Jehoshua Bruck
Jie Gao
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Abstract
Location information is useful both for network organization and for sensor data integrity. In this article, we study the anchor-free 2D localization problem by using local angle measurements. We prove that given a unit disk graph and the angles between adjacent edges, it is NP-hard to find a valid embedding in the plane such that neighboring nodes are within distance 1 from each other and non-neighboring nodes are at least distance √2/2 away. Despite the negative results, however, we can find a planar spanner of a unit disk graph by using only local angles. The planar spanner can be used to generate a set of virtual coordinates that enable efficient and local routing schemes such as geographical routing or approximate shortest path routing. We also proposed a practical anchor-free embedding scheme by solving a linear program. We show by simulation that it gives both a good local embedding, with neighboring nodes embedded close and non-neighboring nodes far away, and a satisfactory global view such that geographical routing and approximate shortest path routing on the embedded graph are almost identical to those on the original (true) embedding.
- Aspnes, J., Goldenberg, D., and Yang, Y. R. 2004. On the computational complexity of sensor network localization. In Proceedings of the 1st International Workshop on Algorithmic Aspects of Wireless Sensor Networks (ALGOSENSORS), 32--44.Google Scholar
- Biswas, P. and Ye, Y. 2004. Semidefinite programming for ad hoc wireless sensor network localization. In Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, 46--54. Google ScholarDigital Library
- Borg, I. and Groenen, P. 1997. Modern Multidimensional Scaling: Theory and Applications. Springer.Google Scholar
- Bose, P., Morin, P., Stojmenovic, I., and Urrutia, J. 1999. Routing with guaranteed delivery in ad hoc wireless networks. In Proceedings of the 3rd International Workshop on Discrete Algorithms and Mehtods for Mobile Computing and Communications (DialM'99), 48--55. Google ScholarDigital Library
- Breu, H. and Kirkpatrick, D. G. 1998. Unit disk graph recognition is NP-hard. Comput. Geometry Theory Appl. 9, 1-2, 3--24. Google ScholarDigital Library
- Bryant, V. W. 1989. Straight line representation of planar graphs. Elem. Math. 44, 64--66.Google Scholar
- Bǎdoiu, M., Demaine, E. D., Hajiaghayi, M. T., and Indyk, P. 2004. Low-Dimensional embedding with extra information. In Proceedings of the 20th Annual Symposium on Computational Geometry, 320--329. Google ScholarDigital Library
- Doherty, L., Ghaoui, L. E., and Pister, S. J. 2001. Convex position estimation in wireless sensor networks. In Proceedings of the Annual Joint Conference of the Computer and Communications Societies (IEEE Infocom), vol. 3. 1655--1663.Google Scholar
- Efrat, A., Erten, C., Forrester, D., Iyer, A., and Kobourov, S. G. 2006. Force-Directed approaches to sensor localization. In Proceedings of the 8th Workshop on Algorithm Engineering and Experiments (ALENEX), 108--118.Google Scholar
- Fáry, I. 1948. On straight line representations of planar graphs. Acta Scientiarum Mathematicarum (Szeged) 11, 229--233.Google Scholar
- Gao, J., Guibas, L. J., Hershberger, J., Zhang, L., and Zhu, A. 2001. Geometric spanner for routing in mobile networks. In Proceedings of the 2nd ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc'01), 45--55. Google ScholarDigital Library
- Gavoille, C., Peleg, D., Pérennes, S., and Raz, R. 2001. Distance labeling in graphs. In Proceedings of the 12th Annual ACM-SIAM Symposium on Discrete Algorithms, 210--219. Google ScholarDigital Library
- Goldenberg, D. K., Bihler, P., Yang, Y. R., Cao, M., Fang, J., Morse, A. S., and Anderson, B. D. O. 2006. Localization in sparse networks using sweeps. In Proceedings of the 12th Annual International Conference on Mobile Computing and Networking (MobiCom'06). ACM Press, New York, 110--121. Google ScholarDigital Library
- Gotsman, C. and Koren, Y. 2004. Distributed graph layout for sensor networks. In Proceedings of the International Symposium on Grpah Drawing. Google ScholarDigital Library
- Hofmann-Wellenhof, B., Lichtenegger, H., and Collins, J. 2001. Global Positioning Systems: Theory and Practice, 5 ed. Springer.Google Scholar
- Karp, B. and Kung, H. 2000. GPSR: Greedy perimeter stateless routing for wireless networks. In Proceedings of the 6th ACM Annual International Conference on Mobile Computing and Networking (MobiCom'00), 243--254. Google ScholarDigital Library
- Kuhn, F., Moscibroda, T., and Wattenhofer, R. 2004. Unit disk graph approximation. In Proceedings of the Joint Workshop on Foundations of Mobile Computing, 17--23. Google ScholarDigital Library
- Kuhn, F., Wattenhofer, R., Zhang, Y., and Zollinger, A. 2003. Geometric ad-hoc routing: Of theory and practice. In Proceedings of the 22nd Annual Symposium on Principles of Distributed Computing (PODC'03). ACM Press, New York, 63--72. Google ScholarDigital Library
- Kuhn, F. and Zollinger, A. 2003. Ad-hoc networks beyond unit disk graphs. In Proceedings of the Joint Workshop on Foundations of Mobile Computing, 69--78. Google ScholarDigital Library
- Li, X.-Y., Calinescu, G., and Wan, P.-J. 2002. Distributed construction of planar spanner and routing for ad hoc networks. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom), 1268--1277.Google Scholar
- Li, Z., Trappe, W., Zhang, Y., and Nath, B. 2005. Robust statistical methods for securing wireless localization in sensor networks. In Proceedings of the 4th International Symposium on Information Processing in Sensor Networks (IPSN'05). IEEE Press, Piscataway, NJ, 12. Google ScholarDigital Library
- Moore, D., Leonard, J., Rus, D., and Teller, S. 2004. Robust distributed network localization with noisy range measurements. In Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems (SenSys'04). ACM Press, New York, 50--61. Google ScholarDigital Library
- Moscibroda, T., O'Dell, R., Wattenhofer, M., and Wattenhofer, R. 2004. Virtual coordinates for ad hoc and sensor networks. In Proceedings of the Joint Workshop on Foundations of Mobile Computing, 8--16. Google ScholarDigital Library
- Niculescu, D. and Nath, B. 2001. Ad hoc positioning system (APS). In Proceedings of the IEEE Conference and Exhibition on Global Telecommunications (GlobeCom), 2926--2931.Google Scholar
- Niculescu, D. and Nath, B. 2003. Ad hoc positioning system (APS) using AOA. In Proceedings of the Annual Joint Conference of the IEEE Computer and Communications Societies (InfoCom), Vol. 22. 1734--1743.Google Scholar
- Niculescu, D. and Nath, B. 2004. Error characteristics of ad hoc positioning systems (APS). In Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc'04), 20--30. Google ScholarDigital Library
- Priyantha, N. B., Chakraborty, A., and Balakrishnan, H. 2000. The cricket location-support system. In Proceedings of the 6th ACM Annual International Conference on Mobile Computing and Networking (MobiCom'00), 32--43. Google ScholarDigital Library
- Rajaraman, R. 2002. Topology control and routing in ad hoc networks: A survey. SIGACT News 33, 2, 60--73. Google ScholarDigital Library
- Rao, A., Papadimitriou, C., Shenker, S., and Stoica, I. 2003. Geographic routing without location information. In Proceedings of the 9th ACM Annual International Conference on Mobile Computing and Networking (MobiCom'03), 96--108. Google ScholarDigital Library
- Savvides, A., Han, C.-C., and Strivastava, M. B. 2001. Dynamic fine-grained localization in ad-hoc networks of sensors. In Proceedings of the 7th ACM Annual International Conference on Mobile Computing and Networking (MobiCom'01), 166--179. Google ScholarDigital Library
- Savvides, A., Park, H., and Strivastava, M. B. 2003. The n-hop multilateration primitive for node localization problems. Mobile Netw. Appl. 8, 443--451. Google ScholarDigital Library
- Shang, Y., Ruml, W., Zhang, Y., and Fromherz, M. P. J. 2003. Localization from mere connectivity. In Proceedings of the 4th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiCom'03), 201--212. Google ScholarDigital Library
- So, A. M.-C. and Ye, Y. 2005. Theory of semidefinite programming for sensor network localization. In Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'05). Society for Industrial and Applied Mathematics, Philadelphia, PA, 405--414. Google ScholarDigital Library
- Whitehouse, K. and Culler, D. 2006. A robustness analysis of multi-hop ranging-based localization approximations. In Proceedings of the 5th International Conference on Information Processing in Sensor Networks (IPSN'06). ACM Press, New York, 317--325. Google ScholarDigital Library
- Whitehouse, K., Karlof, C., Woo, A., Jiang, F., and Culler, D. 2005. The effects of ranging noise on multihop localization: An empirical study. In Proceedings of the 4th International Symposium on Information Processing in Sensor Networks (IPSN'05). IEEE Press, Piscataway, NJ, 10. Google ScholarDigital Library
- Zhou, G., He, T., Krishnamurthy, S., and Stankovic, J. A. 2004. Impact of radio irregularity on wireless sensor networks. In Proceedings of the 2nd International Conference on Mobile Systems, Applications, and Services (MobiSys'04). ACM Press, New York, 125--138. Google ScholarDigital Library
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- Localization and routing in sensor networks by local angle information
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