Topology Control with Limited Geometric Information
Topology control is the problem of selecting neighbors for each node in a wireless network, so that the resulting network has a number of useful properties. More precisely, a topology control protocol P takes as input a network G and aims to construct a spanning subgraph GP, that is sparse, “energy minimizing” and has sufficient connectivity so as to guarantee multiple short paths between pairs of nodes in G. Currently, topology control protocols assume that nodes in G reside in some Euclidean (usually, 2-dimensional) space and rely on geometric information such as node locations and pairwise distances between nodes to produce GP with appropriate properties. However, these protocols are extremely sensitive to errors in location information and this feature makes them impractical because errors in location and distance information are pervasive in practical systems. This paper presents and analyzes two randomized topology control protocols that are tolerant to errors in pairwise distance estimates. The first protocol, called RTC (short for randomized topology control) uses no geometric information, relying only on connectivity information and is therefore completely immune to errors in location or distance information. The second protocol, called ε-RTC, generalizes the first protocol. Allowing for errors in distance estimates, but assuming that relative errors are bounded above by ε, the second protocol produces an output network that is symmetric, connected, sparse, and has good spanner properties. As \(\varepsilon \longrightarrow 0\), ε-RTC behaves like the XTC protocol (R. Wattenhofer and A. Zollinger, “XTC: A practical topology control algorithm for ad-hoc networks”, WMAN 2004) and for large values of ε, it behaves like RTC. Our results hold whenever the input network is a unit disk graph or even a quasi unit disk graph.
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- 1.Barriére, L., Fraigniaud, P., Narayanan, L.: Robust position-based routing in wireless ad hoc networks with unstable transmission ranges. In: Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications (DIALM), pp. 19–27 (2001)Google Scholar
- 2.Bulusu, N., Heidemann, J., Estrin, D.: GPS-less low cost outdoor localization for very small devices. IEEE Wireless Communications 7(5), 27–34 (2000)Google Scholar
- 3.Capkun, S., Hamdi, M., Hubaux, J.: Gps-free positioning in mobile ad-hoc networks. In: Proceedings of the 34th Annual Hawaii International Conference on System Sciences (HICSS), vol. 9, p. 9008. IEEE Computer Society Press, Washington, DC, USA (2001)Google Scholar
- 5.Harris, F.K., Belecki, N.B., Soulen Jr., R.J.: Measurements and instruments. In: Fink, D.G., Beaty, H.W. (eds.) Standard Handbook for Electrical Engineers, pp. 3–1–3–98. McGraw-Hill, New York (1987)Google Scholar
- 6.Li, L., Halpern, J., Bahl, V., Wang, Y.-M., Wattenhofer, R.: Analysis of a cone-based distributed topology control algorithm for wireless multihop networks. In: Twentieth ACM Symposium on Principles of Distributed Computing (PODC) (2001)Google Scholar
- 7.Li, X.-Y., Calinescu, G., Wan, P.: Distributed construction of planar spanner and routing for ad hoc wireless networks. In: Proceedings of the 21st Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM) (2002)Google Scholar
- 9.Li, X.-Y., Wang, Y.: Efficient construction of low weight bounded degree planar spanner. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697. Springer, Heidelberg (2003)Google Scholar
- 10.Lillis, K., Pemmaraju, S.: Topology control with limited geometric information (2005), Full paper http://www.cs.uiowa.edu/~sriram/randomTopControl.pdf
- 11.Moore, D., Leonard, J., Rus, D., Teller, S.: Robust distributed network localization with noisy range measurements. In: Proceedings of the Second ACM Conference on Embedded Networked Sensor Systems (SenSys) (2004)Google Scholar
- 13.Priyantha, N.B., Chakraborty, A., Balakrishnan, H.: The cricket location-support system. In: Mobile Computing and Networking, pp. 32–43 (2000)Google Scholar
- 14.Song, W.-Z., Wang, Y., Li, X.-Y., Frieder, O.: Localized algorithms for energy efficient topology in wireless ad hoc networks. In: Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc), pp. 98–108. ACM Press, New York (2004)Google Scholar
- 15.Wattenhofer, R., Zollinger, A.: XTC: A practical topology control algorithm for ad-hoc networks. In: 4th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN) (2004)Google Scholar