Algorithms for Covering Multiple Barriers
In this paper, we consider the problems for covering multiple intervals on a line. Given a set B of m line segments (called “barriers”) on a horizontal line L and another set S of n horizontal line segments of the same length in the plane, we want to move all segments of S to L so that their union covers all barriers and the maximum movement of all segments of S is minimized. Previously, an \(O(n^3\log n)\)-time algorithm was given for the problem but only for the special case \(m=1\). In this paper, we propose an \(O(n^2\log n\log \log n+nm\log m)\)-time algorithm for any m, which improves the previous work even for \(m=1\). We then consider a line-constrained version of the problem in which the segments of S are all initially on the line L. Previously, an \(O(n\log n)\)-time algorithm was known for the case \(m=1\). We present an algorithm of \(O((n+m)\log (n+ m))\) time for any m. These problems may have applications in mobile sensor barrier coverage in wireless sensor networks.
Unable to display preview. Download preview PDF.
- 9.Kumar, S., Lai, T., Arora, A.: Barrier coverage with wireless sensors. In: Proc. of the 11th Annual International Conference on Mobile Computing and Networking (MobiCom), pp. 284–298 (2005)Google Scholar
- 10.Li, S., Shen, H.: Minimizing the maximum sensor movement for barrier coverage in the plane. In: Proc. of the 2015 IEEE Conference on Computer Communications (INFOCOM), pp. 244–252 (2015)Google Scholar
- 11.Li, S., Wang, H.: Algorithms for covering multiple barriers. arXiv:1704.06870 (2017)
- 13.Mehrandish, M.: On Routing, Backbone Formation and Barrier Coverage in Wireless Ad Doc and Sensor Networks. Ph.D. thesis, Concordia University, Montreal, Quebec, Canada (2011)Google Scholar
- 14.Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: Proc. of IEEE Wireless Communications and Networking Conference (WCNC), pp. 653–658 (2011)Google Scholar
- 15.Wang, H., Zhang, X.: Minimizing the maximum moving cost of interval coverage. In: Elbassioni, K., Makino, K. (eds.) ISAAC 2015. LNCS, vol. 9472, pp. 188–198. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48971-0_17. Full version to appear in International Journal of Computational Geometry and Application (IJCGA)CrossRefGoogle Scholar