Optimization of wireless sensor networks deployment with coverage and connectivity constraints

Abstract

Wireless sensor networks have been widely deployed in the last decades to provide various services, like environmental monitoring or object tracking. Such a network is composed of a set of sensor nodes which are used to sense and transmit collected information to a base station. To achieve this goal, two properties have to be guaranteed: (i) the sensor nodes must be placed such that the whole environment of interest (represented by a set of targets) is covered, and (ii) every sensor node can transmit its data to the base station (through other sensor nodes). In this paper, we consider the Minimum Connected k-Coverage (MCkC) problem, where a positive integer \(k \ge 1\) defines the coverage multiplicity of the targets. We propose two mathematical programming formulations for the MCkC problem on square grid graphs and random graphs. We compare them to a recent model proposed by Rebai et al. (Comput Oper Res 59:11–21, 2015). We use a standard mixed integer linear programming solver to solve several instances with different formulations. In our results, we point out the quality of the LP-bound of each formulation as well as the total CPU time or the proportion of solved instances to optimality within a given CPU time.

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References

  1. Bonsma, P. (2012). Max-leaves spanning tree is APX-hard for cubic graphs. Journal of Discrete Algorithms, 12, 14–23.

    Article  Google Scholar 

  2. Chakrabarty, K., Iyengar, S. S., Qi, H., & Cho, E. (2002). Grid coverage for surveillance and target location in distributed sensor networks. IEEE Transactions on Computers, 51(12), 1448–1453.

    Article  Google Scholar 

  3. Das B, Bharghavan V (1997) Routing in ad-hoc networks using minimum connected dominating sets. In Communications, ICC ’97 Montreal, towards the knowledge millennium (Vol. 1, pp. 376–380). IEEE

  4. Fan N, Watson J (2012) Solving the connected dominating set problem and power dominating set problem by integer programming. In Combinatorial Optimization and Applications: 6th International Conference (COCOA), Springer, Lecture Notes in Computer Science (Vol. 7402, pp. 371–383). https://doi.org/10.1007/978-3-642-31770-5_33.

  5. Fourer, R., Gay, D. M., & Kernighan, B. W. (1993). AMPL: A modeling language for mathematical programming. Danvers: The Scientific Press (now an imprint of Boyd & Fraser Publishing Co.).

    Google Scholar 

  6. Fujie, T. (2003). An exact algorithm for the maximum leaf spanning tree problem. Computers & Operations Research, 30(13), 1931–1944.

    Article  Google Scholar 

  7. Fujie, T. (2004). The maximum-leaf spanning tree problem: Formulations and facets. Networks, 43(4), 212–223.

    Article  Google Scholar 

  8. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. New York: W. H. Freeman & Co.

    Google Scholar 

  9. Gavish, B. (1982). Topological design of centralized computer networks-formulations and algorithms. Networks, 12(4), 355–377.

    Article  Google Scholar 

  10. Gendron, B., Lucena, A., da Cunha, A. S., & Simonetti, L. (2014). Benders decomposition, branch-and-cut, and hybrid algorithms for the minimum connected dominating set problem. INFORMS Journal on Computing, 26(4), 645–657.

    Article  Google Scholar 

  11. Gonçalves, D., Pinlou, A., Rao, M., & Thomassé, S. (2011). The domination number of grids. SIAM Journal on Discrete Mathematics, 25(3), 1443–1453.

    Article  Google Scholar 

  12. Guha, S., & Khuller, S. (1998). Approximation algorithms for connected dominating sets. Algorithmica, 20(4), 374–387.

    Article  Google Scholar 

  13. IBM-ILOG (2014) IBM ILOG CPLEX 12.6 reference manual. http://www-01.ibm.com/support/knowledgecenter/SSSA5P_12.6.0/ilog.odms.studio.help/Optimization_Studio/topics/COS_home.html. Accessed 24 June 2018.

  14. Ke, W., Liu, B., & Tsai, M. (2011). The critical-square-grid coverage problem in wireless sensor networks is NP-Complete. Computer Networks, 55(9), 2209–2220. https://doi.org/10.1016/j.comnet.2011.03.004.

    Article  Google Scholar 

  15. Lucena, A., Maculan, N., & Simonetti, L. (2010). Reformulations and solution algorithms for the maximum leaf spanning tree problem. Computational Management Science, 7(3), 289–311.

    Article  Google Scholar 

  16. Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960). Integer programming formulation of traveling salesman problems. Journal of ACM, 7(4), 326–329.

    Article  Google Scholar 

  17. Rebai, M., Le Berre, M., Snoussi, H., Hnaien, F., & Khoukhi, L. (2015). Sensor deployment optimization methods to achieve both coverage and connectivity in wireless sensor networks. Computers & Operations Research, 59, 11–21.

    Article  Google Scholar 

  18. Rebai, M., Afsar, H. M., & Snoussi, H. (2016). Exact methods for sensor deployment problem with connectivity constraint in wireless sensor networks. International Journal of Sensor Networks (IJSNET), 21(3), 157–168. https://doi.org/10.1504/IJSNET.2016.078324.

    Article  Google Scholar 

  19. Reich, A. (2016). Complexity of the maximum leaf spanning tree problem on planar and regular graphs. Theoretical Computer Science, 626(C), 134–143.

    Article  Google Scholar 

  20. Reis, M., Lee, O., & Usberti, F. (2015). Flow-based formulation for the maximum leaf spanning tree problem. Electronic Notes in Discrete Mathematics, 50, 205–210.

    Article  Google Scholar 

  21. Roveti DK (2001) Choosing a humidity sensor: A review of three technologies. http://www.sensorsmag.com/sensors/humidity-moisture/choosing-a-humidity-sensor-a-review-three-technologies-840. Accessed 24 June 2018.

  22. Wang X, Xing G, Zhang Y, Lu C, Pless R, Gill C (2003) Integrated coverage and connectivity configuration in wireless sensor networks. In: Proceedings of the 1st international conference on embedded networked sensor systems, SenSys’03 (pp. 28–39). ACM

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Correspondence to Stéphane Rovedakis.

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Elloumi, S., Hudry, O., Marie, E. et al. Optimization of wireless sensor networks deployment with coverage and connectivity constraints. Ann Oper Res 298, 183–206 (2021). https://doi.org/10.1007/s10479-018-2943-7

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Keywords

  • Wireless sensor networks
  • Grid networks
  • Random graphs
  • Sensor deployment
  • Minimum connected k-coverage
  • Mixed integer linear programming
  • Formulations