An algorithm to optimize deployment of charging base stations for WRSN
 137 Downloads
Abstract
Optimizing deployment of charging base stations in wireless rechargeable sensor networks can considerably reduce the cost. Previously, the charging base stations are simply installed at some fixed special points (e.g., the grid points) after partitioning the area distributed by sensor nodes. In this paper, a new algorithm of planning the charging base stations is proposed based on the greedy algorithm and the location relationship of the sensor nodes. The proposed algorithm exploits the local search ability and avoids falling into an exponential increase of the number of the charging base stations (i.e., combinatorial explosion). The simulated results show that the proposed algorithm can result in less number and flexible deployed locations of the charging base stations. In addition, this algorithm provides a novel solution for the point coverage problems.
Keywords
Wireless rechargeable sensor network Greedy algorithm Charging base stationAbbreviations
 APBGCS
Adaptive pairbased greedy cone selection
 CCG
Charging circlegreedy
 IoTs
Internet of things
 LSABC
Layoff simulated annealbased charging
 NBGCS
Nodebased greedy cone selection
 NP
Nondeterministic polynomial
 PBGCS
Pairbased greedy cone selection
 SABC
Simulated annealbased charging
 WPT
Wireless power transfer
 WRSN
Wireless rechargeable sensor network
 WSN
Wireless sensor network
1 Introduction
The massive Internet of things (IoTs) [1] which provide big data for cloud computing [2, 3, 4, 5, 6] and traditional networks [7] have been applied to many fields in reality. As an important part of the IoT [8, 9], the wireless sensor network (WSN) [10, 11, 12] has the capabilities of data collection [13, 14, 15], data storage, and wireless communication [16, 17]. WSN plays a significant role in the construction of smart cities [18, 19], smart agriculture [20], and public utility monitoring [21], etc. However, WSNs are traditionally powered by batteries [22], which result in a limit lifetime of the networks. Many researchers effectively extend the network life cycle by reducing energy consumption or improving the energy performance of sensor network [23, 24, 25, 26, 27, 28, 29]. A potential solution of power supply for the sensor nodes in WSNs is using wireless power transfer (WPT) technologies [30] to realize a wireless rechargeable sensor network (WRSN) where some charging base stations are dedicatedly deployed to provide the power permanently, or mobile charging devices are dispatched to approach and charge the sensor nodes.
Although higher power transfer efficiency can be obtained for the nearfield WPT than the farfield WPT, largersized coils and good alignment are required in reality for the nearfield WPT because of the nonradiated magnetic coupling and radiated covering properties for the nearfield and farfield WPT technologies, respectively. In practice, the farfield WPT with the property of radiation is more suitable for WRSN, because of the relatively large distance from the base station to the sensors, which is usually much larger than the size of the sensor nodes (especially under the requirement of compact size for sensor nodes).
Existing approaches on WRSN charging can be divided into two types, i.e., the mobile charging strategy and the static charging strategy. The main optimization goal of the mobile charging strategies [31, 32, 33, 34, 35, 36] is to reduce the charging process cost (e.g., the number of the mobile charging devices such as the charging vehicles and the charging time) as much as possible while ensuring that the sensors can work continuously. Although the mobile charging strategy looks like more flexibility, it is not automatic enough and depends on the dispatch algorithm. In addition, the mobile charging strategy usually relies on the nearfield WPT and short charging time is assumed. However, the environment (e.g., the accessible distance) of the distributed sensors will prevent the charging devices from charging the sensors effectively because of the restriction of the sizes and directions of the transmitting and receiving coils for the nearfield WPT. Because of the advantage of convenience and stability, the static charge strategy is chosen in many applications, at which this paper is focused.
For the static charge strategy, the authors of [37] optimized the number of the charging base stations by considering the point provisioning and path provisioning problems. However, the work of [37] is essentially similar to the traditional wireless network coverage problem [38], and only the case of the uniformly distributed sensor nodes is discussed. The authors of [39] proposed a redundancy algorithm, which is essentially an improved simulated annealing algorithm, to optimize the number of charging base stations. However, the simulation validation does not consider the power consumptions of the sensor nodes in [39], which are actually related to the charging distance and charging efficiency in reality. The authors of [40] proposed an improved firefly algorithm to solve the multiobjective optimization problem. However, only an example with few sensor nodes is taken in [40]. The authors of [41] placed the wireless charging base stations on a network grid point after uniformly portioning the area where the sensors were distributed. Under the assumption of the base station with a certain height and a fixed radiation angle, a nodebased greedy cone selecting algorithm and a pairbased greedy cone selecting algorithm were proposed. Furthermore, the adaptive pair of the greedy cone selection (APBGCS) algorithm was proposed in [42] based on the algorithms in [41], which is suitable for the case with more sensors. However, the numbers of the base stations in [41, 42] are insufficiently optimized, although the planning was simpler, since the sensors’ distributed area was partitioned uniformly and the charging base stations were fixed at the grid points. In addition, the number of the charging base stations and the complexity of the algorithm depend on the size of the cells after portioning. In reality, the charging base stations can be optimized at better positions, not only at some special points (e.g., the grid points). The deployment problem of charging base station is obviously a nonconvex optimization problem [43] which has been studied for wireless sensor networks [44, 45, 46, 47, 48]. The local optimal solution of this problem is not necessarily the global optimal solution actually. In this paper, a new algorithm, called the charging circlegreedy (CCG) algorithm by combining both the merits of the nodes’ location consideration and the charging area partition, is proposed to achieve better optimization. Multiple simulations are also given for validations in this paper.
2 CCG algorithm method
2.1 WRSN network model
2.2 Problem definition
The problem is defined as a minimum number of charging base stations that are required to provide enough power to the N randomly distributed charging sensor nodes in the twodimensional region Ω. The coverage range of a charging base station is a circle with radius R. One sensor node can be covered by multiple charging base stations according to its power consumption. Building some base stations to cover many discrete sensor nodes in a plane region [41] is a nonlinear programming problem, which are basically NPhard problems [49, 50]. The NPhard problems can be solved only by approximation methods.
2.3 Methods
where the largest inscribed square of a circle covered by a base station is 2^{0.5}R. If each sensor node is only required to be covered once, M_{max} in (1) is actually the upper limit of M, regardless of the number of sensor nodes in the area Ω.
In practice, the location information of the sensor nodes can be obtained. The sensor nodes can be combined according to their topology information. Each combination contains the sensor nodes which can be covered by a charging base station. In this situation, the increase of the sensor nodes (especially when the sensor nodes are crowded) leads to the exponential increase of the charging base stations, because a charging base station exists potentially as long as the distance between arbitrary two sensor nodes is shorter than 2R. Selecting the optimal set of charging base stations from the order of exponential numbers by using the existing methods [39] or the ergodic method to find the optimal solution will result in combinatorial explosion problem [52], consequently, exceeding M_{max} for the number of base stations and nonpolynomial time complexity [53, 54]. In actual, this is similar to the optimization version of a set cover problem [55] which is a NPhard problem.

Step 1: Classify all the sensor nodes u_{i} (i = 1, 2… N) according to their ycoordinate values and store them into Q_{i} in which all the ycoordinate values belongs to [2(i1)R, 2iR]. The total set of the sensor nodes is Q = {Q_{1}, Q_{2}... Q_{T}};

Step 2: Let i = 1;

Step 3: Find the sensor nodes with the smallest xcoordinate value in Q_{i}, denoted as u_{k};

Step 4: Find a set of sensor nodes whose distances from u_{k} are not greater than 2R, denoted as s_{k};

Step 5: List the sensor node pair whose distance is greater than 2R in s_{k}, and exclude one of the sensor nodes in this node pair from s_{k}; the excluded priority: the node not located in Q_{i} > the node with a higher xcoordinate value in Q_{i} > the node u_{k};

Step 6 Exclude some of the nodes in s_{k} until all nodes in s_{k} can be covered by a circle with radius R; the excluded priority: the sensor node not located in Q_{i} > the node with a higher xcoordinate value in Q_{i} > the node u_{k};

Step 7: Store s_{k} in S; in s_{k}, exclude the sensor nodes satisfying the number of coverage (i.e., satisfying the power replenishment) from Q and leave the sensor nodes not satisfying the number of coverage in Q; and repeat step 3 through step 7 until Q_{i} = ∅; and

Step 8: Let i = i + 1, repeat step 3 to step 8 until Q = ∅, and end the algorithm.
 a)
Find the two sensors which are the farthest away each other in the set s_{k}, denoted as p_{1} and p_{2}; find the midpoint c_{i} of p_{1} and p_{2}; find the sensor node in the set s_{k} that is the farthest from c_{i} (except p_{1} and p_{2}) in the set s_{k} and denoted as p_{3}; judge whether the distance between p_{3} and c_{i} is greater than R: if it is, enter step b; otherwise, go to step d;
 b)
Take sensor p_{1}, p_{2}, and p_{3} as the vertices and make a triangle where c_{i} updates the outer center of this triangle; if the distance between sensors and c_{i} in s_{k} is greater than R, enter step c; otherwise, go to step d;
 c)
If only one sensor of p_{1}, p_{2}, and p_{3} does not belong to Q_{i}, remove the sensor that does not belong to Q_{i} from the set s_{k}; if two sensors in p_{1}, p_{2}, and p_{3} do not belong to Q_{i}, then remove the sensor with larger xcoordinate value in this two sensors from the set s_{k}; otherwise, remove the sensor with the largest xcoordinate value in this three sensors (p_{1}, p_{2}, p_{3}) from the set s_{k}; return step a; and
 d)
Put the set s_{k} into set S, where c_{i} is the location of the base station.
3 Results of simulation
4 Discussion
 (1)
The algorithm can be considered as covering a bounded region Ω with multiple circles with an area of πR^{2}. When all the sensor nodes only need to be covered once, the maximum number of charging base stations is M_{max}. That is, the CCG algorithm is convergent.
 (2)
A sorting algorithm is used in step 1 to partition the sensor nodes referring to the ycoordinate values. The time complexity of step 1 is O(n). In step 3, the worst case is that all the sensor nodes are in Q_{i} and the corresponding complexity of step 3 is O(n^{2}). In step 4, if all the sensor nodes are clustered in s_{i}, the time complexity is O(n^{4}), and the time complexity of the remaining steps are constants. So the time complexity of the CCG algorithm is O(n^{4}). Actually, this is the worst time complexity in theory. In reality, all the nodes will not be distributed within the range of one base station. Therefore, the average time complexity of the CCG algorithm is commonly O(n^{2}).
Aiming to the optimization target (i.e., the number of the charging base stations), the CCG algorithm has low complexity, is simple to use without lengthy formula derivation and complicated calculation, and has flexible deployment of the wireless charging base station. Actually, each sensor nodes consume different powers depending on the functions which are not considered comprehensively in this paper. In the future work, we will design a more efficient wireless charging base station deployment algorithm for the different power consumptions of the sensor nodes.
5 Conclusions
In order to optimize the deployment and the number of the charging base stations in wireless rechargeable sensor networks, the charging circle greedy algorithm has been proposed. This new algorithm makes use of the strong local search ability of the greedy algorithm and avoids the deficiency in the overall search ability by setting a travel direction for the greedy circle. Compared to the existing algorithms, the proposed algorithm can result in less number and flexible deployed locations of the charging base stations with lower time complexity. In addition, the charging circle greedy algorithm also inspires some new ideas for solving other point coverage problems.
Notes
Funding
This work is supported by the following funding: Zhejiang Provincial Natural Science Foundation of China under grant No. LY17F010018 and the Natural Science Foundation of China under grant No. 61771175.
Availability of data and materials
Not applicable.
Authors’ contributions
YC and GW conceived the idea. PW and BW complete the algorithm. PW and YC wrote this paper. GW contributed to the reviewing of the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
 1.X. Liu, S. Zhao, A. Liu, N. Xiong, A.V. Vasilakos, Knowledgeaware proactive nodes selection approach for energy management in internet of things. Futur. Gener. Comput. Syst. 92, 11421156 (2017)Google Scholar
 2.B. Lin, W. Guo, N. Xiong, G. Chen, A.V. Vasilakos, H. Zhang, A pretreatment workflow scheduling approach for big data applications in multicloud environments. IEEE Trans. Netw. Serv. Manag. 13(3), 581–594 (2016)CrossRefGoogle Scholar
 3.Z. Wang, T. Li, N. Xiong, Y. Pan, A novel dynamic network data replication scheme based on historical access record and proactive deletion. J. Supercomput. 62(1), 227–250 (2012)CrossRefGoogle Scholar
 4.J. Yin, W. Lo, S. Deng, Y. Li, W. Z, N. Xiong, Colbar: a collaborative locationbased regularization framework for QoS prediction. Inf. Sci. 265, 68–84 (2013)MathSciNetCrossRefGoogle Scholar
 5.N. Xiong, J.W. AV Vasilakos, Y.R. Yang, A. Rindos, Y. Zhou, W.Z. Song, in 2012 IEEE 26th International Parallel and Distributed Processing Symposium. A selftuning failure detection scheme for cloud computing service (Shanghai, 2012), pp. 668–679Google Scholar
 6.Y. Zhou, Y. Zhang, H. Liu, N. Xiong, A.V. Vasilakos, A baremetal and asymmetric partitioning approach to client virtualization. IEEE Trans. Serv. Comput. 7(1), 40–53 (2014)CrossRefGoogle Scholar
 7.N. Xiong, A.V. Vasilakosb, L.T. Yang, C. Wang, R. Kannane, C. Chang, Y. Pan, A novel selftuning feedback controller for active queue management supporting TCP flows. Inf. Sci. 180(11), 2249–2263 2010Google Scholar
 8.K. Huang, Q. Zhang, C. Zhou, N. Xiong, Y. Qin, An efficient intrusion detection approach for visual sensor networks based on traffic pattern learning. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 47(10), 2704–2713 (2017)CrossRefGoogle Scholar
 9.N. Xiong, R. Wen Liu, M. Liang, W. D, Z. Liu, W. H, Effective alternating direction optimization methods for sparsityconstrained blind image deblurring. Sensors 17(12), 174 (2017)CrossRefGoogle Scholar
 10.H. Zheng, W. Guo, N. Xiong, A kernelbased compressive sensing approach for mobile data gathering in wireless sensor network systems. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 8(99), 1–13 2017Google Scholar
 11.W. Guo, N. Xiong, A.V. Vasilakos, G. Chen, C. Yu, Distributed k–connected fault–tolerant topology control algorithms with PSO in future autonomic sensor systems. Int J of Sens Netw 12(1), 53–62 (2012)CrossRefGoogle Scholar
 12.Y. Zhou, D. Zhang, N. Xiong, Postcloud computing paradigms: a survey and comparison. Tsinghua Sci. Technol. 22(6), 714–732 (2017)CrossRefGoogle Scholar
 13.Q. Zhang, Q. Qiu, G. We, K. Guo, N. Xiong, A social community detection algorithm based on parallel grey label propagation. Comput. Netw. 107(1), 133–143 2016Google Scholar
 14.A. Shahzad, M. Lee, H.D. Kim, S. Woo, N. Xiong, New security development and trends to secure the SCADA sensors automated transmission during critical sessions. Symmetry 7(4), 1945–1980 (2015)MathSciNetCrossRefGoogle Scholar
 15.A. Shahzad, M. Lee, C. Lee, N. Xiong, S. Kim, Y. Lee, K. Kim, S. Woo, G. Jeong, The protocol design and new approach for SCADA security enhancement during sensors broadcasting system. Multimed. Tools Appl. 75(22), 14641–14668 (2015)CrossRefGoogle Scholar
 16.X. Jing, H. H, H. Yang, M.H. Au, S. Li, N. Xiong, M. Imran, A.V. Vasilakos, A quantitative risk assessment model involving frequency and threat degree under lineofbusiness services for infrastructure of emerging sensor networks. Sensors 17(3), 642 (2017)CrossRefGoogle Scholar
 17.J. Li, H. H, K. Qiao, N. Xiong, A novel topology linkcontrolling approach for active defense of a node in a network. Sensors 17(3), 553 (2017)CrossRefGoogle Scholar
 18.J. Li, N. Xiong, J.H. Park, C. Liu, M.A. Shihua, S.E. Cho, Intelligent model design of cluster supply chain with horizontal cooperation. J. Intell. Manuf. 23(4), 917–931 2009Google Scholar
 19.N. Xiong, X. Jia, L.T. Yang, A.V. Vasilakos, Y. Li, Y. Pan, A distributed efficient flow control scheme for multirate multicast networks. IEEE Trans. Parallel Distrib. Syst. 21(9), 1254–1266 (2010)CrossRefGoogle Scholar
 20.Y. Yang, N. Xiong, N.Y. Chong, X. Défago, in 2008 The 3rd International Conference on Grid and Pervasive Computing  Workshops. A decentralized and adaptive flocking algorithm for autonomous mobile robots (Kunming, 2008), pp. 262–268Google Scholar
 21.N. Xiong, A.V. Vasilakos, L.T. Yang, L. Song, Y. Pan, R. Kannan, Y. Li, Comparative analysis of quality of service and memory usage for adaptive failure detectors in healthcare systems. IEEE J. Sel. Areas Commun. 27(4), 495–509 (2009)CrossRefGoogle Scholar
 22.S. Rajba, P. Raif, T. Rajba, in 2013 IEEE Symposium on Computational Intelligence in Healthcare and eHealth. Wireless sensor networks in application to patients health monitoring (Singapore, 2013), pp. 94–98Google Scholar
 23.C. Lin, N. Xiong, J.H. Park, T. Kim, Dynamic power management in new architecture of wireless sensor networks. Int. J. Commun. Syst. 22(6), 671–693 (2009)CrossRefGoogle Scholar
 24.Y. Zeng, C.J. Sreenan, N. Xiong, L.T. Yang, J.H. Park, Connectivity and coverage maintenance in wireless sensor networks. J. Supercomput. 52(1), 23–46 (2010)CrossRefGoogle Scholar
 25.W. Fang, Y. Li, H. Zhang, N. Xiong, J. Lai, A.V. Vasilakos, On the throughputenergy tradeoff for data transmission between cloud and mobile devices. Inf. Sci. 283, 79–93 (2014)CrossRefGoogle Scholar
 26.H. Cheng, Z. Su, N. Xiong, Y. Xiao, Energyefficient nodes scheduling algorithms for wireless sensor networks using Markov random field model. Inf. Sci. 329(C), 461–477 (2016)CrossRefGoogle Scholar
 27.W. M, L. Tan, N. Xiong, Data prediction, compression and recovery in clustered wireless sensor networks for environmental monitoring applications. Inf. Sci. 329(C), 800–818 (2016)Google Scholar
 28.H. Cheng, Y. Chen, N. Xiong, F. Li, Layerbased data aggregation and performance analysis in wireless sensor networks. J. Appl. Math. 502381, 1–12 2013Google Scholar
 29.F. Xia, R. Hao, J. Li, N. Xiong, L.T. Yang, Y. Zhang, Adaptive GTS allocation in IEEE 802.15.4 for realtime wireless sensor networks. J. Syst. Archit. 59(10), 1231–1242 (2013)CrossRefGoogle Scholar
 30.A. Kurs, A. Karalis, R. Moffatt, Wireless power transfer via strongly coupled magnetic resonances. Science 317(5834), 83–86 2007Google Scholar
 31.C. Qin, Y. Sun, Y. Zhang, in 2017 29th Chinese Control And Decision Conference. A novel path planning of mobile charger in wireless rechargeable sensor networks (Chongqing, 2017), pp. 2063–2067Google Scholar
 32.C. Lin, R. Han, P^{2}S: a primary and passerby scheduling algorithm for onremand charging architecture in wireless rechargeable sensor networks. IEEE Trans. Veh. Technol. 66(9), 8047–8058 (2017)CrossRefGoogle Scholar
 33.S. Zhang, W. J, L. S, Collaborative mobile charging. IEEE Trans. Comput. 64(3), 654–667 (2014)MathSciNetCrossRefGoogle Scholar
 34.M. Zhao, J. Li, Y. Yang, in Proceeding ITC '11 Proceedings of The 23rd International Teletraffic Congress. Joint Mobile Energy Replenishment and Data Gathering in Wireless Rechargeable Sensor Networks (San Francisco, 2011), pp. 238–245Google Scholar
 35.L. Xie, Y. Shi, Y. Hou, W. Lou, H. Sherali, Multinode wireless energy charging in sensor networks. IEEE/ACM Trans. Networking 23(2), 437–450 (2014)CrossRefGoogle Scholar
 36.L. Xie, Y. Shi, Y.T. Hou, H.D. Sherali, Making sensor networks immortal: an energyrenewal approach with wireless power transfer. IEEE/ACM Trans. Networking 20(6), 1748–1761 (2012)CrossRefGoogle Scholar
 37.S. He, J. Chen, F. Jiang, D. Yau, G. Xing, Y. Sun, Energy provisioning in wireless rechargeable sensor networks. IEEE Trans. Mob. Comput. 12(10), 1931–1942 (2013)CrossRefGoogle Scholar
 38.P. Wu, F. Xiao, C. Sha, H. Huang, R. Wang, N. Xiong, Node scheduling strategies for achieving fullview area coverage in camera sensor networks. Sensors 17(6), 1303 (2017)CrossRefGoogle Scholar
 39.W. Chien, H. Cho, H. Chao, in 2016 International Wireless Communications and Mobile Computing Conference. Enhanced SAbased charging algorithm for WRSN (Paphos, 2016), pp. 1012–1017Google Scholar
 40.G. Sun, Y. Liu, M. Yang, A. Wang, Y. Zhang, in IEEE Global Communications Conference. Charging nodes deployment optimization in wireless rechargeable sensor network (Singapore, 2017), pp. 1–6Google Scholar
 41.J. Liao, J. Jiang, in 2014 7th International Conference on UbiMedia Computing and Workshops. Wireless charger deployment optimization for wireless rechargeable sensor networks (Ulaanbaatar, 2014), pp. 160–164Google Scholar
 42.J.H. Liao, C.M. Hong, J.R. Jiang, An adaptive algorithm for charger deployment optimization in wireless rechargeable sensor networks. Front. Artif. Intell. Appl. 274, 2080–2089 (2015)Google Scholar
 43.W. Cheng, M. Zhao, N. Xiong, K.T. Chui, Nonconvex sparse and lowrank based robust subspace segmentation for data mining. Sensor 17(7), 1633 (2017)CrossRefGoogle Scholar
 44.L. RW Liu, S.C.H.Y. Shi, N. Xiong, D. Wang, Reconstruction of undersampled big dynamic MRI data using nonconvex lowrank and sparsity constraints. Sensors 17(3), 509 (2017)CrossRefGoogle Scholar
 45.S. Wang, H. Yi, W. L, F. Zhou, N. Xiong, Mining probabilistic representative gathering patterns for mobile sensor data. J. Int. Technol. 18(2), 321–332 (2017)Google Scholar
 46.Q. Fan, N. Xiong, K. Zeitouni, Game balanced multifactor multicast routing in sensor grid networks. Inf. Sci. 367, 550–572 (2016)CrossRefGoogle Scholar
 47.Q. Fan, K. Zeitouni, N. Xiong, W. Q, A General Nash Equilibrium Semantic Cache Algorithm in a Sensor Grid Database System. International Conference on Data Management in Cloud, Grid and P2P Systems, vol 8648 (2014), pp. 13–24Google Scholar
 48.T.L. Lin, S.L. Li, H.Y. Chang, A power balance aware wireless charger deployment method for complete coverage in wireless rechargeable sensor networks. Energies 9(9), 695 (2016)CrossRefGoogle Scholar
 49.R.G. Michael, S.J. David, Computers and Intractability: A Guide to the Theory of NPCompleteness (W. H. Freeman and Company, New York, 1979), pp. 187–288Google Scholar
 50.N. Nguyen, B. Liu, The mobile sensor deployment problem and the target coverage problem in mobile wireless sensor networks are NPhard. IEEE Syst. J. 9(99), 1–4 (2018)CrossRefGoogle Scholar
 51.M. Cardei, J. Wu, Energyefficient coverage problems in wireless adhoc sensor networks. Comput. Commun. 29(4), 413–420 (2006)CrossRefGoogle Scholar
 52.L. Li, D. Wang, X. Shen, M. Yang, in 2009 International Conference on Computational Intelligence and Software Engineering. A method for combinatorial explosion avoidance of AI planner and the application on test case generation (Wuhan, 2009), pp. 1–4Google Scholar
 53.C. Chung, A. Matsuoka, Y. Yang, in IEEE/ACM 5th International Workshop on Games and Software Engineering. Serious games for NPhard problems: challenges and insights (Austin, 2016), pp. 29–32Google Scholar
 54.L.V. Ahn, Games with a purpose. Computer 39(6), 92–94 (2006)CrossRefGoogle Scholar
 55.K.S. Hung, K.S. Lui, On perimeter coverage in wireless sensor networks. IEEE Trans. Wirel. Commun. 9(7), 2156–2164 (2010)CrossRefGoogle Scholar
Copyright information
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.