, Volume 23, Issue 1, pp 105–161 | Cite as

An overlapping Voronoi diagram-based system for multi-criteria optimal location queries

  • Ji Zhang
  • Po-Wei Harn
  • Wei-Shinn Ku
  • Min-Te Sun
  • Xiao Qin
  • Hua Lu
  • Xunfei JiangEmail author


This paper presents a novel Multi-criteria Optimal Location Query (MOLQ), which can be applied to a wide range of applications. After providing a formal definition of the novel query type, we propose an Overlapping Voronoi Diagram (OVD) model that defines OVDs and Minimum OVDs (MOVDs), and an OVD overlap operation. Based on the OVD model, we design advanced approaches to answer the query in Euclidean space. Due to the high complexity of Voronoi diagram overlap computation, we improve the overlap operation by replacing the real boundaries of Voronoi diagrams with their Minimum Bounding Rectangles (MBR). Moreover, if there are changes to a limited number of objects, re-evaluating queries over updated object sets would be expensive. Thus, we also propose an MOVD updating model and an advanced algorithm to incrementally update MOVDs to avoid the high cost of query re-evaluation. Our experimental results show that the proposed algorithms can evaluate the novel query type effectively and efficiently.


Voronoi diagram Optimal location query 



This research has been funded in part by the U.S. National Science Foundation grants IIS-1618669 (III) and ACI-1642133 (CICI).


  1. 1.
    Aurenhammer F (1991) Voronoi diagrams–a survey of a fundamental geometric data structure. ACM Comput Surv 23(3):345–405CrossRefGoogle Scholar
  2. 2.
    Aurenhammer F, Klein R, Lee D-T (2013) Voronoi diagrams and delaunay triangulations. World Scientific Publishing Co IncGoogle Scholar
  3. 3.
    Bajaj CL (1988) The algebraic degree of geometric optimization problems. Discret Comput Geom 3:177–191CrossRefGoogle Scholar
  4. 4.
    Boissonnat J-D, Delage C (2005) Convex Hull and Voronoi diagram of additively weighted points. In: ESA, pp 367–378Google Scholar
  5. 5.
    Chandrasekaran R, Tamir A (1990) Algebraic optimization: the Fermat-Weber location problem. Math Program 46:219–224CrossRefGoogle Scholar
  6. 6.
    Cheema MA, Zhang W, Lin X, Zhang Y, Li X (2012) Continuous reverse k nearest neighbors queries in euclidean space and in spatial networks. VLDB J 21(1):69–95CrossRefGoogle Scholar
  7. 7.
    Chen Z, Liu Y, Wong RC-W, Xiong J, Mai G, Long C (2014) Efficient algorithms for optimal location queries in road networks. In: SIGMOD conference, pp 123–134Google Scholar
  8. 8.
    Farhana M, Choudhury J, Culpepper S, Sellis T, Cao X (2016) Maximizing bichromatic reverse spatial and textual K nearest neighbor queries. PVLDB 9(6):456–467Google Scholar
  9. 9.
    de Berg M, Cheong O, van Kreveld M, Mark O (2008) Computational geometry: algorithms and applications, 3rd edn. SpringerGoogle Scholar
  10. 10.
    Demiryurek U, Shahabi C (2012) Indexing network Voronoi diagrams. In: The 17th International conference on database systems for advanced applications, DASFAA, pp 526–543Google Scholar
  11. 11.
    Devillers O (2002) On deletion in Delaunay triangulations. Int J Comput Geom Appl 12(03):193–205CrossRefGoogle Scholar
  12. 12.
    Dinis J, Mamede M (2011) Updates on Voronoi Diagrams. In: ISVD, pp 192–199Google Scholar
  13. 13.
    Dong P (2008) Generating and updating multiplicatively weighted Voronoi diagrams for point, line and polygon features in GIS. Comput Geosci 34(4):411–421CrossRefGoogle Scholar
  14. 14.
    Du Y, Zhang D, Xia T (2005) The optimal-location query. In: SSTD, pp 163–180Google Scholar
  15. 15.
    Finke U, Hinrichs KH (1995) Overlaying simply connected planar subdivisions in linear time. In: Proceedings of the eleventh annual symposium on computational geometry. ACM, pp 119–126Google Scholar
  16. 16.
    Fortune S (1986) A sweepline algorithm for Voronoi diagrams. In: Proceedings of the second annual symposium on computational geometry. ACM, pp 313–322Google Scholar
  17. 17.
    Fortune S (1992) Numerical stability of algorithms for 2D delaunay triangulations. In: Proceedings of the eighth annual symposium on computational geometry, pp 83–92Google Scholar
  18. 18.
    Gao Y, Zheng B, Chen G, Li Q (2009) Optimal-location-selection query processing in spatial databases. IEEE Trans Knowl Data Eng 21(8):1162–1177CrossRefGoogle Scholar
  19. 19.
    Ghaemi P, Shahabi K, Wilson JP, Banaei-Kashani F (2012) Continuous maximal reverse nearest neighbor query on spatial networks. In: ACM SIGSPATIAL, pp 61–70Google Scholar
  20. 20.
    Green PJ, Sibson R (1978) Computing Dirichlet tessellations in the plane. Comput J 21(2):168–173CrossRefGoogle Scholar
  21. 21.
    Green PJ, Sibson R (1978) Computing Dirichlet tessellations in the plane. Comput J 21(2):168–173CrossRefGoogle Scholar
  22. 22.
    Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computation of Voronoi. ACM Trans Graph (TOG) 4(2):74–123CrossRefGoogle Scholar
  23. 23.
    Guibas LJ, Knuth DE, Sharir M (1992) Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7(1):381–413CrossRefGoogle Scholar
  24. 24.
    Guibas LJ, Stolfi J (1985) Primitives for the manipulation of general subdivisions and computation of Voronoi diagrams. ACM Trans Graph 4(2):74–123CrossRefGoogle Scholar
  25. 25.
    Haldane JBS (1948) Note on the median of a multivariate distribution. Biometrika 35:414–415CrossRefGoogle Scholar
  26. 26.
    Harn P-W, Ji Z, Sun M-T, Ku W-S (2016) A framework for updating multi-criteria optimal location query. In: ACM SIGSPATIALGoogle Scholar
  27. 27.
    Jalal G, Krarup J (2003) Geometrical solution to the fermat problem with arbitrary weights. Annals OR 123(1–4):67–104CrossRefGoogle Scholar
  28. 28.
    Karavelas MI, Yvinec M (2002) Dynamic additively weighted Voronoi diagrams in 2D. In: ESA, pp 586–598Google Scholar
  29. 29.
    Korn F, Muthukrishnan S (2000) Influence sets based on reverse nearest neighbor queries. In: SIGMOD conference, pp 201–212Google Scholar
  30. 30.
    Korn F, Muthukrishnan S, Srivastava D (2002) Reverse nearest neighbor aggregates over data streams. In: VLDB, pp 814–825Google Scholar
  31. 31.
    Liu R, Fu AW-C, Chen Z, Huang S, Liu Y (2016) Finding multiple new optimal locations in a road network. In: ACM SIGSPATIALGoogle Scholar
  32. 32.
    Mostafavi MA, Gold C, Dakowicz M (2003) Delete and insert operations in voronoi/delaunay methods and applications. Comput Geosci 29(4):523–530CrossRefGoogle Scholar
  33. 33.
    Mu L (2004) Polygon characterization with the multiplicatively weighted Voronoi diagram. Prof Geogr 56(2):223–239Google Scholar
  34. 34.
    Ohya T, Iri M, Murota K (1984) Improvements of the incremental method for the Voronoi diagram with computational comparison of various algorithms. J Oper Res Soc Japan 27(4):306–336Google Scholar
  35. 35.
    Okabe A, Boots B, Sugihara K, Chiu SN (2000) Spatial tessellations: concepts and applications of Voronoi diagrams. Probability and statistics, 2nd edn. Wiley, NYCCrossRefGoogle Scholar
  36. 36.
    Pagliara F, Preston J, David S (2010) Residential location choice: models and applications. SpringerGoogle Scholar
  37. 37.
    Qi J, Zhang R, Kulik L, Lin D, Xue Y (2012) The min-dist location selection query. In: ICDEGoogle Scholar
  38. 38.
    Morris JG, Love RF, Wesolowsky GO (1988) Facilities location models and methodsGoogle Scholar
  39. 39.
    Stanoi I, Riedewald M, Agrawal D, El Abbadi A (2001) Discovery of influence sets in frequently updated databases. In: VLDB, pp 99–108Google Scholar
  40. 40.
    Sugihara K, Iri M (1992) Construction of the Voronoi diagram for’one million’generators in single-precision arithmetic. Proc IEEE 80(9):1471–1484CrossRefGoogle Scholar
  41. 41.
    Tao Y, Papadias D, Lian X (2004) Reverse kNN search in arbitrary dimensionality. In: VLDB, pp 744–755Google Scholar
  42. 42.
    Tao Y, Papadias D, Lian X, Xiao X (2007) Multidimensional reverse k NN search. VLDB J 16(3):293–316CrossRefGoogle Scholar
  43. 43.
    Tao Y, Yiu ML, Mamoulis N (2006) Reverse nearest neighbor search in metric spaces. IEEE Trans Knowl Data Eng 18(9):1239–1252CrossRefGoogle Scholar
  44. 44.
    Üster H, Love RF (2002) A generalization of the rectangular bounding method for continuous location models. Comput Math Appl 44(1–2):181–191CrossRefGoogle Scholar
  45. 45.
    Vardi Y, Zhang C-H (2001) A modified Weiszfeld algorithm for the Fermat-Weber location problem. Math Program 90:559–566CrossRefGoogle Scholar
  46. 46.
    Verkhovsky BS, Polyakov YS (2003) Feedback algorithm for the single-facility minisum problem. Ann Europ Acad Sci 1:127–136Google Scholar
  47. 47.
    Weisbrod G, Ben-Akiva M, Lerman S (1980) Tradeoffs in residential location decisions: transportation versus other factors. Transp Polic Decis-Making, 1(1)Google Scholar
  48. 48.
    Weiszfeld E, Plastria F (2009) On the point for which the sum of the distances to n given points is minimum. Annals OR 167(1):7–41CrossRefGoogle Scholar
  49. 49.
    Xia T, Zhang D, Kanoulas E, Du Y (2005) On computing top-t most influential spatial sites. In: VLDB, pp 946–957Google Scholar
  50. 50.
    Xiao X, Yao B, Li F (2011) Optimal location queries in road network databases. In: ICDE, pp 804–815Google Scholar
  51. 51.
    Yang C, Lin K-I (2001) An index structure for efficient reverse nearest neighbor queries. In: ICDE, pp 485–492Google Scholar
  52. 52.
    Yao B, Xiao X, Li F, Wu Y (2014) Dynamic monitoring of optimal locations in road network databases. In: VLDB, pp 697–720Google Scholar
  53. 53.
    Yiu ML, Papadias D, Mamoulis N, Tao Y (2006) Reverse nearest neighbors in large graphs. IEEE Trans Knowl Data Eng 18(4):540–553CrossRefGoogle Scholar
  54. 54.
    Zhang D, Du Y, Xia T, Tao Y (2006) Progressive computation of the min-dist optimal-location query. In: VLDB, pp 643–654Google Scholar
  55. 55.
    Ji Z, Ku W-S, Jiang X, Qin X, Sun M-T, Lu H (2015) A framework for multi-criteria optimal location selection. In: ACM SIGSPATIALGoogle Scholar
  56. 56.
    Ji Z, Ku W-S, Sun M-T, Qin X, Lu H (2014) Multi-criteria optimal location query with overlapping Voronoi diagrams. In: EDBT, pp 391–402Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ji Zhang
    • 1
  • Po-Wei Harn
    • 2
  • Wei-Shinn Ku
    • 1
  • Min-Te Sun
    • 3
  • Xiao Qin
    • 1
  • Hua Lu
    • 4
  • Xunfei Jiang
    • 5
    Email author
  1. 1.Department of Computer Science and Software EngineeringAuburn UniversityAuburnUSA
  2. 2.Institute for Information IndustryTaipeiTaiwan
  3. 3.Department of Computer Science and Information EngineeringNational Central UniversityTaoyuanTaiwan
  4. 4.Department of Computer ScienceAalborg UniversityAalborgDenmark
  5. 5.Department of Computer ScienceEarlham CollegeRichmondUSA

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