Abstract
Energy efficiency is a critical issue that attracts numerous interest of many researchers in wireless mobile sensor networks. Emerging IoT applications have brought the MinSum Sink-based Linear Barrier Coverage (MinSum SLBC) problem which aims to use sink-based mobile sensors (such as drones) to cover a line barrier (such as borders possibly for monitoring illegal intrusion). In the scenario, all the sensors are initially located at k sink stations, while the aim is to find the final positions of the sensors on the line barrier, such that the line barrier is completely covered and the total movement of the sensors is minimized. In this paper, we first study geometry properties of an optimal solution of MinSum SLBC, and reveal that an optimal solution of MinSum SLBC actually consist of intersecting segments of tangent sensors. Then, we devise a segmentation algorithm for computing a near-optimal position of each segment that is possibly part of the optimum. Lastly, by selecting segments consisting of tangent sensors via transforming to the shortest path problem, we eventually derive a factor-\((1+\varepsilon )\) approximation algorithm with a time complexity \(O(k^2(\log \frac{2r}{\varepsilon }+\log k)\), where \(\varepsilon >0\) is any given positive real number.
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References
Gao, X., Chen, Z., Fan, W., Chen, G.: Energy efficient algorithms for k-sink minimum movement target coverage problem in mobile sensor network. IEEE/ACM Trans. Netw. 25(6), 3616–3627 (2017)
Boubrima, A., Bechkit, W., Rivano, H.: On the deployment of wireless sensor networks for air quality mapping: optimization models and algorithms. IEEE/ACM Trans. Netw. 27(4), 1629–1642 (2019)
Zou, W., Guo, L., Huang, P.: Min-max movement of sink-based mobile sensors in the plane for barrier coverage. In: 2019 20th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT), pp. 1–6. IEEE (2019)
Cherry, A., Gudmundsson, J., Mestre, J.: Barrier coverage with uniform radii in 2D. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 57–69. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_5
Erzin, A., Lagutkina, N.: Barrier coverage problem in 2D. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds.) ALGOSENSORS 2018. LNCS, vol. 11410, pp. 118–130. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14094-6_8
Erzin, A., Lagutkina, N.: FPTAS for barrier covering problem with equal touching circles in 2D. Optim. Lett. 15(4), 1397–1406 (2021)
Bhattacharya, B., Burmester, M., Yuzhuang, H., 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)
Chen, D.Z., Tan, X., Wang, H., Wu, G.: Optimal point movement for covering circular regions. Algorithmica 72(2), 379–399 (2015)
Carmi, P., Katz, M.J., Saban, R., Stein, Y.: Improved PTASs for convex barrier coverage. In: Solis-Oba, R., Fleischer, R. (eds.) WAOA 2017. LNCS, vol. 10787, pp. 26–40. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89441-6_3
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). https://doi.org/10.1007/978-3-642-14785-2_3
Andrews, A.M., Wang, H.: Minimizing the aggregate movements for interval coverage. Algorithmica 78(1), 47–85 (2017)
Tan, X., Wu, G.: New algorithms for barrier coverage with mobile sensors. In: Lee, D.-T., Chen, D.Z., Ying, S. (eds.) FAW 2010. LNCS, vol. 6213, pp. 327–338. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14553-7_31
Benkoczi, R., Friggstad, Z., Gaur, D., Thom, M.: Minimizing total sensor movement for barrier coverage by non-uniform sensors on a line. In: Bose, P., Gąsieniec, L.A., Römer, K., Wattenhofer, R. (eds.) ALGOSENSORS 2015. LNCS, vol. 9536, pp. 98–111. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28472-9_8
Dobrev, S., et al.: Complexity of barrier coverage with relocatable sensors in the plane. Theor. Comput. Sci. 579, 64–73 (2015)
Guo, L., Zou, W., Wu, C., Xu, D., Du, D.-Z.: Minsum movement of barrier and target coverage using sink-based mobile sensors on the plane. In: 41th IEEE International Conference on Distributed Computing Systems, ICDCS 2021, Washington DC, USA, 7–10 July 2021, pp. 696–706. IEEE (2021)
Acknowledgment
This research work is supported by Natural Science Foundation of China (No. 61772005) and Natural Science Foundation of Fujian Province (No 2017J01753).
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Zou, W., Guo, L., Hao, C., Liu, L. (2021). A Fast FPTAS for Two Dimensional Barrier Coverage Using Sink-Based Mobile Sensors with MinSum Movement. In: Wu, W., Du, H. (eds) Algorithmic Aspects in Information and Management. AAIM 2021. Lecture Notes in Computer Science(), vol 13153. Springer, Cham. https://doi.org/10.1007/978-3-030-93176-6_23
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DOI: https://doi.org/10.1007/978-3-030-93176-6_23
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