Advertisement

Minimizing the Aggregate Movements for Interval Coverage

  • Aaron M. Andrews
  • Haitao Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)

Abstract

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.

Keywords

Line Segment Trivial Solution Time Algorithm Mobile Sensor Left Generator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, A., Wang, H.: Minimizing the aggregate movements for interval coverage (2014). arXiv:1412.2300
  2. 2.
    Bar-Noy, A., Rawitz, D., Terlecky, P.: Maximizing barrier coverage lifetime with mobile sensors. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 97–108. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  3. 3.
    Bhattacharya, B., Burmester, B., Hu, Y., Kranakis, E., Shi, Q., Wiese, A.: Optimal movement of mobile sensors for barrier coverage of a planar region. Theoretical Computer Science 410(52), 5515–5528 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chen, D., Gu, Y., Li, J., Wang, H.: Algorithms on minimizing the maximum sensor movement for barrier coverage of a linear domain. Discrete and Computational Geometry 50, 374–408 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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
  6. 6.
    Czyzowicz, J., et al.: 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
  7. 7.
    Czyzowicz, J., et al.: 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
  8. 8.
    Li, M., Sun, X., Zhao, Y.: Minimum-cost linear coverage by sensors with adjustable ranges. In: Cheng, Y., Eun, D.Y., Qin, Z., Song, M., Xing, K. (eds.) WASA 2011. LNCS, vol. 6843, pp. 25–35. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  9. 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. 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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUtah State UniversityLoganUSA

Personalised recommendations