Abstract
We propose a distributed scheme called Adaptive-Group-Merge for sensor networks that, given a parameter k, approximates a geometric shape by a k-vertex polygon. The algorithm is well suited to the distributed computing architecture of sensor networks, and we prove that its approximation quality is within a constant factor of the optimal. We also show through simulation that our scheme outperforms several other alternatives in preserving important shape features, and achieves approximation quality almost as good as the optimal, centralized scheme. Because many applications of sensor networks involve observations and monitoring of physical phenomena, the ability to represent complex geometric shapes faithfully but using small memory is vital in many settings.
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References
Bulusu, N., Heidemann, J., Estrin, D.: GPS-less low cost outdoor optimization for very small devices. IEEE Personal Communications Magazine 7(5), 28–34 (2000)
Chan, T.: Faster core-set constructions and data stream algorithms in fixed dimensions. In: Proc. 20th Annu. ACM Sympos. Comput. Geom., pp. 152–159 (2004)
Chintalapudi, K.K., Govindan, R.: Localized edge detection in sensor fields. In: IEEE Intl. Workshop on Sensor Network Protocols and Applications, pp. 59–70 (2003)
Douglas, D., Peucker, T.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Canadian Cartographer 10(2), 112–122 (1973)
Dudley, R.M.: Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory 10, 227–236 (1974)
Gilbert, A.C., Kotidis, Y., Muthukrishnan, S., Strauss, M.J.: One-pass wavelet decompositions of data streams. IEEE Trans. on Knowledge and Data Engineering 15(3), 541–554 (2003)
Govindan, R., Kohler, E., Estrin, D., Bian, F., Chintalapudi, K., Gnawali, O., Rangwala, S., Gummadi, R., Stathopoulos, T.: Tenet: An architecture for tiered embedded networks. Technical report, University of California, Los Angeles, November 10 (2005)
Hellerstein, J.M., Hong, C.-M., Madden, S., Stanek, K.: Beyond average: Toward sophisticated sensing with queries. In: Zhao, F., Guibas, L.J. (eds.) IPSN 2003. LNCS, vol. 2634, pp. 63–79. Springer, Heidelberg (2003)
Hershberger, J., Snoeyink, J.: Speeding up the Douglas-Peucker line simplification algorithm. In: Proc. 5th Intl. Symp. on Spatial Data Handling, pp. 134–143 (1992)
Kolesnikov, A.: Efficient Algorithms for Vectorization and Polygonal Approximation. PhD thesis, Department of Computer Science, University of Joensuu (2003)
Kotz, D., Newport, C., Elliott, C.: The mistaken axioms of wireless-network research. Technical Report TR2003-467, Dept. of Computer Science, Dartmouth College (July 2003)
Madden, S., Franklin, M.J., Hellerstein, J., Hong, W.: Tag: a tiny aggregation service for ad-hoc sensor networks. In: Proc. of OSDI (2002)
Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, London (1998)
Moses, R., Krishnamurthy, D., Patterson, R.: A self-localization method for wireless sensor networks. EURASIP J. Applied Signal Processing 2003(4), 348–358 (2003)
Nowak, R.D., Mitra, U.: Boundary estimation in sensor networks: Theory and methods. In: Zhao, F., Guibas, L.J. (eds.) IPSN 2003. LNCS, vol. 2634, pp. 80–95. Springer, Heidelberg (2003)
Shrivastava, N., Buragohain, C., Agrawal, D., Suri, S.: Medians and beyond: New aggregation techniques for sensor networks. In: Proc. of SenSys 2004 (2004)
Singh, M., Bakshi, A., Prasanna, V.K.: Constructing topographic maps in networked sensor systems. In: Proc. of Workshop on Algorithms for Wireless and Mobile Networks (ASWAN) (2004)
Toussaint, G.T.: Solving geometric problems with the rotating calipers. In: Proc. IEEE MELECON 1983, pp. A10.02/1–4 (1983)
Yarvis, M., Kushalnagar, N., Singh, H., Rangarajan, A., Liu, Y., Singh, S.: Exploiting heterogeneity in sensor networks. In: Proc. of IEEE INFOCOM 2005 (2005)
Zhao, J., Govindan, R.: Understanding packet delivery performance in dense wireless sensor networks. In: Proc. of the 1st Intl. Conf. on Embedded Networked Sensor Systems, SenSys 2003, pp. 1–13 (2003)
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Buragohain, C., Gandhi, S., Hershberger, J., Suri, S. (2006). Contour Approximation in Sensor Networks. In: Gibbons, P.B., Abdelzaher, T., Aspnes, J., Rao, R. (eds) Distributed Computing in Sensor Systems. DCOSS 2006. Lecture Notes in Computer Science, vol 4026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11776178_22
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DOI: https://doi.org/10.1007/11776178_22
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Print ISBN: 978-3-540-35227-3
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