Solving Multiple Bichromatic Mutual Nearest Neighbor Queries with the GPU

  • Marta Fort
  • J. Antoni Sellarès
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8505)


In this paper we propose and solve multiple bichromatic mutual nearest neighbor queries in the plane considering multiplicative weighted Euclidean distances. These multiple queries are related to the mutual influence of two sets of facilities of different type, in which facilities of the first type cooperates with facilities of the second type in order to obtain reciprocal benefits. The studied problems find applications, for example, in collaborative marketing. We present a parallel algorithm, to be run on a Graphics Processing Unit, for solving multiple bichromatic mutual nearest neighbor queries. We also present the complexity analysis of the algorithm, and provide and discuss experimental results that show the scalability of our approach.


Graphic Processing Unit Index Structure Total Work Global Memory Query Point 
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.


  1. 1.
    Achtert, E., Böhm, C., Kroger, P., Kunath, P., Pryakhin, A., Renz, M.: Efficient reverse k-nearest neighbor search in arbitrary metric spaces. SIGMOD (2006)Google Scholar
  2. 2.
    Brito, M.R., Chavez, E.L., Quiroz, A.J., Yukich, J.E.: Connectivity of the mutual k-nearest neighbor graph in clustering and outlier detection. Stat. Probab. Lett. 35(1), 33–42 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Barrientos, R.J., Gómez, J.I., Tenllado, C., Matias, M.P., Marin, M.: kNN query processing in metric spaces using GPUs. In: Jeannot, E., Namyst, R., Roman, J. (eds.) Euro-Par 2011, Part I. LNCS, vol. 6852, pp. 380–392. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  4. 4.
    Brown, S., Snoeyink, J.: Gpu nearest neighbors using a minimal kd-tree, In: Second Workshop on Massive Data Algorithmics, (MASSIVE) (2010)Google Scholar
  5. 5.
    Cayton, L.: A nearest neighbor data structure for Graphics Hardware. VLDB-ADMS pp. 1–6 (2010)Google Scholar
  6. 6.
    Cheung, K.L., Fu, A.W.-C.: Enhanced nearest neighbour search on the R-tree. SIGMOD 27(3), 16–21 (1998)CrossRefGoogle Scholar
  7. 7.
    Chen, Y., Patel, J.: Efficient evaluation of all-nearest-neighbor queries. ICDE pp. 1056–1065 (2007)Google Scholar
  8. 8.
    Drezner, T.: Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. J. Retail. 70(1), 49–64 (1994)CrossRefGoogle Scholar
  9. 9.
    Drezner, T., Drezner, Z.: Validating the Gravity-Based Competitive Location Model Using Inferred Attractiveness. Annals OR 111(1–4), 227–237 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Fort, M., Sellarès, J.A.: Finding influential location regions based on reverse k-neighbor queries. Knowl.Based Syst. 47, 35–52 (2013)CrossRefGoogle Scholar
  11. 11.
    Gao, Y., Chen, G., Li, Q., Zheng, B., Li, C.: Processing mutual nearest neighbor queries for moving object trajectories. In: Proc. 9th Int. Conf. on Mobile Data Management, pp. 116–123 (2008)Google Scholar
  12. 12.
    Garcia, V., Debreuve, E., Nielsen, F., Barlaud, M.: k-nearest neighbor search: fast GPU-based implementation and application to high-dimensional feature matching. In: Proceedings IEEE 17th Int. Conf. on Image Processing (ICIP) pp. 3757–3760 (2010)Google Scholar
  13. 13.
    Gowda, K.C., Krishna, G.: Agglomerative clustering using the concept of mutual nearest neighborhood. Pattern Recog. 10(2), 105–112 (1978)CrossRefzbMATHGoogle Scholar
  14. 14.
    Gowda, K.C., Krishna, G.: The condensed nearest neighbor rule using the concept of mutual nearest neighborhood. IEEE Trans. Inf. Theory 25(4), 488–490 (1979)CrossRefGoogle Scholar
  15. 15.
    Gao, Y., Zheng, B., Chen, G., Li, Q., Chen, C., Chen, G.: Efficient mutual nearest neighbor query processing for moving object trajectories, Information Sciences, 180(11), pp. 2176–2195 (2010)Google Scholar
  16. 16.
    Gao, Y., Zheng, B., Chen, G., Li, Q.: On efficient mutual nearest neighbor query processing in spatial databases. Data Knowl. Eng. 68(8), 705–727 (2009)CrossRefGoogle Scholar
  17. 17.
    Hjaltason, G.R., Samet, H.: Distance browsing in spatial databases. ACM Trans. Database Syst. 24(2), 265–318 (1999)CrossRefGoogle Scholar
  18. 18.
    Jin, W., Tung, A.K.H., Han, J., Wang, W.: Ranking Outliers Using Symmetric Neighborhood Relationship. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 577–593. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  19. 19.
    Korn, F., Muthukrishnan, S.: Influence sets based on reverse nearest neighbor queries. SIGMOD (2000)Google Scholar
  20. 20.
    Miranda, N., Chávez, E., Piccoli, M.F., Reyes, N.: (Very) Fast (All) k-Nearest Neighbors in Metric and Non Metric Spaces without Indexing. In: Brisaboa, N., Pedreira, O., Zezula, P. (eds.) SISAP 2013. LNCS, vol. 8199, pp. 300–311. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  21. 21.
    Stanoi, I., Riedewald, M., Agrawal, D., Abbadi, A.E.: Discovery of influence sets in frequently updated databases. In: Proceedings 27th Int. Conf. on Very Large Data Bases (VLDB) pp. 99–108 (2001)Google Scholar
  22. 22.
    Wong, R.C.-W., Tao, Y., Fu, A.W.C., Xiao, X.: On efficient spatial matching. In: Proceedings 33rd International Conference on Very Large Data Base, pp. 579–590 (2007)Google Scholar
  23. 23.
    Wu, W., Yang, F., Chan, C.Y., Tan, K.: FINCH: evaluating reverse k-Nearest-Neighbor queries on location data. In Proceedings of VLDB 1(1), pp. 1056–1067 (2008)Google Scholar
  24. 24.
    Yao, B., Li, F., Kumar, P.: K-nearest neighbor queries and knn-joins in large relational databases (almost) for free. In Proceedings of ICDE 2010, pp. 4–15 (2010)Google Scholar
  25. 25.
    Zhang, J., Mamoulis, N., Papadias, D., Tao, Y.: All-nearest-neighbors queries in spatial databases. In: Proceedings of 16th International Conference on Scientific and Statistical Database Management (SSDBM). pp. 297–306 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dept. Informàtica, Matemàtica Aplicada i EstadísticaUniversitat de GironaGironaSpain

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