Abstract
Coverage has been one of the most fundamental yet challenging issues in wireless networks and found many applications, such as routing and broadcasting. Given a set of weighted unit disks (coverage areas) and a set of nodes to be covered, we study the minimum weight coverage problem under two specific topologies. The first one assumes that the centers of the disks lie inside a strip while the nodes lie outside of this strip. The second topology assumes that the centers of the disks lie within a unit circle while the nodes lie outside of this circle. For each topology, we present a polynomial-time algorithm to find a disk subset of minimum total weight to cover all nodes. Both of our algorithms relies on dynamic programming.
This work was supported in part by NSF of USA under grant CNS-0831831.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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)
Baysan, M., Sarac, K., Chandrasekaran, R., Bereg, S.: A Polynomial Time Solution to Minimum Forwarding Set Problem in Wireless Networks under Unit Disk Coverage Model. IEEE Transactions on Parallel and Distributed Systems, 913–924 (2008)
Br”onnimann, 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. Approximation and Online Algorithms, 135–146 (2010)
Gonzalez, T.: Covering a set of points in multidimensional space* 1. 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., et al.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Comb. Optim. 1382, 6905 (2008)
Johnson, D.: The NP-completeness column: an ongoing guide. Journal of Algorithms 13(3), 502–524 (1992)
Narayanappa, S., Vojtechovskỳ, P.: An improved approximation factor for the unit disk covering problem. In: Proc. Can. Conf. on Comp. Geom., Citeseer (2006)
Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 475–484. ACM, New York (1997)
Wan, P., Xu, X., 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)
Wu, J., Lou, W.: Forward-node-set-based broadcast in clustered mobile ad hoc networks. Wireless Communications and Mobile Computing 3(2), 155–173 (2003)
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) (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 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, X., Wang, Z. (2011). Wireless Coverage via Dynamic Programming. 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_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-23490-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23489-7
Online ISBN: 978-3-642-23490-3
eBook Packages: Computer ScienceComputer Science (R0)