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Effectiveness-based Voronoi partition: a new tool for solving a class of location optimization problems

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Abstract

In this article we provide a framework for optimal placement or deployment of facilities in a region of interest. We present a generalization of Voronoi partition, where functions modeling the effectiveness of facilities are used in the place of the usual distance measure used in the standard Voronoi partition and its variations. We illustrate the usefulness of the generalization in designing strategies for optimal deployment of multiple vehicles equipped with sensors, optimal placement of base stations in a cellular network design problem, and locational optimization of power plants.

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References

  1. Drezner Z.: Facility Location: A Survey of Applications and Methods. Springer, New York (1995)

    Book  Google Scholar 

  2. Okabe A., Boots B., Sugihara K., Chiu S.: Spatial Tessellations. Concepts and Applications of Voronoi Diagrams. Wiley, Chichester (2000)

    Book  MATH  Google Scholar 

  3. Du Q., Faber V., Gunzburger M.: Centroidal Voronoi tessellations: applications and algorithms. SIAM Rev. 41(4), 637–676 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cortes J., Martinez S., Bullo F.: Spatially-distributed coverage optimization and control with limited-range interactions. ESAIM Control Optim. Calc. Var. 11(4), 691–719 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ma M., Yang Y.: Adaptive triangular deployment algorithm for unatended mobile sesnor networks. IEEE Trans. Comput. 56(7), 946–948 (2007)

    Article  MathSciNet  Google Scholar 

  6. Lee, H.-J., Kim, Y.-H., Han, Y.-H., Park, C.Y.: Centroid-based movement assisted sensor deployment schemes in wireless sensor networks. In: IEEE Vehicular Technology Conference, pp. 1–5 (2009)

  7. Guruprasad K.R., Ghose D.: Automated multi-agent search using centroidal voronoi configuration. IEEE Trans. Autom. Sci. Eng. 8(2), 420–423 (2011)

    Article  Google Scholar 

  8. Guruprasad, K.R., Ghose, D.: Performance of a class of multi-robot deploy and search strategies based on centroidal Voronoi configurations. Int. J. Syst. Sci. (2012). http://www.tandfonline.com. doi:10.1080/00207721.2011.618327

  9. Khalek, A.A., Al-kanj, L., Dawy, Z., Turkiyyah, G.: Site placement and site selection algorithms for UMTS radio planning with quality constraints. In: Proc of IEEE 17th conference on telecommunication, pp. 375–381, Doha (2010)

  10. Pimenta, L.C.A., Kumar, V., Mesquita, R.C., Pereira, A.S.: Sensing and coverage for a network of heterogeneous robots. In: Proc. of IEEE Conference on Decision and Control, pp. 3947–3952, Cancun (2008)

  11. Gusrialdi, A., Hirche, S., Hatanaka, T., Fujita, M.: Voronoi based coverage control with anisotropic sensors. In: Proceedings the American Control Conference, pp. 736–741 (2008)

  12. Laventall K., Cortés J.: Coverage control by multi-robot networks with limited-range anisotropic sensory. Int. J. Control 82(6), 1113–1121 (2009)

    Article  MATH  Google Scholar 

  13. Guruprasad, K.R., Ghose, D.: Heterogeneous sensor based Voronoi decomposition for spatially distributed limited range locational optimization. Kim, D.-S., Sugihara, K. (eds.): Voronoi’s Impact on Modern Science, Book 4, vol. 2, pp. 78–87. Proceedings of 5th Annual International Symposium On Voronoi Diagrams (ISVD 2008), Kiev, Sept 2008

  14. Guruprasad, K.R., Ghose, D.: Generalization of Voronoi partition: a sensor network perspective. In: Proc of IISc Centanary International Conference and Exhibition on Aerospace Engineering (ICEAE), pp. 18–22, Bangalore, 18–22 May 2009

  15. Guruprasad, K.R.: Generalized Voronoi partition: A new tool for optimal placement of base stations. In: Proc of 5th IEEE International Conference on Advanced Networking and Telecommunication Systems, Bengaluru, 18–21 Dec 2011

  16. Voronoi G.: Nouvelles applications des paramètres continus à à la théorie des formes quadratiques. Journal für die Reine und Angewandte Mathematik 133, 97–178 (1907)

    Google Scholar 

  17. Dirichlet, G.L.: Über die Reduktion der positiven quadratischen Formen mit drei unbestimmten ganzen Zahlen. für die Reine Und Angewandte Mathematik 40, 209–227 (1850)

    Article  MATH  Google Scholar 

  18. Delaunay B.: Sur la sphère vide, Izvestia Akademii Nauk SSSR. Otdelenie Matematicheskikh i Estestvennykh Nauk 7, 793–800 (1934)

    Google Scholar 

  19. Arbelaez, P.A., Cohen, L.D.: Generalized Voronoi tessellations for vector-valued image segmentation. In: Proc. of 2nd IEEE Workshop on Variational, Geometric and Level Set Methods in Computer Vision (VLSM’03), pp. 49–56, Nice, Sept 2003

  20. Aurenhammer F.: Voronoi Diagrams—a survey of a fundamental geometric data structure. ACM Comput. Surveys 23(3), 345–405 (1991)

    Article  Google Scholar 

  21. Kundu P.K., Cohen I.M.: Fluid Mechanics, 2nd edn. Academic Press, New York (2002)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, India

    K. R. Guruprasad

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  1. K. R. Guruprasad
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Correspondence to K. R. Guruprasad.

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Guruprasad, K.R. Effectiveness-based Voronoi partition: a new tool for solving a class of location optimization problems. Optim Lett 7, 1733–1743 (2013). https://doi.org/10.1007/s11590-012-0519-z

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  • DOI: https://doi.org/10.1007/s11590-012-0519-z

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