Abstract
A network is called localizable if the positions of all the nodes of the network can be computed uniquely. If a network is localizable and embedded in plane with generic configuration, the positions of the nodes may be computed uniquely in finite time. Therefore, identifying localizable networks is an important function. If the complete information about the network is available at a single place, localizability can be tested in polynomial time. In a distributed environment, networks with trilateration orderings (popular in real applications) and wheel extensions (a specific class of localizable networks) embedded in plane can be identified by existing techniques. We propose a distributed technique which efficiently identifies a larger class of localizable networks. This class covers both trilateration and wheel extensions. In reality, exact distance is almost impossible or costly. The proposed algorithm based only on connectivity information. It requires no distance information.
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References
Aspnes, J., Eren, T., Goldenberg, D., Morse, A., Whiteley, W., Yang, Y., Anderson, B., Belhumeur, P.: A theory of network localization. IEEE Transactions on Mobile Computing 5(12), 1663–1678 (2006)
Biswas, P., Toh, K.-C., Ye, Y.: A distributed sdp approach for large-scale noisy anchor-free graph realization with applications to molecular conformation. SIAM J. Sci. Comput. 30(3), 1251–1277 (2008), http://dx.doi.org/10.1137/05062754X
Cakiroglu, A., Erten, C.: Fully decentralized and collaborative multilateration primitives for uniquely localizing wsns. EURASIP Journal on Wireless Communications and Networking 2010, Article ID 605658, 7 pages (2010)
Čapkun, S., Hamdi, M., Hubaux, J.P.: Gps-free positioning in mobile ad hoc networks. Cluster Computing 5, 157–167 (2002)
Connelly, R.: Generic global rigidity. Discrete and Computational Geometry 33(4), 549–563 (2005), http://dx.doi.org/10.1007/s00454-004-1124-4
Hendrickson, B.: Conditions for unique graph realizations. SIAM J. Comput. 21, 65–84 (1992)
Jackson, B., Jordán, T.: Connected rigidity matroids and unique realizations of graphs. Journal of Combinatorial Theory Series B 94(1), 1–29 (2005)
Kwon, O.H., Song, H.J., Park, S.: Anchor-free localization though flip-error-resistant map stitching in wireless sensor network. IEEE Transactions on Parallel and Distributed Systems 21(11) (2010)
Laman, G.: On graphs and rigidity of plane skeletal structures. Journal of Engineering Mathematics 4(4) (December 1970)
Moore, D., Leonard, J., Rus, D., Teller, S.: Robust distributed network localization with noisy range measurements. In: SenSys 2004: Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems, pp. 50–61. ACM, New York (2004), http://doi.acm.org/10.1145/1031495.1031502
Niculescu, D., Nath, B.: Dv based positioning in ad hoc networks. Journal Telecommunication Systems 22, 267–280 (2003)
Sau, B., Mukhopadhyaya, K.: Length-based anchor-free localization in a fully covered sensor network. In: Proc. of the First International Conference on COMmunication Systems and NETworks, COMSNETS 2009, pp. 137–146. IEEE Press, Piscataway (2009), http://dl.acm.org/citation.cfm?id=1702135.1702157
Sau, B., Mukhopadhyaya, K.: Localizability of wireless sensor networks: Beyond wheel extension. ArXiv e-prints (August 2013), http://arxiv.org/abs/1308.6464
Savvides, A., Han, C., Strivastava, M.: Dynamic fine-grained localization in ad-hoc networks of sensors. In: Proc. of the 7th Annual International Conference on Mobile Computing and Networking (MobiCom 2001), pp. 166–179. ACM, Rome (2001)
Saxe, J.: Embeddability of weighted graphs in k-space is strongly np-hard. In: Proc. 17th. Allerton Conference in Communications, Control and Computing, pp. 480–489 (1979)
Yang, Z., Liu, Y., Li, X.: Beyond trilateration: on the localizability of wireless ad hoc networks. IEEE/ACM Trans. Netw. 18(6), 1806–1814 (2010)
Zhu, Z., So, A.C., Ye, Y.: Universal rigidity: Towards accurate and efficient localization of wireless networks. In: IEEE INFOCOM 2010 (2010)
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Sau, B., Mukhopadhyaya, K. (2013). Localizability of Wireless Sensor Networks: Beyond Wheel Extension. In: Higashino, T., Katayama, Y., Masuzawa, T., Potop-Butucaru, M., Yamashita, M. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2013. Lecture Notes in Computer Science, vol 8255. Springer, Cham. https://doi.org/10.1007/978-3-319-03089-0_23
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DOI: https://doi.org/10.1007/978-3-319-03089-0_23
Publisher Name: Springer, Cham
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