Abstract
One of the most fundamental tasks of wireless sensor networks is to provide coverage of the deployment region. In this paper, we study the coverage of a line segment with a set of wireless sensors with adjustable coverage ranges. Each coverage range of a sensor is an interval centered at that sensor whose length is decided by the power the sensor chooses. The objective is to find a range assignment with the minimum cost. There are two variants of the optimization problem. In the discrete variant, each sensor can only choose from a finite set of powers while in the continuous variant, each sensor can choose power from a given interval. For the discrete variant of the problem, we present a polynomial-time exact algorithm. For the continuous variant of the problem, we develop constant-approximation algorithms when the cost for all sensors is proportional to r κ for some constant κ ≥ 1, where r is the covering radius corresponding to the chosen power. Specifically, if κ = 1, we give a simple 1.25-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS); if κ > 1, we give a simple 2-approximation algorithm.
This work is supported by a grant from City University of Hong Kong [Project No. 7002611].
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References
Abrams, Z., Goel, A., Plotkin, S.: Set k-cover algorithms for energy efficient monitoring in wireless sensor networks. In: Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, pp. 424–432. ACM, New York (2004)
Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-Factor Approximation for Minimum-Weight (Connected) Dominating Sets in Unit Disk Graphs. In: Díaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol. 4110, pp. 3–14. Springer, Heidelberg (2006)
Brönnimann, H., Goodrich, M.: Almost optimal set covers in finite VC-dimension. Discrete and Computational Geometry 14(1), 463–479 (1995)
Călinescu, G., Mandoiu, I., Wan, P., Zelikovsky, A.: Selecting forwarding neighbors in wireless ad hoc networks. Mobile Networks and Applications 9(2), 101–111 (2004)
Carmi, P., Katz, M., Lev-Tov, N.: Covering points by unit disks of fixed location. Algorithms and Computation, 644–655 (2007)
Dai, D., Yu, C.: A 5 + ε-approximation algorithm for minimum weighted dominating set in unit disk graph. Theoretical Computer Science 410(8-10), 756–765 (2009)
Erlebach, T., Mihalák, M.: A (4 + ε)-approximation for the minimum-weight dominating set problem in unit disk graphs. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 135–146. Springer, Heidelberg (2010)
Gonzalez, T.: Covering a set of points in multidimensional space. Information Processing Letters 40(4), 181–188 (1991)
Hochbaum, D., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. Journal of the ACM (JACM) 32(1), 130–136 (1985)
Hou, J., Yau, D., Ma, C., Yang, Y., Zhang, H., Hou, I., Rao, N., Shankar, M.: Coverage in wireless sensor networks. Guide to Wireless Sensor Networks, 47–79 (2009)
Huang, Y., Gao, X., Zhang, Z., Wu, W.: A better constant-factor approximation for weighted dominating set in unit disk graph. Journal of Combinatorial Optimization 18(2), 179–194 (2009)
Narayanappa, S., Vojtechovskỳ, P.: An improved approximation factor for the unit disk covering problem. In: Canadian Conference on Computational Geometry, Citeseer (2006)
Wan, P.-J., Xu, X.-H., Wang, Z.: Wireless Coverage with Disparate Ranges. In: ACM MOBIHOC (2011)
Wan, P., Yi, C.: Coverage by randomly deployed wireless sensor networks. IEEE Transactions on Information Theory 52, 2658–2669 (2006)
Wang, J., Zhong, N.: Efficient point coverage in wireless sensor networks. Journal of Combinatorial Optimization 11(3), 291–304 (2006)
Yun, Z., Bai, X., Xuan, D., Lai, T., Jia, W.: Optimal Deployment Patterns for Full Coverage and k-Connectivity (k ≤ 6) Wireless Sensor Networks. IEEE/ACM Transactions on Networking 18(3), 934–947 (2010)
Zou, F., Wang, Y., Xu, X., Li, X., Du, H., Wan, P., Wu, W.: New approximations for minimum-weighted dominating sets and minimum-weighted connected dominating sets on unit disk graphs. Theoretical Computer Science 412(3), 198–208 (2011) (Journal version of a COCOA 2009 paper)
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Li, M., Sun, X., Zhao, Y. (2011). Minimum-Cost Linear Coverage by Sensors with Adjustable Ranges. In: Cheng, Y., Eun, D.Y., Qin, Z., Song, M., Xing, K. (eds) Wireless Algorithms, Systems, and Applications. WASA 2011. Lecture Notes in Computer Science, vol 6843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23490-3_3
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DOI: https://doi.org/10.1007/978-3-642-23490-3_3
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