOFSEM 2007: Theory and Practice of Computer Science. SOFSEM 2007. Lecture Notes in Computer Science, vol 4362. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69507-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-540-69507-3_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69506-6
Online ISBN: 978-3-540-69507-3
eBook Packages: Computer ScienceComputer Science (R0)