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GOAL: a clustering-based method for the group optimal location problem

  • Fangshu Chen
  • Jianzhong Qi
  • Huaizhong LinEmail author
  • Yunjun Gao
  • Dongming Lu
Regular Paper
  • 34 Downloads

Abstract

Optimal location problems are important problems and are particularly useful for strategic planning of resources. However, existing studies mainly focus on computing one or k optimal locations. We study the Group OptimAl Location (GOAL) problem, which computes a minimum set of locations such that establishing facilities at these locations guarantees that every facility user can access at least one facility within a given distance \(r\in {\mathcal {R}}^+\). We propose two algorithms, GOAL-Greedy and GOAL-DP, to first solve the problem in the Euclidean space. These two algorithms are supported by a clustering-based method to compute an initial solution of the problem, which yields an upper bound of the number of locations needed to solve the problem. We propose a grid partitioning-based strategy to refine the initial solution and obtain the final solution. We further extend our algorithms to road networks. We perform extensive experiments on the proposed algorithms. The results show that the proposed algorithms can solve the problem effectively and efficiently in both Euclidean spaces and road networks.

Keywords

Location selection Clustering Grid partition Road network 

Notes

Acknowledgements

This work was supported in part by the Key Disciplines of Computer Science and Technology of Shanghai Polytechnic University (No. XXKZD1604), the Research Project of Shanghai Polytechnic University (project number EGD18XQD02), Australian Research Council (ARC) Discovery project (project number DP180103332), the Cultural Relic Protection Science and Technology project of Zhejiang Province, the Key Research and Development Program of Zhejiang Province, the NSFC under Grants (project number 61522208), and the ZJU-Hikvision Joint Project. Huaizhong Lin is the corresponding author.

References

  1. 1.
    Alt H, Arkin EM, Brönnimann H, Erickson J, Fekete SP, Knauer C, Lenchner J, Mitchell JSB, Whittlesey K (2006) Minimum-cost coverage of point sets by disks. In: Proceedings of the twenty-second annual symposium on Computational geometry, ACM, pp 449–458Google Scholar
  2. 2.
    Ammari HM (2012) On the problem of k-coverage in mission-oriented mobile wireless sensor networks. Comput Netw 56(7):1935–1950CrossRefGoogle Scholar
  3. 3.
    Bhattacharya BB (2010) Maximizing voronoi regions of a set of points enclosed in a circle with applications to facility location. J Math Modell Algorithms 9(4):375–392MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cabello S, Díaz-Báñez JM, Langerman S, Seara C, Ventura I (2010) Facility location problems in the plane based on reverse nearest neighbor queries. Eur J Oper Res 202(1):99–106MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen F, Lin H, Gao Y, Dongming L (2016) Capacity constrained maximizing bichromatic reverse nearest neighbor search. Expert Syst Appl 43:93–108CrossRefGoogle Scholar
  6. 6.
    Chen Z, Liu Y, Chi-Wing WR, Xiong J, Mai G, Long C (2014) Efficient algorithms for optimal location queries in road networks. In: SIGMOD, pp 123–134Google Scholar
  7. 7.
    Chen Z, Liu Y, Wong RC-W, Xiong J, Mai G, Long C (2015) Optimal location queries in road networks. ACM Trans Database Syst 40(3):17MathSciNetCrossRefGoogle Scholar
  8. 8.
    Clarkson KL, Varadarajan K (2007) Improved approximation algorithms for geometric set cover. Discrete Comput Geom 37(1):43–58MathSciNetCrossRefGoogle Scholar
  9. 9.
    Du Y, Zhang D, Xia T (2005) The optimal-location query. In: International symposium on spatial and temporal databases, pp 163–180Google Scholar
  10. 10.
    Erlebach T, Jansen K, Seidel E (2001) Polynomial-time approximation schemes for geometric graphs. In: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics, pp 671–679Google Scholar
  11. 11.
    Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. In: KDD, AAAI Press, pp 226–231Google Scholar
  12. 12.
    Gao Y, Shuyao Qi L, Chen BZ, Li X (2015) On efficient k-optimal-location-selection query processing in metric spaces. Inf Sci 298:98–117MathSciNetCrossRefGoogle Scholar
  13. 13.
    He X, Cai D, Shao Y, Bao H, Han J (2011) Laplacian regularized gaussian mixture model for data clustering. IEEE Trans Knowl Data Eng 23(9):1406–1418CrossRefGoogle Scholar
  14. 14.
    Hochbaum DS, Maass W (1985) Approximation schemes for covering and packing problems in image processing and vlsi. J ACM 32(1):130–136MathSciNetCrossRefGoogle Scholar
  15. 15.
    Huang J, Wen Z, Qi J, Zhang R, Chen J, He Z (2011) Top-k most influential locations selection. In: CIKM, pp 2377–2380Google Scholar
  16. 16.
    Kavaliauskas M, Rudzkis R (2005) Multivariate data clustering for the gaussian mixture model. Inf Lith Acad Sci 16(1):61–74MathSciNetzbMATHGoogle Scholar
  17. 17.
    Lee C-H, Chung C-W, Chun S-J (2010) Effective processing of continuous group-by aggregate queries in sensor networks. J Syst Softw 83(12):2627–2641CrossRefGoogle Scholar
  18. 18.
    Li F, Yao B, Kumar P (2011) Group enclosing queries. IEEE Trans Knowl Data Eng 23(10):1526–1540CrossRefGoogle Scholar
  19. 19.
    Lin H, Chen F, Gao Y, Lu D (2013) Optregion: finding optimal region for bichromatic reverse nearest neighbors. In: International conference on database systems for advanced applications, Springer, pp 146–160Google Scholar
  20. 20.
    Liu Y, Wong CW, Wang K, Li Z, Chen C, Chen Z (2013) A new approach for maximizing bichromatic reverse nearest neighbor search. Knowl Inf Syst 36(1):23–58CrossRefGoogle Scholar
  21. 21.
    Mohammadi M, Jolai F, Rostami H (2011) An m/m/c queue model for hub covering location problem. Math Comput Modell 54(11):2623–2638MathSciNetCrossRefGoogle Scholar
  22. 22.
    Mouratidis K, Papadias D, Papadimitriou S (2008) Tree-based partition querying: a methodology for computing medoids in large spatial datasets. VLDB J 17(4):923–945CrossRefGoogle Scholar
  23. 23.
    Qi J, Zhenghua X, Xue Y, Wen Z (2012) A branch and bound method for min-dist location selection queries. Proc Twenty-Third Australas Database Conf 124:51–60Google Scholar
  24. 24.
    Qi J, Zhang R, Kulik L, Lin D, Xue Y (2012) The min-dist location selection query. In: ICDE, pp 66–377Google Scholar
  25. 25.
    Sakai K, Sun M-T, Ku W-S, Lai TH, Vasilakos AV (2015) A framework for the optimal-coverage deployment patterns of wireless sensors. IEEE Sens J 15(12):7273–7283CrossRefGoogle Scholar
  26. 26.
    Shmoys DB, Tardos É, Aardal K (1997) Approximation algorithms for facility location problems. In: Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pp 265–274Google Scholar
  27. 27.
    Sibson R (1973) SLINK: an optimally efficient algorithm for the single-link cluster method. Comput J 16(1):30–34MathSciNetCrossRefGoogle Scholar
  28. 28.
    Suárez-Vega R, Gutiérrez-Acuña JL, Rodríguez-Díaz M (2015) Locating a supermarket using a locally calibrated huff model. Int J Geogr Inf Sci 29(2):217–233CrossRefGoogle Scholar
  29. 29.
    Sun Y, Qi J, Zhang R, Chen Y, Xiaoyong D (2015) Mapreduce based location selection algorithm for utility maximization with capacity constraints. Computing 97(4):403–423MathSciNetCrossRefGoogle Scholar
  30. 30.
    Sun Y, Zhang R, Xue AY, Qi J, Du X (2016) Reverse nearest neighbor heat maps: a tool for influence exploration. In: ICDE, pp 966–977Google Scholar
  31. 31.
    Wong RC-W, Tamer Özsu M, Yu PS, Fu AW-C, Liu L (2009) Efficient method for maximizing bichromatic reverse nearest neighbor. Proc VLDB Endow 2(1):1126–1137CrossRefGoogle Scholar
  32. 32.
    Xiao X, Yao B, Li F (2011) Optimal location queries in road network databases. In: ICDE, pp 804–815Google Scholar
  33. 33.
    Chuanfei X, Yu G, Zimmermann R, Lin S, Ge Y (2013) Group location selection queries over uncertain objects. IEEE Trans Knowl Data Eng 25(12):2796–2808CrossRefGoogle Scholar
  34. 34.
    Chuanfei X, Yanqiu Wang YG, Lin S, Ge Y (2012) Optimal k-constraint coverage queries on spatial objects. Proc Twenty-Third Australas Database Conf 124:41–50Google Scholar
  35. 35.
    Zhang D, Du Y, Xia T, Tao Y (2006) Progressive computation of the min-dist optimal-location query. In: VLDB, pp 643–654Google Scholar
  36. 36.
    Zhou Z, Wu W, Li X, Lee ML, Hsu W (2011) Maxfirst for maxbrknn. In: ICDE, pp 828–839Google Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.The College of Computer Science and Information EngineeringShanghai Polytechnic UniversityShanghaiChina
  2. 2.School of Computing and Information SystemsUniversity of MelbourneMelbourneAustralia
  3. 3.The College of Computer Science and TechnologyZhejiang UniversityHangzhouChina

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