Facility Location Selection Using Community-Based Single Swap: A Case Study

  • Rixin Xu
  • Zijian Zhang
  • Jiamou Liu
  • Nathan Situ
  • Jun Ho Jin
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 747)


This paper focuses on the uncapacitated k-median facility location problem, which asks to locate k facilities in a network that minimize the total routing time, taking into account the constraints of nodes that are able to serve as servers and clients, as well as the level of demand in each client node. This problem is important in a wide range of applications from operation research to mobile ad-hoc networks. Existing algorithms for this problem often lead to high computational costs when the underlying network is very large, or when the number k of required facilities is very large. We aim to improve existing algorithms by taking into considerations of the community structures of the underlying network. More specifically, we extend the strategy of local search with single swap with a community detection algorithm. As a real-world case study, we analyze in detail Auckland North Shore spatial networks with varying distance threshold and compare the algorithms on these networks. The results show that our algorithm significantly reduces running time while producing equally optimal results.


Facility location k-median problem Community structures Spatial networks Auckland Open Data Single swap algorithm 


  1. 1.
  2. 2.
  3. 3.
    Ahlgren, B., Dannewitz, C., Imbrenda, C., Kutscher, D., Ohlman, B.: A survey of information-centric networking. IEEE Commun. Mag. 50(7), 26–36 (2012)CrossRefGoogle Scholar
  4. 4.
    Aikens, C.H.: Facility location models for distribution planning. Eur. J. Oper. Res. 22(3), 263–279 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bell, M.G., Iida, Y., et al.: Transportation Network Analysis. Wiley, New York (1997)CrossRefGoogle Scholar
  8. 8.
    Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. J. Stat. Mech. Theor. Exp. 2008(10), P10008 (2008)CrossRefGoogle Scholar
  9. 9.
    Chaudhuri, S., Garg, N., Ravi, R.: The p-neighbor k-center problem. Inf. Process. Lett. 65(3), 131–134 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Chrobak, M., Kenyon, C., Young, N.E.: The reverse greedy algorithm for the metric K-median problem. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 654–660. Springer, Heidelberg (2005). Scholar
  11. 11.
    Church, R., Velle, C.R.: The maximal covering location problem. Pap. Reg. Sci. 32(1), 101–118 (1974)CrossRefGoogle Scholar
  12. 12.
    Dai, F., Wu, J.: On constructing k-connected k-dominating set in wireless networks. In: Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium, 10 pp. IEEE (2005)Google Scholar
  13. 13.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Frank, C., Römer, K.: Distributed facility location algorithms for flexible configuration of wireless sensor networks. In: Aspnes, J., Scheideler, C., Arora, A., Madden, S. (eds.) DCOSS 2007. LNCS, vol. 4549, pp. 124–141. Springer, Heidelberg (2007). Scholar
  15. 15.
    Girvan, M., Newman, M.E.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. 99(12), 7821–7826 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    González-Brevis, P., Gondzio, J., Fan, Y., Poor, H.V., Thompson, J., Krikidis, I., Chung, P.-J.: Base station location optimization for minimal energy consumption in wireless networks. In: IEEE 73rd Vehicular Technology Conference (VTC Spring), pp. 1–5. IEEE (2011)Google Scholar
  17. 17.
    Guha, S., Khuller, S.: Greedy strikes back: improved facility location algorithms. J. Algorithms 31(1), 228–248 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Huang, C.-M., Lan, K.-C., Tsai, C.-Z.: A survey of opportunistic networks. In: 22nd International Conference on Advanced Information Networking and Applications-Workshops, AINAW 2008, pp. 1672–1677. IEEE (2008)Google Scholar
  19. 19.
    Lambiotte, R., Blondel, V.D., De Kerchove, C., Huens, E., Prieur, C., Smoreda, Z., Van Dooren, P.: Geographical dispersal of mobile communication networks. Phys. A Stat. Mech. Appl. 387(21), 5317–5325 (2008)CrossRefGoogle Scholar
  20. 20.
    Lewis, F.L., et al.: Wireless sensor networks. In: Smart Environments: Technologies, Protocols, and Applications, pp. 11–46 (2004)Google Scholar
  21. 21.
    Liao, K., Guo, D.: A clustering-based approach to the capacitated facility location problem. Trans. GIS 12(3), 323–339 (2008)CrossRefGoogle Scholar
  22. 22.
    Liu, J., Minnes, M.: Deciding the isomorphism problem in classes of unary automatic structures. Theor. Comput. Sci. 412(18), 1705–1717 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Liu, J., Wei, Z.: Community detection based on graph dynamical systems with asynchronous runs. In: Second International Symposium on Computing and Networking (CANDAR), pp. 463–469. IEEE (2014)Google Scholar
  24. 24.
    Miller, H.J., Han, J.: Geographic Data Mining and Knowledge Discovery. CRC Press (2009)Google Scholar
  25. 25.
    Moskvina, A., Liu, J.: How to build your network? A structural analysis. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, pp. 2597–2603. AAAI Press (2016)Google Scholar
  26. 26.
    Moskvina, A., Liu, J.: Togetherness: an algorithmic approach to network integration. In: IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM), pp. 223–230. IEEE (2016)Google Scholar
  27. 27.
    Newman, M.E.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. 103(23), 8577–8582 (2006)CrossRefGoogle Scholar
  28. 28.
    Pantazopoulos, P., Stavrakakis, I., Passarella, A., Conti, M.: Efficient social-aware content placement in opportunistic networks. In: Seventh International Conference on Wireless On-Demand Network Systems and Services (WONS), pp. 17–24. IEEE (2010)Google Scholar
  29. 29.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440 (1998)CrossRefzbMATHGoogle Scholar
  30. 30.
    Yan, B., Chen, Y., Liu, J.: Dynamic relationship building: exploitation versus exploration on a social network. In: Bouguettaya, A., et al. (eds.) WISE 2017. LNCS, vol. 10569, pp. 75–90. Springer, Cham (2017). Scholar
  31. 31.
    Yang, K.-Q., Yang, L., Gong, B.-H., Lin, Z.-C., He, H.-S., Huang, L.: Geographical networks: geographical effects on network properties. Front. Phys. China 3(1), 105–111 (2008)CrossRefGoogle Scholar
  32. 32.
    Zhong, C., Arisona, S.M., Huang, X., Batty, M., Schmitt, G.: Detecting the dynamics of urban structure through spatial network analysis. Int. J. Geogr. Inf. Sci. 28(11), 2178–2199 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Beijing Institute of Technology BeijingBeijingChina
  2. 2.University of AucklandAucklandNew Zealand

Personalised recommendations