Abstract
Given a set of n sensor nodes distributed randomly over a 2-D plane, this paper addresses the problem of computing the area covered by the sensors assuming that each sensor covers a circular area of radius r. To make the computation simple, instead of considering real circles, a digital geometry based approach is followed here. A detailed study on intersection of digital circles reveals many interesting properties that lead to the development of a novel O(n logn) centralized algorithm using simple arithmetic operations for computing the area covered by n uniform digital circles. Next, a distributed version of the same is proposed to select a subset of nodes to cover a given area. Comparison with earlier works by simulation shows that the proposed distributed algorithm improves the estimated area coverage significantly.
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References
Aurenhammer, F.: Improved algorithms for discs and balls using power diagrams. Journal of Algorithms 9(2), 151–161 (1988)
Bhowmick, P., Bhattacharya, B.B.: Number-theoretic interpretation and construction of a digital circle. Discrete Applied Mathematics 156(12), 2381–2399 (2008)
Bresenham, J.: A linear algorithm for incremental digital display of circular arcs. Commun. ACM 20(2), 100–106 (1977)
Foley, J.D., Dam, A.V., Feiner, S.K., Hughes, J.F.: Computer graphics: principles and practice. 2 edn.
Gallais, A., Carle, J., Simplot-Ryl, D., Stojmenovi, I.: Localized sensor area coverage with low communication overhead. IEEE Transactions on Mobile Computing 7(5), 661–672 (2008)
Huang, C.F., Tseng, Y.C.: The coverage problem in a wireless sensor network. In: Proceedings of the 2nd ACM International Conference on Wireless Sensor Networks and Applications, WSNA, pp. 115–121. ACM, New York (2003)
Kershner, R.: The number of circles covering a set. American Journal of Mathematics 61(3), 665–671 (1939)
McIlroy, M.D.: Best approximate circles on integer grids. ACM Trans. Graph. 2(4), 237–263 (1983)
Meguerdichian, S., Koushanfar, F., Potkonjak, M., Srivastava, M.B.: Coverage problems in wireless ad-hoc sensor networks. In: Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies, IEEE INFOCOM, vol. 3, pp. 1380–1387 (2001)
Pal, S., Bhowmick, P., Biswas, A.: Facet: A fast approximate circularity estimation technique. In: Second International Conference on Emerging Applications of Information Technology (EAIT), pp. 106–109 (2011)
Pervin, N., Layek, D., Das, N.: Localized algorithm for connected set cover partitioning in wireless sensor networks. In: 1st International Conference on Parallel Distributed and Grid Computing (PDGC), pp. 229–234 (2010)
Saha, D., Das, N.: Distributed area coverage by connected set cover partitioning in wireless sensor networks. In: First International Workshop on Sustainable Monitoring through Cyber-Physical Systems (SuMo-CPS), In Conjunction with ICDCN, Mumbai, India (2013)
Saha, D., Das, N.: A fast fault tolerant partitioning algorithm for wireless sensor networks. In: Third International Conference on Advances in Computing and Information Technology (ACITY), pp. 227–237. CSIT-AIRCC Digital Library, Chennai (2013)
Sharir, M.: Intersection and closest-pair problems for a set of planar discs. SIAM Journal on Computing 14(2), 448–468 (1985)
Yan, T., He, T., Stankovic, J.A.: Differentiated surveillance for sensor networks. In: Proceedings of the 1st International Conference on Embedded Networked Sensor Systems, SenSys 2003, pp. 51–62. ACM (2003)
Yu, Z., Teng, J., Li, X., Xuan, D.: On wireless network coverage in bounded areas. In: Proceedings IEEE INFOCOM, pp. 1195–1203 (2013)
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Saha, D., Das, N., Pal, S. (2014). A Digital-Geometric Approach for Computing Area Coverage in Wireless Sensor Networks. In: Natarajan, R. (eds) Distributed Computing and Internet Technology. ICDCIT 2014. Lecture Notes in Computer Science, vol 8337. Springer, Cham. https://doi.org/10.1007/978-3-319-04483-5_15
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DOI: https://doi.org/10.1007/978-3-319-04483-5_15
Publisher Name: Springer, Cham
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