M-trees are well-know structures used to speed-up queries in databases. In this paper, we evaluate the applicability of m-trees to graph databases. In classical schemes based on metric-trees, the routing information kept in a metric-tree node is a selected element from the sub-cluster that represents. Nevertheless, defining a graph that represents a set of graphs is not a trivial task. We evaluate different graphs-class prototype as routing nodes in the metric tree. The considered prototypes are: Median Graphs, Closure Graphs, First-Order Random Graphs, Function-Described Graphs and Second-Order Random Graphs.


Metric-tree Graph Indexing Median Graph First-Order Random Graph Function-Described Graph Second-Order Random Graph 


  1. 1.
    Konstantinidis, K., Gasteratos, A., Andreadis, I.: Image retrieval based on fuzzy colour histogram processing. In: Optics Communications, vol. 248, pp. 375–386 (2005)Google Scholar
  2. 2.
    Datta, R., Joshi, D., Li, J., Wang, J.Z.: Image Retrieval: Ideas, Influences, and Trends of the New Age. ACM Computing Surveys 40(2), Article 5 (2008)Google Scholar
  3. 3.
    Jouili, S., Tabone, S.: Hypergraph-based image retrieval for graph-based representation. Pattern Recognition 45(11), 4054–4068 (2012)CrossRefGoogle Scholar
  4. 4.
    Lebrun, J., Gosselin, P., Philipp, S.: Inexact graph matching based on kernels for object retrieval in image databases. Image and Vision Computing 29(11), 716–729 (2011)CrossRefGoogle Scholar
  5. 5.
    Le Saux, B., Bunke, H.: Feature Selection for Graph-Based Image Classifiers. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 147–154. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  6. 6.
    Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)CrossRefGoogle Scholar
  7. 7.
    Neuhaus, M., Riesen, K., Bunke, H.: Fast Suboptimal Algorithms for the Computation of Graph Edit Distance. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Berretti, S., Del Bimbo, A., Vicario, E.: Efficient Matching and Indexing of Graph Models in Content-Based Retrieval. IEEE Transactions on Pattern Analysis and Machine Intelligence 23(10), 1089–1105 (2001)CrossRefGoogle Scholar
  9. 9.
    Zhao, J.L., Cheng, H.K.: Graph Indexing for Spatial Data Traversal in Road Map Databases. Computers & Operations Research 28, 223–241 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms and applications. IEEE Trans. on PAMI 23(10), 1144–1151 (2001)CrossRefGoogle Scholar
  11. 11.
    Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: Generalized Median Graph Computation by Means of Graph Embedding in Vector Spaces. Pattern Recognition 43(4), 1642–1655 (2010)zbMATHCrossRefGoogle Scholar
  12. 12.
    Ferrer, M., Valveny, E., Serratosa, F.: Median graphs: A genetic approach based on new theoretical properties. Pattern Recognition 42(9), 2003–2012 (2009)zbMATHCrossRefGoogle Scholar
  13. 13.
    Ferrer, M., Valveny, E., Serratosa, F.: Median graph: A new exact algorithm using a distance based on the maximum common subgraph. Pattern Recognition Letters 30(5), 579–588 (2009)CrossRefGoogle Scholar
  14. 14.
    Serratosa, F., Solé-Ribalta, A., Vidiella, E.: Graph Indexing and Retrieval Based on Median Graphs. In: Martínez-Trinidad, J.F., Carrasco-Ochoa, J.A., Kittler, J. (eds.) MCPR 2010. LNCS, vol. 6256, pp. 311–321. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Bunke, H., Munger, A., Jiang, X.: Combinatorial search versus genetic algorithms: A case study based on the generalized median graph problem. Pattern Recognition Letter 20, 1271–1277 (1999)CrossRefGoogle Scholar
  16. 16.
    Solé-Ribalta, A., Serratosa, F.: Graduated Assignment Algorithm for Finding the Common Labelling of a Set of Graphs. In: Hancock, E.R., Wilson, R.C., Windeatt, T., Ulusoy, I., Escolano, F. (eds.) SSPR&SPR 2010. LNCS, vol. 6218, pp. 180–190. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Wong, A.K.C., You, M.: Entropy and distance of random graphs with application to structural pattern recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 7, 599–609 (1985)zbMATHCrossRefGoogle Scholar
  18. 18.
    Serratosa, F., Alquézar, R., Sanfeliu, A.: Function-described graphs for modeling objects represented by attributed graphs. Pattern Recognition 36(3), 781–798 (2003)CrossRefGoogle Scholar
  19. 19.
    Serratosa, F., Alquézar, R., Sanfeliu, A.: Synthesis of Function-Described Graphs and clustering of Attributed Graphs. International Journal of Pattern Recognition and Artificial Intelligence 16(6), 621–655 (2002)CrossRefGoogle Scholar
  20. 20.
    Sanfeliu, A., Serratosa, F., Alquézar, R.: Second-Order Random Graphs for modeling sets of Attributed Graphs and their application to object learning and recognition. Intern. Journal of Pattern Recognition and Artificial Intelligence 18(3), 375–396 (2004)CrossRefGoogle Scholar
  21. 21.
    He, H., Singh, A.K.: Closure-Tree: An Index Structure for Graph Queries. In: Proc. International Conference on Data Engineering, p. 38 (2006)Google Scholar
  22. 22.
    Ciaccia, P., Patella, M., Zezula, P.: M-tree: An Efficient Access Method for Similarity Search in Metric Spaces. In: Proc. 23rd VLDB Conference, pp. 426–435 (1997)Google Scholar
  23. 23.
    Serratosa, F., Solé-Ribalta, A., Cortés, X.: K-nn Queries in Graph Databases Using M-Trees. In: Real, P., Diaz-Pernil, D., Molina-Abril, H., Berciano, A., Kropatsch, W. (eds.) CAIP 2011, Part I. LNCS, vol. 6854, pp. 202–210. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  24. 24.
    Fernández, A., Gómez, S.: Solving Non-uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms. Journal of Classification (25), 43–65 (2008)Google Scholar
  25. 25.
    Yan, X., Yu, P.S., Han, J.: Graph indexing: a frequent structure-based approach. In: ACM SIGMOD International Conference on Management of Data, pp. 335–346 (2004)Google Scholar
  26. 26.
    Shasha, D., Wang, J.T.L., Giugno, R.: Algorithmics and applications of tree and graph searching. In: ACM SIGMOD-SIGACT-SIGART, pp. 39–52 (2002)Google Scholar
  27. 27.
    Lee, S.Y., Hsu, F.: Spatial Reasoning and Similarity Retrieval of Images using 2D C-Strings Knowledge Representation. Pattern Recognition 25(3), 305–318 (1992)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Lozano, M.A., Escolano, F., Bonev, B., Suau, P., Aguilar, W., Saez, J.A., Cazorla, M.A.: Region and constellations based categorization of images with unsupervised graph learning. Image and Vision Computing 27, 960–978 (2009)Google Scholar
  29. 29.
    Solé-Ribalta, A., Serratosa, F.: Graduated Models and Algorithms for computing the Common Labelling of a set of Attributed Graphs. In: CVIU, vol. 115 (7), pp. 929–945 (2011)Google Scholar
  30. 30.
    Solé-Ribalta, A., Serratosa, F.: A Probabilistic Framework to Obtain a Common Labelling between Attributed Graphs. In: Vitrià, J., Sanches, J.M., Hernández, M. (eds.) IbPRIA 2011. LNCS, vol. 6669, pp. 516–523. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  31. 31.
    Riesen, K., Bunke, H.: IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning. In: da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.) S+SSPR 2008. LNCS, vol. 5342, pp. 287–297. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francesc Serratosa
    • 1
  • Xavier Cortés
    • 1
  • Albert Solé-Ribalta
    • 1
  1. 1.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliSpain

Personalised recommendations