Minimizing the Aggregate Movements for Interval Coverage
We consider an interval coverage problem. Given n intervals of the same length on a line L and a line segment B on L, we wish to move the intervals along L such that every point of B is covered by at least one interval and the sum of the moving distances of all intervals is minimized. As a basic geometry problem, it also has applications in mobile sensor barrier coverage. The previous work solved the problem in \(O(n^2)\) time. In this paper, we present an \(O(n\log n)\) time algorithm.
KeywordsLine Segment Trivial Solution Time Algorithm Mobile Sensor Left Generator
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- 1.Andrews, A., Wang, H.: Minimizing the aggregate movements for interval coverage (2014). arXiv:1412.2300
- 5.Chen, D., Tan, X., Wang, H., Wu, G.: Optimal point movement for covering circular regions. Algorithmica (2013), online First. doi: 10.1007/s00453-013-9857-1
- 9.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
- 10.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