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Fast Frequent Free Tree Mining in Graph Databases

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Abstract

Free tree, as a special undirected, acyclic and connected graph, is extensively used in computational biology, pattern recognition, computer networks, XML databases, etc. In this paper, we present a computationally efficient algorithm F3TM (Fast Frequent Free Tree Mining) to find all frequently-occurred free trees in a graph database, \({\cal D} = \{g_1, g_2, \cdots, g_N\}\). Two key steps of F3TM are candidate generation and frequency counting. The frequency counting step is to compute how many graphs in \(\cal D\) containing a candidate frequent free tree, which is proved to be the subgraph isomorphism problem in nature and is NP-complete. Therefore, the key issue becomes how to reduce the number of false positives in the candidate generation step. Based on our observations, the cost of false positive reduction can be prohibitive itself. In this paper, we focus ourselves on how to reduce the candidate generation cost and minimize the number of infrequent candidates being generated. We prove a theorem that the complete set of frequent free trees can be discovered from a graph database by growing vertices on a limited range of positions of a free tree. We propose two pruning algorithms, namely, automorphism-based pruning and canonical mapping-based pruning, which significantly reduce the candidate generation cost. We conducted extensive experimental studies using a real application dataset and a synthetic dataset. The experiment results show that our algorithm F3TM outperforms the up-to-date algorithms by an order of magnitude in mining frequent free trees in large graph databases.

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References

  1. Agrawal, R., Srikant, R.: Fast algorithms for mining association rules in large databases. In: Proceedings of 20th International Conference on Very Large Data Bases (VLDB94), pp. 487–499 (1994)

  2. Aho, A.V., Hopcroft, J.E.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Boston, MA (1974)

    MATH  Google Scholar 

  3. Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. In: Proceedings of the Seventh International Conference on World Wide Web (WWW98), pp. 107–117 (1998)

  4. Chakrabarti, S., Dom, B.E., Kumar, S.R., Raghavan, P., Rajagopalan, S., Tomkins, A., Gibson, D., Kleinberg, J.: Mining the web’s link structure. Computer 32(8), 60–67 (1999)

    Article  Google Scholar 

  5. Chen, Z., Lin, F., Liu, H., Liu, Y., Ma, W.-Y., Wenyin, L.: User intention modeling in web applications using data mining. World Wide Web 5(3), 181–191 (2002)

    Article  Google Scholar 

  6. Chi, Y., Yang, Y., Muntz, R.R.: Indexing and mining free trees. In: Proceedings of the Third IEEE International Conference on Data Mining (ICDM03), Washington, DC, p. 509. IEEE Computer Society, Los Alamitos, CA (2003)

    Chapter  Google Scholar 

  7. Chi, Y., Yang, Y., Muntz, R.R.: Canonical forms for labelled trees and their applications in frequent subtree mining. Knowl. Inf. Syst. 8(2), 203–234 (2005)

    Article  Google Scholar 

  8. Cooley, R., Mobasher, B., Srivastava, J.: Web mining: information and pattern discovery on the world wide web. In: Proceedings of the 9th International Conference on Tools with Artificial Intelligence (ICTAI97), Washington, DC, p. 558. IEEE Computer Society, Los Alamitos, CA (1997)

    Chapter  Google Scholar 

  9. Cui, J.-H., Kim, J., Maggiorini, D., Boussetta, K., Gerla, M.: Aggregated multicasta comparative study. Cluster Comput. 8(1), 15–26 (2005)

    Article  Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  11. Han, J., Yan, X., Yu, P.S.: Mining and searching graphs and structures. In: Proceeding of the 22th International Conference on Data Engineering (ICDE06), Philadelphia, PA. IEEE Computer Society Press, Los Alamitos, CA (2006)

    Google Scholar 

  12. Hein, J., Jiang, T., Wang, L., Zhang, K.: On the complexity of comparing evolutionary trees. Discrete Appl. Math. 71(1–3), 153–169 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Huan, J., Wang, W., Prins, J.: Efficient mining of frequent subgraphs in the presence of isomorphism. In: Proceedings of the Third IEEE International Conference on Data Mining (ICDM03), Washington, DC, p. 549. IEEE Computer Society, Los Alamitos, CA (2003)

    Chapter  Google Scholar 

  14. Inokuchi, A., Washio, T., Motoda, H.: An a priori-based algorithm for mining frequent substructures from graph data. In: Proceedings of the 4th European Conference on Principles of Data Mining and Knowledge Discovery (PKDD00), pp. 13–23. Springer, Berlin Heidelberg New York (2000)

    Chapter  Google Scholar 

  15. Kuramochi, M., Karypis, G.: Frequent subgraph discovery. In: Proceedings of the 2001 IEEE International Conference on Data Mining (ICDM01), pp. 313–320. IEEE Computer Society, Los Alamitos, CA (2001)

    Chapter  Google Scholar 

  16. Liu, T.-L., Geiger, D.: Approximate tree matching and shape similarity. In: International Conference of Computer Vision (ICCV99), pp. 456–462 (1999)

  17. Mckay, B.D.: Nauty user’s guide. In: Technical Report TR-CS-90-02, the Department of Computer Science. Australia National University (1990)

  18. Rückert, U., Kramer, S.: Frequent free tree discovery in graph data. In: Proceedings of the 2004 ACM symposium on Applied computing (SAC04), pp. 564–570. ACM, New York (2004)

    Chapter  Google Scholar 

  19. Shamir, R., Tsur, D.: Faster subtree isomorphism. In: Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS97), Washington, DC, p. 126. IEEE Computer Society, Los Alamitos, CA (1997)

    Chapter  Google Scholar 

  20. Shasha, D., Wang, J.T.L., Giugno, R.: Algorithmics and applications of tree and graph searching. In: Proceedings of the Twenty-first ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems (PODS02), pp. 39–52. ACM, New York (2002)

    Chapter  Google Scholar 

  21. Termier, A., Rousset, M.-C., Sebag, M.: Treefinder: a first step towards XML data mining. In: Proceedings of the 2002 IEEE International Conference on Data Mining (ICDM02), Washington, DC, p. 450. IEEE Computer Society, Los Alamitos, CA (2002)

    Chapter  Google Scholar 

  22. Ullmann, J.R.: An algorithm for subgraph isomorphism. J. Assoc. Comput. Mach. 23(1), 31–42 (1976)

    MathSciNet  Google Scholar 

  23. Valiente, G.: Algorithms on Trees and Graphs. Springer, Berlin Heidleberg New York (2002)

    MATH  Google Scholar 

  24. Yan, X., Han, J.: gspan: graph-based substructure pattern mining. In: Proceedings of the 2002 IEEE International Conference on Data Mining (ICDM02), Washington, DC, p. 721. IEEE Computer Society, DC, Los Alamitos, CA (2002)

    Google Scholar 

  25. Yan, X., Han, J.: Closegraph: mining closed frequent graph patterns. In: Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD03), pp. 286–295. ACM, New York (2003)

    Chapter  Google Scholar 

  26. Zaki, M.-M.J.: Efficiently mining frequent trees in a forest: algorithms and applications. IEEE Trans. Knowl. Data Eng. 17(8), 1021–1035 (2005)

    Article  Google Scholar 

  27. Zhao, Q., Bhowmick, S.S., Mohania, M., Kambayashi, Y.: Discovering frequently changing structures from historical structural deltas of unordered XML. In: Proceedings of the Thirteenth ACM International Conference on Information and Knowledge Management (CIKM04), pp. 188–197 (2004)

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Authors and Affiliations

  1. The Chinese University of Hong Kong, Hong Kong, China

    Peixiang Zhao & Jeffrey Xu Yu

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  1. Peixiang Zhao
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  2. Jeffrey Xu Yu
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Correspondence to Peixiang Zhao.

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Zhao, P., Yu, J.X. Fast Frequent Free Tree Mining in Graph Databases. World Wide Web 11, 71–92 (2008). https://doi.org/10.1007/s11280-007-0031-z

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  • DOI: https://doi.org/10.1007/s11280-007-0031-z

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