Minimum-Cost Linear Coverage by Sensors with Adjustable Ranges
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.
KeywordsDynamic Programming Wireless Sensor Network Discrete Variant Optimal Assignment Unit Disk Graph
Unable to display preview. Download preview PDF.
- 1.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)Google Scholar
- 2.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)CrossRefGoogle Scholar
- 5.Carmi, P., Katz, M., Lev-Tov, N.: Covering points by unit disks of fixed location. Algorithms and Computation, 644–655 (2007)Google Scholar
- 10.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)Google Scholar
- 12.Narayanappa, S., Vojtechovskỳ, P.: An improved approximation factor for the unit disk covering problem. In: Canadian Conference on Computational Geometry, Citeseer (2006)Google Scholar
- 13.Wan, P.-J., Xu, X.-H., Wang, Z.: Wireless Coverage with Disparate Ranges. In: ACM MOBIHOC (2011)Google Scholar
- 17.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)MathSciNetCrossRefzbMATHGoogle Scholar