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Coverage in Wireless Ad Hoc Sensor Networks
June 2003 (vol. 52 no. 6)
pp. 753-763

Abstract—Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking. One of the fundamental problems in sensor networks is the calculation of the coverage. It is assumed that the sensor has the uniform sensing ability. We provide efficient distributed algorithms to optimally solve the best-coverage problem raised. In addition, we consider a more general sensing model: The sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum best-coverage-path with the least energy consumption and how to find an optimum best-coverage-path that travels a small distance. In addition, we justify the correctness of the method proposed that uses the Delaunay triangulation to solve the best coverage problem and show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.

[1] S. Meguerdichian, F. Koushanfar, M. Potkonjak, and M.B. Srivastava, Coverage Problems in Wireless Ad-Hoc Sensor Networks Proc. IEEE Infocom '01, pp. 1380-1387, 2001.
[2] S. Capkun, M. Hamdi, and J.P. Hubaux, GPS-Free Positioning in Mobile Ad-Hoc Networks Proc. Hawaii Int'l Conf. System Sciences, 2001.
[3] S. Meguerdichian, F. Koushanfar, G. Qu, and M. Potkonjak, Exposure in Wireless Ad-Hoc Sensor Network Proc. IEEE MOBICOM '01, pp. 139-150, 2001.
[4] S. Fortune, Voronoi Diagrams and Delaunay Triangulations Computing in Euclidean Geometry, F.K. Hwang and D.-Z. Du, eds., pp. 193-233, Singapore: World Scientific, 1992.
[5] H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer-Verlag, 1987.
[6] F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, 1985.
[7] X.-Y. Li, Localized Delaunay Triangulation Is as Good as Unit Disk Graph J. Computer Networks, submitted for publication.
[8] X.-Y. Li, G. Calinescu, and P.-J. Wan, Distributed Construction of Planar Spanner and Routing for Ad Hoc Wireless Networks Proc. 21st Ann. Joint Conf. IEEE Computer and Comm. Socs. (INFOCOM), vol. 3, 2002.
[9] X.-Y. Li, P.-J. Wan, and Y. Wang, Power Efficient and Sparse Spanner for Wireless Ad Hoc Networks Proc. IEEE Int'l Conf. Computer Comm. and Networks (ICCCN01), pp. 564-567, 2001.
[10] X.-Y. Li, P.-J. Wan, Y. Wang, and O. Frieder, Sparse Power Efficient Topology for Wireless Networks Proc. IEEE Hawaii Int'l Conf. System Sciences (HICSS), 2002.
[11] G.T. Toussaint, The Relative Neighborhood Graph of a Finite Planar Set Pattern Recognition, vol. 12, no. 4, pp. 261-268, 1980.
[12] J.W. Jaromczyk and G.T. Toussaint, Relative Neighborhood Graphs and Their Relatives Proc. IEEE, vol. 80, no. 9, pp. 1502-1517, 1992.
[13] K.R. Gabriel and R.R. Sokal, A New Statistical Approach to Geographic Variation Analysis Systematic Zoology, vol. 18, pp. 259-278, 1969.
[14] K.J. Supowit, The Relative Neighborhood Graph, with an Application to Minimum Spanning Trees J. ACM, vol. 30, 1983.
[15] J.W. Jaromczyk and M. Kowaluk, Constructing the Relative Neighborhood Graph in Three-Dimensional Euclidean Space Discrete Applied Math., vol. 31, pp. 181-192, 1991.
[16] J.W. Jaromczyk, M. Kowaluk, and F. Yao, An Optimal Algorithm for Constructing$\beta$-Skeletons in$l_p$Metric SIAM J. Computing, 1991.
[17] D.W. Matula and R.R. Sokal, Properties of Gabriel Graphs Relevant to Geographical Variation Research and the Clustering of Points in the Plane Geographical Analysis, vol. 12, pp. 205-222, 1984.
[18] M. Marengoni, B.A. Draper, A. Hanson, and R.A. Sitaraman, System to Place Observers on a Polyhedral Terrain in Polynomial Time Image and Vision Computing, vol. 18, pp. 773-780, 1996.
[19] W.W. Gregg, W.E. Esaias, G.C. Feldman, R. Frouin, S.B. Hooker, C.R. McClain, and R.H. Woodward, Coverage Opportunities for Global Ocean Color in a Multimission Era IEEE Trans. Geoscience and Remote Sensing, vol. 36, pp. 1620-1627, 1998.
[20] A. Molina, G.E. Athanasiadou, and A.R. Nix, The Automatic Location of Base Stations for Optimized Cellular Coverage: A New Combinatorial Approach Proc. IEEE 49th Vehicular Technology Conf., vol. 1, pp. 606-610, 1999.
[21] P. Hall, Introduction to the Theory of Coverage Processes. New York: Wiley, 1998.
[22] P. Gupta and P.R. Kumar, Critical Power for Asymptotic Connectivity in Wireless Networks Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming, W.M. McEneaney, G. Yin, and Q. Zhang, eds., 1998.
[23] T.J. Cormen, C.E. Leiserson, and R.L. Rivest, Introduction to Algorithms. MIT Press and McGraw-Hill, 1990.
[24] P. Bose, L. Devroye, W. Evans, and D. Kirkpatrick, On the Spanning Ratio of Gabriel Graphs and Beta-Skeletons Proc. Latin Am. Theoretical Infocomatics (LATIN), 2002.
[25] D.P. Dobkin, S.J. Friedman, and K.J. Supowit, Delaunay Graphs Are Almost as Good as Complete Graphs Discrete Computational Geometry, 1990.
[26] J.M. Keil and C.A. Gutwin, Classes of Graphs which Approximate the Complete Euclidean Graph Discrete Computational Geometry, vol. 7, 1992.

Index Terms:
Coverage, wireless networks, sensors, computational geometry, distributed algorithms.
Xiang-Yang Li, Peng-Jun Wan, Ophir Frieder, "Coverage in Wireless Ad Hoc Sensor Networks," IEEE Transactions on Computers, vol. 52, no. 6, pp. 753-763, June 2003, doi:10.1109/TC.2003.1204831
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