Incremental Rank Updates for Moving Query Points

  • Lars Kulik
  • Egemen Tanin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4197)


The query for retrieving the rank of all neighbors of a moving object at any given time, a continuous rank query, is an important case of continuous nearest neighbor (CNN) queries. An application for ranking queries is given by an ambulance driver who needs to keep track of the closest hospitals at all times. We present a set of incremental algorithms that facilitate efficient rank updates for some or all neighbors of a moving query point. The proposed algorithms allow us not only to maintain the exact rank of all n neighbors at any given time but also to track the rank of a subset of all neighbors. We show that updates for these continuous rank queries can be performed in linear time for arbitrary polygonal curves in two dimensions and in logarithmic time for movements along a fixed direction. Instead of using Voronoi diagrams, our algorithms are based on small subsets of all bisectors between neighbors. We prove that it is sufficient to keep track of only n–1 bisectors for all n neighbors. The algorithms for maintaining the rank only require minimal incremental updates on the bisector sets.


Voronoi Diagram Query Point Continuous Query Rank Query Near Neighbor Query 


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  1. 1.
    Aurenhammer, F.: Voronoi diagrams: A survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)CrossRefGoogle Scholar
  2. 2.
    Benetis, R., Jensen, C.S., Karciauskas, G., Saltenis, S.: Nearest neighbor and reverse nearest neighbor queries for moving objects. In: Proceedings of the IEEE IDEAS, Edmonton, Canada, pp. 44–53 (July 2002)Google Scholar
  3. 3.
    Chon, H.D., Agrawal, D., El Abbadi, A.: Range and KNN query processing for moving objects in grid model. Mobile Networks and Applications 8(4), 401–412 (2003)CrossRefGoogle Scholar
  4. 4.
    Hjaltason, G., Samet, H.: Ranking in spatial databases. In: Egenhofer, M.J., Herring, J.R. (eds.) SSD 1995. LNCS, vol. 951, pp. 83–95. Springer, Heidelberg (1995)Google Scholar
  5. 5.
    Hjaltason, G., Samet, H.: Distance browsing in spatial databases. ACM Transactions on Database Systems 24(2), 265–318 (1999)CrossRefGoogle Scholar
  6. 6.
    Hjaltason, G., Samet, H.: Index-driven similarity search in metric spaces. ACM Transactions on Database Systems 28(4), 517–580 (2003)CrossRefGoogle Scholar
  7. 7.
    Hu, H., Xu, J., Lee, D.L.: A generic framework for monitoring continuous spatial queries over moving objects. In: Proceedings of the ACM SIGMOD, Baltimore, MD, pp. 479–490 (June 2005)Google Scholar
  8. 8.
    Iwerks, G.S., Samet, H., Smith, K.: Continuous k-nearest neighbor queries for continuously moving points with updates. In: Aberer, K., Koubarakis, M., Kalogeraki, V. (eds.) VLDB 2003. LNCS, vol. 2944, pp. 512–523. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Mokbel, M.F.: Continuous query processing in spatio-temporal databases. In: Lindner, W., Mesiti, M., Türker, C., Tzitzikas, Y., Vakali, A.I. (eds.) EDBT 2004. LNCS, vol. 3268, pp. 100–111. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Mouratidis, K., Hadjieleftheriou, M., Papadias, D.: Conceptual partitioning: An efficient method for continuous nearest neighbor monitoring. In: Proceedings of the ACM SIGMOD, Baltimore, MD, pp. 634–645 (June 2005)Google Scholar
  11. 11.
    Okabe, A., Boots, B., Sugihara, K., Chiu, S.N.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. Wiley, Chichester (2000)MATHGoogle Scholar
  12. 12.
    O’Rourke, J.: Computational Geometry in C. Cambridge University, Cambridge (1994)MATHGoogle Scholar
  13. 13.
    Roussopoulos, N., Kelley, S., Vincent, F.: Nearest neighbor queries. In: Proceedings of the ACM SIGMOD, San Jose, CA, pp. 71–79 (May 1995)Google Scholar
  14. 14.
    Saltenis, S., Jensen, C.S., Leutenegger, S.T., Lopez, M.A.: Indexing the positions of continuously moving objects. In: Proceedings of ACM SIGMOD, Dallas, TX, pp. 331–342 (May 2000)Google Scholar
  15. 15.
    Samet, H.: Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS. Addison-Wesley, Reading (1990)Google Scholar
  16. 16.
    Samet, H.: The Design and Analysis of Spatial Data Structures. Addison-Wesley, Reading (1990)Google Scholar
  17. 17.
    Samet, H.: Foundations of Multidimensional Data Structures. Morgan Kaufmann, San Francisco (2006)MATHGoogle Scholar
  18. 18.
    Song, Z., Roussopoulos, N.: K-nearest neighbor search for moving query point. In: Jensen, C.S., Schneider, M., Seeger, B., Tsotras, V.J. (eds.) SSTD 2001. LNCS, vol. 2121, pp. 79–96. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Tao, Y., Papadias, D.: Time-parameterized queries in spatio-temporal databases. In: Proceedings of the ACM SIGMOD, Madison, WI, pp. 334–345 (June 2002)Google Scholar
  20. 20.
    Tao, Y., Papadias, D.: Spatial queries in dynamic environments. ACM Transactions on Database Systems 28(2), 101–139 (2003)CrossRefGoogle Scholar
  21. 21.
    Tao, Y., Papadias, D., Shen, Q.: Continuous nearest neighbor search. In: Proceedings of the VLDB, pp. 287–298 (August 2002) Google Scholar
  22. 22.
    Xiong, X., Mokbel, M.F., Aref, W.G.: SEA-CNN: Scalable processing of continuous k-nearest neighbor queries in spatio-temporal databases. In: Proceedings of the IEEE ICDE, Tokyo, Japan, pp. 643–654 (April 2005)Google Scholar
  23. 23.
    Zhang, J., Zhu, M., Papadias, D., Tao, Y., Lee, D.: Location-based spatial queries. In: Proceeding of the ACM SIGMOD, San Diego, CA, pp. 443–453 (June 2003)Google Scholar
  24. 24.
    Zheng, B., Lee, D.L.: Semantic caching in location-dependent query processing. In: Proceedings of the SSTD, Redondo Beach, CA, pp. 97–116 (July 2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lars Kulik
    • 1
  • Egemen Tanin
    • 1
  1. 1.Department of Computer Science and Software Engineering, NICTA Victoria LaboratoryUniversity of MelbourneVictoriaAustralia

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