Abstract
The minimum sensor cover is an important optimization problem in wireless sensor networks, which can be seen as a special case of the minimum set cover problem. The minimum set cover problem is a well-known problem in combinatorial optimization, which has no polynomial-time (ρlnδ)-approximation for 0<ρ<1 unless NP⊆DTIME(n O(loglogn)) where δ is the maximum cardinality of a subset in the input collection. However, the minimum sensor cover problem has polynomial-time constant-approximations because this special case has a geometric structure. The design technique, called partition, is employed to take the advantage of this geometric structure. Especially, the double partition plays an important role. In this article, we would like to give an exploratory essay for the double partition technique together with research progress on approximations for the minimum sensor cover problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ambühl, C., Erlebach, T., Mihalák, M., Nunkesser, M.: Constant-approximation for minimum-weight (connected) dominating sets in unit disk graphs. In: Proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2006). LNCS, vol. 4110, pp. 3–14. Springer, Berlin (2006)
Baker, B.S.: Approximation algorithms for NP-complete problems on planar graphs. In: Proc. FOCS, pp. 265–273 (1983)
Boginski, V.L., Commander, C.W., Pardalos, P.M., Ye, Y. (eds.): Sensors: Theory, Algorithms, and Applications. Springer, Berlin (2012)
Cardei, M., Thai, M., Li, Y., Wu, W.: Energy-efficient target coverage in wireless sensor networks. In: IEEE INFOCOM, pp. 1976–1984 (2005)
Dai, D., Yu, C.: A (5+ε)-approximation algorithm for minimum weighted dominating set in unit disk graph. Theor. Comput. Sci. 410, 756–765 (2009)
Ding, L., Wu, W., Willson, J.K., Wu, L., Lu, Z., Lee, W.: Constant-approximation for target coverage problem in wireless sensor networks. In: Proc. of the 31st Annual Joint Conf. of IEEE Communication and Computer Society (INFOCOM) (2012)
Du, D.-Z., Ko, K.-I., Hu, X.: Design and Analysis of Approximation Algorithms, pp. 142–157. Springer, Berlin (2012)
Du, D.-Z., Wan, P.: Connected Dominating Set: Theory and Applications. Springer, Berlin (2012)
Du, H., Wu, W., Shan, S., Kim, D., Lee, W.: Constructing weakly connected dominating set for secure clustering in distributed sensor network. J. Comb. Optim. 23, 301–307 (2012)
Erlebach, T., Mihalak, M.: A (4+ε)-approximation for the minimum-weight dominating set problem in unit disk graphs. In: WAOA 2009, pp. 135–146 (2009)
Gao, X., Huang, Y., Zhang, Z., Wu, W.: (6+ε)-approximation for minimum weight dominating set in unit disk graphs. In: Proceedings of the 14th Annual International Computing and Combinatorics Conference (COCOON 2008). LNCS, vol. 5092, pp. 551–557. Springer, Berlin (2008)
Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flows and other fractional packing problems. In: Proc. 39th Annual Symposium on the Foundations of Computer Science, pp. 300–309 (1998)
Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and VLSI. J. ACM 32, 130–136 (1985)
Huang, Y., Gao, X., Zhang, Z., Wu, W.: A better constant-factor approximation for weighted dominating set in unit disk graph. J. Comb. Optim. 18, 174–194 (2009)
Sorokin, A., Boyko, N., Boginski, V., Uryasev, S., Pardalos, P.: Mathematical programming techniques for sensor networks. Algorithms 2, 565–581 (2009)
Wang, C., Willson, J., Park, M.A., Farago, A., Wu, W.: On dual power assignment optimization for biconnectivity. J. Comb. Optim. 19, 174–183 (2010)
Willson, J.K., Ding, L., Wu, W., Wu, L., Lu, Z., Lee, W.: A better constant-approximation for coverage problem in wireless sensor networks. Preprint
Wu, W., Gao, X., Pardalos, P.M., Du, D.-Z.: Wireless networking, dominating and packing. Optim. Lett. 4, 347–358 (2010)
Yang, Y., Cardei, M.: Adaptive energy efficient sensor scheduling for wireless sensor networks. Optim. Lett. 4(3), 359–369 (2010)
Zhang, H., Hou, J.C.: Maintaining sensing coverage and connectivity in large sensor networks. Ad Hoc Sens. Wirel. Netw. 1, 89–124 (2005)
Zhang, Y., Li, W.: Modeling and energy consumption evaluation of a stochastic wireless sensor networks. Preprint (2011)
Zou, F., Li, X., Gao, S., Wu, W.: Node-weighted Steiner tree approximation in unit disk graphs. J. Comb. Optim. 18, 342–349 (2009)
Zou, F., Wang, Y., Xu, X., Du, H., Li, X., Wan, P., Wu, W.: New approximations for weighted dominating sets and connected dominating sets in unit disk graphs. Theor. Comput. Sci. 412(3), 198–208 (2011)
Acknowledgements
This work was supported in part by National Science Foundation of USA under grants CNS101630 and CCF0829993.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this paper
Cite this paper
Wu, L., Wu, W., Lu, Z., Zhu, Y., Du, DZ. (2013). Sensor Cover and Double Partition. In: Goldengorin, B., Kalyagin, V., Pardalos, P. (eds) Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8588-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8588-9_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8587-2
Online ISBN: 978-1-4614-8588-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)