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Fast Estimation of Coverage Area in a Pervasive Computing Environment

  • Dibakar Saha
  • Nabanita Das
  • Bhargab B. Bhattacharya
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 28)

Abstract

In many applications of pervasive computing and communication, it is often mandatory that a certain service area be fully covered by a given deployment of nodes or access points. Hence, a fast and accurate method of estimating the coverage area is needed. However, in a scenario with a limited computation and communication capability as in self-organized mobile networks, where the nodes are not static, computation-intensive algorithms are not suitable. In this paper, we have presented a simple algorithm for estimating the area covered by a set of nodes randomly deployed over a 2-D region. We assume that the nodes are identical and each of them covers a circular area. For fast estimation of the collective coverage of n such circles, we approximate each real circle by the tightest square that encloses it as well as by the largest square that is inscribed within it, and present an O(n logn) time algorithm for computation. We study the variation of the estimated area between these two bounds, for random deployment of nodes. In comparison with an accurate digital circle based method, the proposed algorithms estimate the area coverage with only 10% deviation, while reducing the complexity of area computation significantly. Moreover, for an over-deployed network, the estimation provides an almost exact measure of the covered area.

Keywords

Pervasive Computing Wireless Sensor Networks (WSN) Coverage Digital Circle Range 

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References

  1. 1.
    Luo, C.J., Tang, B., Zhou, M.T., Cao, Z.: Analysis of the wireless sensor networks efficient coverage. In: Proc. International Conference on Apperceiving Computing and Intelligence Analysis (ICACIA), pp. 194–197 (2010)Google Scholar
  2. 2.
    Six, H.W., Wood, D.: The rectangle intersection problem revisited. BIT Numerical Mathematics 20, 426–433 (1980)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bentley, J.L., Wood, D.: An optimal worst case algorithm for reporting intersections of rectangles. IEEE Transactions on Computers C-29, 571–577 (1980)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Sharir, M.: Intersection and closest-pair problems for a set of planar discs. SIAM Journal on Computing 14, 448–468 (1985)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Aurenhammer, F.: Improved algorithms for discs and balls using power diagrams. Journal of Algorithms 9, 151–161 (1988)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Gallais, A., Carle, J., Simplot-ryl, D., Stojmenovic, I.: Localized sensor area coverage with low communication overhead. IEEE Transactions on Mobile Copmuting, 661–672 (2008)Google Scholar
  7. 7.
    Slijepcevic, S., Potkonjak, M.: Power efficient organization of wireless sensor networks. In: Proc. IEEE International Conference on Communications, vol. 2, pp. 472–476 (2001)Google Scholar
  8. 8.
    Pervin, N., Layek, D., Das, N.: Localized algorithm for connected set cover partitioning in wireless sensor networks. In: Proc. 1st International Conference on Parallel Distributed and Grid Computing (PDGC), pp. 229–234 (2010)Google Scholar
  9. 9.
    Huang, C.F., Tseng, Y.C.: The coverage problem in a wireless sensor network. In: Proc. 2nd ACM International Conference on Wireless Sensor Networks and Applications, pp. 115–121. ACM (2003)Google Scholar
  10. 10.
    Hsin, C., Liu, M.: Network coverage using low duty-cycled sensors: Random coordinated sleep algorithms. In: Proc. Third International Symposium on Information Processing in Sensor Networks, pp. 433–442 (2004)Google Scholar
  11. 11.
    Sheu, J.P., Yu, C.H., Tu, S.C.: A distributed protocol for query execution in sensor networks. In: Proc. IEEE Wireless Communications and Networking Conference, vol. 3, pp. 1824–1829 (2005)Google Scholar
  12. 12.
    Saha, D., Das, N.: Distributed area coverage by connected set cover partitioning in wireless sensor networks. In: Proc. First International Workshop on Sustainable Monitoring through Cyber-Physical Systems (SuMo-CPS). ICDCN, Mumbai (2013)Google Scholar
  13. 13.
    Saha, D., Das, N.: A fast fault tolerant partitioning algorithm for wireless sensor networks. In: Proc. Third International Conference on Advances in Computing and Information Technology (ACITY), vol. 3, pp. 227–237 (2013)Google Scholar
  14. 14.
    Ke, W., Liu, B., Tsai, M.: The critical-square-grid coverage problem in wireless sensor networks is NP-complete. Journal of Computer Networks, 2209–2220 (2010)Google Scholar
  15. 15.
    Saha, D., Das, N., Pal, S.: A digital-geometric approach for computing area coverage in wireless sensor networks. In: Natarajan, R. (ed.) ICDCIT 2014. LNCS, vol. 8337, pp. 134–145. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  16. 16.
    Bhowmick, P., Bhattacharya, B.B.: Number-theoretic interpretation and construction of a digital circle. Discrete Applied Mathematics 156, 2381–2399 (2008)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Dibakar Saha
    • 1
  • Nabanita Das
    • 1
  • Bhargab B. Bhattacharya
    • 1
  1. 1.Advanced Computing and Microelectronics UnitIndian Statistical InstituteKolkataIndia

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