Complexity of Barrier Coverage with Relocatable Sensors in the Plane
We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: the feasibility of barrier coverage, the problem of minimizing the largest relocation distance of a sensor (MinMax), and the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the problems are shown to be NP-complete. We also study the case when sensors use perpendicular movement to one of the barriers. We show that when the barriers are parallel, both the MinMax and MinSum problems can be solved in polynomial time. In contrast, we show that even the feasibility problem is NP-complete if two perpendicular barriers are to be covered, even if the sensors are located at integer positions, and have only two possible sensing ranges. On the other hand, we give an O(n 3/2) algorithm for a natural special case of this last problem.
Unable to display preview. Download preview PDF.
- 1.Balister, P., Bollobas, B., Sarkar, A., Kumar, S.: Reliable density estimates for coverage and connectivity in thin strips of finite length. In: Proceedings of MobiCom 2007, pp. 75–86 (2007)Google Scholar
- 4.Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the maximum sensor movement for barrier coverage of a line segment. In: Ruiz, P.M., Garcia-Luna-Aceves, J.J. (eds.) ADHOC-NOW 2009. LNCS, vol. 5793, pp. 194–212. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 5.Czyzowicz, J., Kranakis, E., Krizanc, D., Lambadaris, I., Narayanan, L., Opatrny, J., Stacho, L., Urrutia, J., Yazdani, M.: On minimizing the sum of sensor movements for barrier coverage of a line segment. In: Nikolaidis, I., Wu, K. (eds.) ADHOC-NOW 2010. LNCS, vol. 6288, pp. 29–42. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 7.Huang, C.F., Tseng, Y.C.: The coverage problem in a wireless sensor network. In: Proceedings of WSNA, pp. 115–121 (2003)Google Scholar
- 8.Kumar, S., Lai, T.H., Arora, A.: Barrier coverage with wireless sensors. In: Proceedings of MobiCom 2005, pp. 284–298 (2005)Google Scholar
- 9.Meguerdichian, S., Koushanfar, F., Potkonjak, M., Srivastava, M.B.: Coverage problems in wireless ad-hoc sensor networks. In: Proceedings of INFOCOM 2001, vol. 3, pp. 1380–1387 (2001)Google Scholar
- 10.Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: Proceedings of IEEE WCNC 2011, pp. 1464–1469 (2011)Google Scholar
- 11.Yan, G., Qiao, D.: Multi-round sensor deployment for guaranteed barrier coverage. In: Proceedings of IEEE INFOCOM 2010, pp. 2462–2470 (2010)Google Scholar