Skip to main content
SpringerLink
Log in

Doing their best: How to provide service by limited number of drones?

  • Original Paper
  • Published:
Wireless Networks Aims and scope Submit manuscript

Abstract

Exploiting drones as flying base stations to assist the terrestrial cellular networks or replace them is promising in 5G and beyond. One of the challenging problems is optimally deploying multiple drones to achieve coverage for the ground users. Usually, the goal is to find the minimum number of drones and their placement when all users are served. In this work, we consider a more realistic scenario. We focus on the situation where the number of drones is given in advance, and this number is significantly smaller than the number required to cover all ground users. This assumption is reasonable in emergency cases or battlefields where the number of ground users (for example, soldiers or firefighters) is much larger than the number of drones. Additionally, we consider the case when the ground users have a rank, interpreted as weight, and we aim to deploy drones’ swarm such that the sum of the weights of the ground users covered by the swarm is maximized while the drones in the swarm are connected (without involving a third party entity that provides connectivity in the swarm). Our solution significantly improves currently best known approximation ratio for the problem from 1/144 to 1/28.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Al-Hourani, A., Kandeepan, S., & Jamalipour, A. (2014). Modeling air-to-ground path loss for low altitude platforms in urban environments. In 2014 IEEE Global Communications Conference, pp. 2898–2904.

  2. Al-Hourani, A., Kandeepan, S., & Lardner, S. (2014). Optimal lap altitude for maximum coverage. IEEE Wireless Communications Letters, 3(6), 569–572.

    Article  Google Scholar 

  3. Alzenad, M., El-Keyi, A., Lagum, F., & Yanikomeroglu, H. (2017). 3-D placement of an unmanned aerial vehicle base station (UAV-BS) for energy-efficient maximal coverage. IEEE Wireless Communications Letters, 6(4), 434–437.

    Article  Google Scholar 

  4. Cherif, N., Jaafar, W., Yanikomeroglu, H., & Yongacoglu, A. (2020). On the optimal 3D placement of a UAV base station for maximal coverage of UAV users. In GLOBECOM 2020–2020 IEEE Global Communications Conference, pp. 1–6.

  5. Cherif, N., Alzenad, M., Yanikomeroglu, H., & Yongacoglu, A. (2020). Downlink coverage and rate analysis of an aerial user in vertical heterogeneous networks (vhetnets). IEEE Transactions on Wireless Communications, 20(3), 1501–1516.

    Article  Google Scholar 

  6. Danilchenko, K., & Segal, M. (2020). Connected Ad-Hoc swarm of drones. In: Proceedings of the 6th ACM Workshop on Micro Aerial Vehicle Networks, Systems, and Applications, DroNet ’20, New York, NY, USA. Association for Computing Machinery.

  7. Danilchenko, K., Segal, M., & Nutov, Z. (2020). Covering users by a connected swarm efficiently. In: International Symposium on Algorithms and Experiments for Sensor Systems, Wireless Networks and Distributed Robotics, Springer, pp. 32–44.

  8. De Berg, M., Cabello, S., & Har-Peled, S. (2009). Covering many or few points with unit disks. Theory of Computing Systems, 45(3), 446–469.

    Article  MathSciNet  MATH  Google Scholar 

  9. Di Puglia, L., Pugliese, F. G., Zorbas, D., & Razafindralambo, T. (2016). Modelling the mobile target covering problem using flying drones. Optimization Letters, 10(5), 1021–1052.

    Article  MathSciNet  MATH  Google Scholar 

  10. Funke, S., Kesselman, A., Kuhn, F., Lotker, Z., & Segal, M. (2007). Improved approximation algorithms for connected sensor cover. Wireless Networks, 13(2), 153–164.

    Article  Google Scholar 

  11. Garg, N. (2005). Saving an epsilon: A 2-approximation for the \(k\)-MST problem in graphs. In STOC, pp. 396–402.

  12. Hou, T., Liu, Y., Sun, X., Song, Z., & Chen, Y. (2019). Non-orthogonal multiple access in multi-UAV networks. In: 2019 IEEE 90th Vehicular Technology Conference (VTC2019-Fall), pp. 1–5. IEEE.

  13. Huang, L., Li, J., & Shi, Q. (2015). Approximation algorithms for the connected sensor cover problem. In: International computing and combinatorics conference, Springer, pp. 183–196.

  14. Huang, L., Li, J., & Shi, Q. (2020). Approximation algorithms for the connected sensor cover problem. Theoretical Computer Science, 809, 563–574.

    Article  MathSciNet  MATH  Google Scholar 

  15. Jin, K., Li, J., Wang, H., Zhang, B., & Zhang, N. (2018). Near-linear time approximation schemes for geometric maximum coverage. Theoretical Computer Science, 725, 64–78.

    Article  MathSciNet  MATH  Google Scholar 

  16. Johnson, D. S., Minkoff, M., & Phillips, S. (2000). The prize collecting steiner tree problem: Theory and practice. In: SODA, pp. 760–769

  17. Kalantari, E., Yanikomeroglu, H., & Yongacoglu, A. (2016). On the number and 3D placement of drone base stations in wireless cellular networks. In: 2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), pp. 1–6

  18. Khuller, S., Purohit, M., & Sarpatwar, K. K. (2014). Analyzing the optimal neighborhood: Algorithms for budgeted and partial connected dominating set problems. In: SODA, pp. 1702–1713.

  19. Khuller, S., Purohit, M., & Sarpatwar, K. K. (2020). Analyzing the optimal neighborhood: Algorithms for partial and budgeted connected dominating set problems. SIAM Journal on Discrete Mathematics, 34(1), 251–270.

    Article  MathSciNet  MATH  Google Scholar 

  20. Khuwaja, A. A., Chen, Y., Zhao, N., Alouini, M.-S., & Dobbins, P. (2018). A survey of channel modeling for UAV communications. IEEE Communications Surveys & Tutorials, 20(4), 2804–2821.

    Article  Google Scholar 

  21. Li, J., Wang, H., Zhang, B., & Zhang, N. (2015). Linear time approximation schemes for geometric maximum coverage. In: International computing and combinatorics conference, pp. 559–571

  22. Lyu, J., Zeng, Y., Zhang, R., & Lim, T. J. (2016). Placement optimization of UAV-mounted mobile base stations. IEEE Communications Letters, 21(3), 604–607.

    Article  Google Scholar 

  23. Matsuda, Y., & Takahashi, S. (2019). A 4-approximation algorithm for k-prize collecting steiner tree problems. Optimization Letters, 13(2), 341–348.

    Article  MathSciNet  MATH  Google Scholar 

  24. Mozaffari, M., Saad, W., Bennis, M., & Debbah, M. (2016). Efficient deployment of multiple unmanned aerial vehicles for optimal wireless coverage. IEEE Communications Letters, 20(8), 1647–1650.

    Article  Google Scholar 

  25. Namvar, N., Homaifar, A., Karimoddini, A., & Maham, B. (2019). Heterogeneous UAV cells: An effective resource allocation scheme for maximum coverage performance. IEEE Access, 7, 164708–164719.

    Article  Google Scholar 

  26. Rahimi, Z., Sobouti, M. J., Ghanbari, R., Seno, S. A. H., Mohajerzadeh, A., Ahmadi, H., & Yanikomeroglu, H. (2021). An efficient 3D positioning approach to minimize required UAVS for IoT network coverage. IEEE Internet of Things Journal, 9(1), 558–571.

    Article  Google Scholar 

  27. Ravi, R., Sundaram, R., Marathe, M. V., Rosenkrantz, D. J., & Ravi, S. S. (1996). Spanning trees-short or small. SIAM Journal on Discrete Mathematics, 9(2), 178–200.

    Article  MathSciNet  MATH  Google Scholar 

  28. Rihan, M., Selim, M. M., Chen, X., & Huang, L. (2019). D2D communication underlaying UAV on multiple bands in disaster area: Stochastic geometry analysis. IEEE Access, 7, 156646–156658.

    Article  Google Scholar 

  29. Savkin, A. V., & Huang, H. (2019). Asymptotically optimal deployment of drones for surveillance and monitoring. Sensors, 19(9), 2068.

    Article  Google Scholar 

  30. Srinivas, A., Zussman, G., & Modiano, E. (2009). Construction and maintenance of wireless mobile backbone networks. IEEE/ACM Transactions on Networking, 17(1), 239–252.

    Article  Google Scholar 

  31. Zaidi, S. K., Hasan, S. F., & Gui, X. (2019). Outage analysis of ground-aerial noma with distinct instantaneous channel gain ranking. IEEE Transactions on Vehicular Technology, 68(11), 10775–10790.

    Article  Google Scholar 

  32. Zeng, Y., Zhang, R., & Lim, T. J. (2016). Wireless communications with unmanned aerial vehicles: Opportunities and challenges. IEEE Communications Magazine, 54(5), 36–42.

    Article  Google Scholar 

  33. Zhang, X., & Duan, L. (2019). Fast deployment of UAV networks for optimal wireless coverage. IEEE Transactions on Mobile Computing, 18(3), 588–601.

    Article  Google Scholar 

  34. Zhao, H., Wang, H., Weiyu, W., & Wei, J. (2018). Deployment algorithms for UAV airborne networks toward on-demand coverage. IEEE Journal on Selected Areas in Communications, 36(9), 2015–2031.

    Article  Google Scholar 

  35. Zhong, X., Huo, Y., Dong, X., & Liang, Z. (2020). Qos-compliant 3-D deployment optimization strategy for UAV base stations. IEEE Systems Journal, 15(2), 1795–1803.

    Article  Google Scholar 

  36. Zorbas, D., Di Puglia, L., Pugliese, T. R., & Guerriero, F. (2016). Optimal drone placement and cost-efficient target coverage. JNCA, 75, 16–31.

    MATH  Google Scholar 

Download references

Acknowledgements

This research has been supported by a grant from Pazy Foundation. The authors thank all reviewers for their valuable comments that greatly improved the presentation of the results.

Author information

Authors and Affiliations

  1. School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beersheba, Israel

    Kiril Danilchenko & Michael Segal

  2. Open University of Israel, Ra’anana, Israel

    Zeev Nutov

Authors
  1. Kiril Danilchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeev Nutov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Segal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Segal.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Danilchenko, K., Nutov, Z. & Segal, M. Doing their best: How to provide service by limited number of drones?. Wireless Netw 29, 209–220 (2023). https://doi.org/10.1007/s11276-022-03120-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11276-022-03120-8

Keywords

Search

Navigation