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Reverse k Nearest Neighbor and Reverse Farthest Neighbor Search on Spatial Networks

  • Quoc Thai Tran
  • David Taniar
  • Maytham Safar
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5740)

Abstract

One of the problems that arise in geographical information systems is finding objects that are influenced by other objects. While most research focuses on kNN (k Nearest Neighbor) and RNN (Reverse Nearest Neighbor) queries, an important type of proximity queries called Reverse Farthest Neighbor (RFN) has not received much attention. Since our previous work shows that kNN and RNN queries in spatial network databases can be efficiently solved using Network Voronoi Diagram (NVD), in this paper, we aim to introduce a new approach to process reverse proximity queries including RFN and RkNN/RkFN queries. Our approach is based on NVD and pre-computation of network distances, and is applicable for spatial road network maps. Being the most fundamental Voronoi-based approach for RFN and RkNN/RkFN queries, our solutions show that they can be efficiently used for networks that have a low and medium level of density.

Keywords

Voronoi Diagram Interest Point Query Point Spatial Network Network Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Achtert, E., Bohm, C., Kroger, P., Kunath, P., Pryakhin, A., Renz, M.: Approximate reverse k-nearest neighbor queries in general metric spaces. In: Proceedings of the 15th ACM International Conference on Information and Knowledge Management, pp. 788–789 (2006)Google Scholar
  2. Achtert, E., Bohm, C., Kroger, P., Kunath, P., Pryakhin, A., Renz, M.: Efficient reverse k-nearest neighbour search in arbitrary metric spaces. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 515–526 (2006)Google Scholar
  3. Aggarwal, A., Hansen, M., Leighton, T.: Solving query-retrieval problems by compacting Voronoi diagrams. In: Proceedings of the 22nd annual ACM Symposium on Theory of Computing, pp. 331–340 (1990)Google Scholar
  4. Dellis, E., Seeger, B.: Efficient computation of reverse skyline queries. In: Proceedings of the 33rd International Conference on Very Large Data Bases, pp. 291–302 (2007)Google Scholar
  5. Deng, K., Zhou, X., Shen, H.: Multi-source Skyline Query Processing in Road Networks. In: Proceedings of the 2007 IEEE 23rd International Conference on Data Engineering, pp. 796–805 (2007)Google Scholar
  6. Dickerson, M., Goodrich, M.: Two-site Voronoi diagrams in geographic networks. In: Proceedings of the 16th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, vol. 59 (2008)Google Scholar
  7. Dijkstra, E.W.: A Note on Two Problems in Connexion with Graphs. Numeriche Mathematik 1(1), 269–271 (1959)MathSciNetCrossRefzbMATHGoogle Scholar
  8. Goh, J.Y., Taniar, D.: Mobile Data mining by Location Dependencies. In: Yang, Z.R., Yin, H., Everson, R.M. (eds.) IDEAL 2004. LNCS, vol. 3177, pp. 225–231. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. Goh, J., Taniar, D.: Mining Frequency Pattern from Mobile Users. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004, Part III. LNCS, vol. 3215, pp. 795–801. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. Graf, M., Winter, S.: Network Voronoi Diagram. Österreichische Zeitschrift für Vermessung und Geoinformation 91(3), 166–174 (2003)Google Scholar
  11. Jensen, C., Kolarvr, J., Pedersen, T., Timko, I.: Nearest neighbor queries in road networks. In: Proceedings of the 11th ACM International Symposium on Advances in Geographic Information Systems, pp. 1–3 (2003)Google Scholar
  12. Korn, F., Muthukrishnan, S.: Influence sets based on reverse nearest neighbor queries. In: Proceedings of the 2000 ACM SIGMOD International Conference on Management of Data, vol. 29(2), pp. 201–212 (2000)Google Scholar
  13. Korn, F., Muthukrishnan, S., Srivastava, D.: Reverse nearest neighbor aggregates over data streams. In: Proceedings of the International Conference on Very Large Data Bases, pp. 814–825 (2002)Google Scholar
  14. Koulahdouzan, M., Shahabi, C.: Voronoi-Based K Nearest Neighbor Search for Spatial Network Databases. In: Proceedings of the 30th International Conference on Very Large Data Bases, vol. 30, pp. 840–851 (2004)Google Scholar
  15. Kumar, Y., Janardan, R., Gupta, P.: Efficient algorithms for reverse proximity query problems. In: Proceedings of the 16th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, vol. 39 (2008)Google Scholar
  16. Okabe, A., Boots, B., Sugihara, K., Chiu, N.: Spatial Tessellations, Concepts and Applications of Voronoi Diagrams, 2nd edn. John Wiley and Sons Ltd., Chichester (2000)CrossRefzbMATHGoogle Scholar
  17. Papadias, D., Mamoulis, N., Zhang, J., Tao, Y.: Query Processing in Spatial Network Databases. In: Proceedings of the 29th International Conference on Very Large Data Bases, vol. 29, pp. 802–813 (2003)Google Scholar
  18. Patroumpas, K., Minogiannis, T., Sellis, T.: Approximate order-k Voronoi cells over positional streams. In: Proceedings of the 15th Annual ACM International Symposium on Advances in Geographic Information Systems, vol. 36 (2007)Google Scholar
  19. Roussopoulos, N., Kelly, S., Vincent, F.: Nearest Neighbor Queries. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 71–79 (1995)Google Scholar
  20. Safar, M.: K Nearest Neighbor Search in Navigation Systems. Mobile Information Systems 1(3), 207–224 (2005)CrossRefGoogle Scholar
  21. Safar, M., Ebrahmi, D.: eDar Algorithm for Continous KNN queries based on PINE. International Journal of Information Technology and Web Engineering 1(4), 1–21 (2006)CrossRefGoogle Scholar
  22. Safar, M., Ibrahimi, D., Taniar, D., Gavrilova, M.: Voronoi-based Reverse Nearest Neighbour Query Processing on Spatial Networks. Multimedia Systems Journal (in press, 2009)Google Scholar
  23. Samet, H., Sankaranarayanan, J., Alborzi, H.: Scalable network distance browsing in spatial databases. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 43–54 (2008)Google Scholar
  24. Sield, T., Kriegel, H.: Optimal Multi-Step k-Nearest Neighbor Search. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 154–165 (1998)Google Scholar
  25. Stephen, R., Gihnea, G., Patel, M., Serif, T.: A context-aware Tour Guide: User implications. Mobile Information Systems 3(2), 71–88 (2007)CrossRefGoogle Scholar
  26. Tao, Y., Papadias, D., Lian, X.: Reverse kNN search in arbitrary dimensionality. In: Proceedings of the 30th International Conference on Very Large Data Bases, pp. 744–755 (2004)Google Scholar
  27. Waluyo, A., Srinivasan, B., Taniar, D.: Optimal Broadcast Channel for Data Dissemination in Mobile Database Environment. In: Zhou, X., Xu, M., Jähnichen, S., Cao, J. (eds.) APPT 2003. LNCS, vol. 2834, pp. 655–664. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  28. Waluyo, A., Srinivasan, B., Taniar, D.: A Taxanomy of Broadcast Indexing Schemes for Multi Channel Data Dissemination in Mobile Database. In: Proceedings of the 18th International Conference on Advanced Information Networking and Applications (AINA 2004), pp. 213–218. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  29. Waluyo, A., Srinivasan, B., Taniar, D.: Research in mobile database query optimization and processing. Mobile Information Systems 1(4), 225–252 (2005)CrossRefGoogle Scholar
  30. Xia, C., Hsu, W., Lee, M.: ERkNN: efficient reverse k-nearest neighbors retrieval with local k-NN distance estimation. In: Proceedings of the 14th ACM International Conference on Information and Knowledge Management, pp. 533–540 (2005)Google Scholar
  31. Xuan, K., Zhao, G., Taniar, D., Srinivasan, B., Safar, M., Gavrilova, M.: Continous Range Search based on Network Voronoi Diagram. International Journal of Grid and Utility Computing (in press, 2009)Google Scholar
  32. Xuan, K., Zhao, G., Taniar, D., Srinivasan, B., Safar, M., Gavrilova, M.: Network Voronoi Diagram based Range Search. In: Proceedings of the 23rd IEEE International Conference on Advanced Information Networking and Applications, AINA (in press, 2009)Google Scholar
  33. Xuan, K., Zhao, G., Taniar, D., Srinivasan, B., Safar, M., Gavrilova, M.: Continous Range Search Query Processing in Mobile Navigation. In: Proceedings of the 14th IEEE International Conference on Parallel and Distributed Systems, ICPADS’s 2008, pp. 361–368. IEEE Computer Society, Los Alamitos (2008)CrossRefGoogle Scholar
  34. Yang, C., Lin, K.: An Index Structure for Efficient Reverse Nearest Neighbor Queries. In: Proceedings of the 17th International Conference on Data Engineering, pp. 485–492 (2001)Google Scholar
  35. Zhao, G., Xuan, K., Taniar, D., Srinivasan, B.: Incremental K-Nearest Neighbor Search On Road Networks. Journal of Interconnection Networks 9(4), 455–470 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Quoc Thai Tran
    • 1
  • David Taniar
    • 1
  • Maytham Safar
    • 2
  1. 1.Clayton School of Information TechnologyMonash UniversityAustralia
  2. 2.Computer Engineering DepartmentKuwait UniversityKuwait

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