Abstract
In this paper we study covering problems that arise in wireless networks with Unmanned Aerial Vehicles (UAVs) swarms. In the general setting we want to place a set of UAVs that should cover a given set of planar users under some constraints and we want to maintain the solution efficiently in a static and dynamic fashion. Specifically, for a set S of n non-negative weighted points in the plane, we consider a set P of m disks (or squares) of radius \(R_{COV}\) where the goal is to place (and maintain under dynamic updates) their location such that the sum of the weights of the points in S covered by disks from P is maximized. In the connected version, we also require that the graph imposed on P should be connected. Moreover, for the static connected version we improve the results from [1] and we obtain a constant factor approximation algorithm. In order to solve our problem under various requirements, we use a variety of techniques including dynamic grid, a reduction to Budgeted Subset Steiner Connected Dominating Set problem, tree partition, and others. We present several simple data structures that maintain an O(1)-approximate solution efficiently, under insertions and deletions of points to/from S where each update operation can be performed in logarithmic time.
K. Danilchenko and M. Segal—This research has been supported by the grant from Pazy Foundation.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Danilchenko, K., Segal, M.: Connected ad-hoc swarm of drones. In: Proceedings of the 6th ACM Workshop on Micro Aerial Vehicle Networks, Systems, and Applications, DroNet 2020, New York, NY, USA. Association for Computing Machinery (2020). https://doi.org/10.1145/3396864.3399699
De Berg, M., Cabello, S., Har-Peled, S.: Covering many or few points with unit disks. Theory Comput. Syst. 45(3), 446–469 (2009)
Garg, N.: Saving an epsilon: a 2-approximation for the \(k\)-MST problem in graphs. In: STOC, pp. 396–402 (2005)
Huang, C.-C., Mari, M., Mathieu, C., Mitchell, J.S.B., Mustafa, N.H.: Maximizing covered area in the Euclidean plane with connectivity constraint. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2019)
Jin, K., Li, J., Wang, H., Zhang, B., Zhang, N.: Near-linear time approximation schemes for geometric maximum coverage. Theoret. Comput. Sci. 725, 64–78 (2018)
Johnson, D.S., Minkoff, M., Phillips, S.: The prize collecting Steiner tree problem: theory and practice. In: SODA, pp. 760–769 (2000)
Khuller, S., Purohit, M., Sarpatwar, K.K.: Analyzing the optimal neighborhood: algorithms for budgeted and partial connected dominating set problems. In: SODA, pp. 1702–1713 (2014)
Kuo, T., Lin, K.C., Tsai, M.: Maximizing submodular set function with connectivity constraint: theory and application to networks. IEEE/ACM Trans. Netw. 23(2), 533–546 (2015)
Li, J., Wang, H., Zhang, B., Zhang, N.: Linear time approximation schemes for geometric maximum coverage. In: International Computing and Combinatorics Conference, pp. 559–571 (2015)
Lyu, J., Zeng, Y., Zhang, R., Lim, T.J.: Placement optimization of UAV-mounted mobile base stations. IEEE Commun. Lett. 21(3), 604–607 (2016)
Mozaffari, M., Saad, W., Bennis, M., Debbah, M.: Efficient deployment of multiple unmanned aerial vehicles for optimal wireless coverage. IEEE Commun. Lett. 20(8), 1647–1650 (2016)
Di Puglia Pugliese, L., Guerriero, F., Zorbas, D., Razafindralambo, T.: Modelling the mobile target covering problem using flying drones. Optim. Lett. 10(5), 1021–1052 (2015). https://doi.org/10.1007/s11590-015-0932-1
Soltani, S., Razzazi, M., Ghasemalizadeh, H.: The most points connected-covering problem with two disks. Theory Comput. Syst. 62(8), 2035–2047 (2018)
Srinivas, A., Zussman, G., Modiano, E.: Construction and maintenance of wireless mobile backbone networks. IEEE/ACM Trans. Netw. 17(1), 239–252 (2009)
Szudzik, M.: An elegant pairing function. In: Wolfram Research (ed.) Special NKS 2006 Wolfram Science Conference, pp. 1–12 (2006)
Zeng, Y., Zhang, R., Lim, T.J.: Wireless communications with unmanned aerial vehicles: opportunities and challenges. IEEE Commun. Mag. 54(5), 36–42 (2016)
Zhao, H., Wang, H., Weiyu, W., Wei, J.: Deployment algorithms for UAV airborne networks toward on-demand coverage. IEEE J. Sel. Areas Commun. 36(9), 2015–2031 (2018)
Zorbas, D., Di Puglia, L., Pugliese, T.R., Guerriero, F.: Optimal drone placement and cost-efficient target coverage. JNCA 75, 16–31 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Danilchenko, K., Segal, M., Nutov, Z. (2020). Covering Users by a Connected Swarm Efficiently. In: Pinotti, C.M., Navarra, A., Bagchi, A. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2020. Lecture Notes in Computer Science(), vol 12503. Springer, Cham. https://doi.org/10.1007/978-3-030-62401-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-62401-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-62400-2
Online ISBN: 978-3-030-62401-9
eBook Packages: Computer ScienceComputer Science (R0)