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Minimizing the Aggregate Movements for Interval Coverage

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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 want 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 has applications in mobile sensor barrier coverage in wireless sensor networks. The previous work solved the problem in \(O(n^2)\) time. In this paper, by discovering many interesting observations and developing new algorithmic techniques, we present an \(O(n\log n)\) time algorithm. We also show an \(\varOmega (n\log n)\) time lower bound for this problem, which implies the optimality of our algorithm.

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References

  1. Akyildiz, I., Su, W., Sankarasubramaniam, Y., Cayirci, E.: Wireless sensor networks: a survey. Comput. Netw. 38(4), 393–422 (2002)

    Article  Google Scholar 

  2. Bar-Noy, A., Rawitz, D., Terlecky, P.: Maximizing barrier coverage lifetime with mobile sensors. In: Proceedings of the 21st European Symposium on Algorithms (ESA), pp. 97–108, (2013)

  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. Theor. Comput. Sci. 410(52), 5515–5528 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, A., Kumar, S., Lai, T.: Designing localized algorithms for barrier coverage. In: Proc. of the 13th Annual ACM International Conference on Mobile Computing and Networking, pp. 63–73, (2007)

  5. Chen, D.Z., Gu, Y., Li, J., Wang, H.: Algorithms on minimizing the maximum sensor movement for barrier coverage of a linear domain. Discret. Comput. Geom. 50, 374–408 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, D.Z., Tan, X., Wang, H., Wu, G.: Optimal point movement for covering circular regions. Algorithmica 72, 379–399 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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: Proceedings of the 8th International Conference on Ad-Hoc, Mobile and Wireless Networks, pp. 194–212, (2009)

  8. 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: Proceedings of the 9th International Conference on Ad-Hoc, Mobile and Wireless Networks, pp. 29–42, (2010)

  9. Hu, S.: ‘Virtual Fence’ along border to be delayed. Washington Post, February 28, (2008)

  10. Kumar, S., Lai, T., Arora, A.: Barrier coverage with wireless sensors. Wirel. Netw. 13(6), 817–834 (2007)

    Article  Google Scholar 

  11. Li, M., Sun, X., Zhao, Y.: Minimum-cost linear coverage by sensors with adjustable ranges. In: Proceedings of the 6th International Conference on Wireless Algorithms, Systems, and Applications, pp. 25–35, (2011)

  12. Li, X., Frey, H., Santoro, N., Stojmenovic, I.: Localized sensor self-deployment with coverage guarantee. ACM SIGMOBILE Mob. Comput. Commun. Rev. 12(2), 50–52 (2008)

    Article  Google Scholar 

  13. Mehrandish, M.: On Routing, Backbone Formation and Barrier Coverage in Wireless Ad Doc and Sensor Networks. PhD thesis, Concordia University, Montreal, Quebec, Canada, (2011)

  14. Mehrandish, M., Narayanan, L., Opatrny, J.: Minimizing the number of sensors moved on line barriers. In: Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), pp. 653–658, (2011)

  15. Tan, X., Wu, G.: New algorithms for barrier coverage with mobile sensors. In: Proceedings of the 4th International Workshop on Frontiers in Algorithmics, pp. 327–338, (2010)

  16. Yang, S., Li, M., Wu, J.: Scan-based movement-assisted sensor deployment methods in wireless sensor networks. IEEE Trans. Parallel Distrib. Syst. 18(8), 1108–1121 (2007)

    Article  Google Scholar 

  17. Zou, Y., Chakrabarty, K.: A distributed coverage and connectivity-centric technique for selecting active nodes in wireless sensor networks. IEEE Trans. Comput. 54(8), 978–991 (2005)

    Article  Google Scholar 

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Acknowledgments

We thank the anonymous reviewers for their comments that help improve the presentation of the paper. This research was supported in part by NSF under Grant CCF-1317143.

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Authors and Affiliations

  1. Department of Computer Science, Utah State University, Logan, UT, 84322, USA

    Aaron M. Andrews & Haitao Wang

Authors
  1. Aaron M. Andrews
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  2. Haitao Wang
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Corresponding author

Correspondence to Haitao Wang.

Additional information

A preliminary version of this paper appeared in the Proceedings of the 14th Algorithms and Data Structures Symposium (WADS 2015).

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Andrews, A.M., Wang, H. Minimizing the Aggregate Movements for Interval Coverage. Algorithmica 78, 47–85 (2017). https://doi.org/10.1007/s00453-016-0153-8

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  • DOI: https://doi.org/10.1007/s00453-016-0153-8

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