Polynomial Time Pattern Matching Algorithm for Ordered Graph Patterns

  • Takahiro Hino
  • Yusuke Suzuki
  • Tomoyuki Uchida
  • Yuko Itokawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7842)


Ordered graphs, each of whose vertices has a unique order on edges incident to the vertex, can represent graph structured data such as Web pages, \(\mbox{\TeX}\) sources, CAD and MAP. In this paper, in order to design computational machine learning for such data, we propose an ordered graph pattern with ordered graph structures and structured variables. We define an ordered graph language for an ordered graph pattern g as the set of all ordered graphs obtained from g by replacing structured variables in g with arbitrary ordered graphs. We present a polynomial time pattern matching algorithm for determining whether or not a given ordered graph is contained in the ordered graph language for a given ordered graph pattern. We also implement the proposed algorithm on a computer and evaluate the algorithm by reporting and discussing experimental results.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angluin, D.: Inductive inference of formal languages from positive data. Information and Control 45(2), 117–135 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Horváth, T., Ramon, J., Wrobel, S.: Frequent subgraph mining in outerplanar graphs. Data Mining and Knowledge Discovery 21(3), 472–508 (2010)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Jiang, X., Bunke, H.: On the coding of ordered graphs. Computing 61(1), 23–38 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Kawamoto, S., Suzuki, Y., Shoudai, T.: Learning characteristic structured patterns in rooted planar maps. In: IMECS 2010, IAENG, pp. 465–470 (2010)Google Scholar
  5. 5.
    Kononenko, I., Kukar, M.: Machine Learning and Data Mining: Introduction to Principles and Algorithms. Horwood Pub. (2007)Google Scholar
  6. 6.
    Kuramochi, M., Karypis, G.: Discovering frequent geometric subgraphs. Information Systems 32(8), 1101–1120 (2007)CrossRefGoogle Scholar
  7. 7.
    Michalski, R.S., Bratko, I., Bratko, A. (eds.): Machine Learning and Data Mining; Methods and Applications. John Wiley & Sons, Inc., NY (1998)Google Scholar
  8. 8.
    Shinohara, T.: Polynomial time inference of extended regular pattern languages. In: Goto, E., Furukawa, K., Nakajima, R., Nakata, I., Yonezawa, A. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  9. 9.
    Shoudai, T., Uchida, T., Miyahara, T.: Polynomial time algorithms for finding unordered tree patterns with internal variables. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 335–346. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Suzuki, Y., Shoudai, T., Uchida, T., Miyahara, T.: Ordered term tree languages which are polynomial time inductively inferable from positive data. Theoretical Computer Science 350(1), 63–90 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Takami, R., Suzuki, Y., Uchida, T., Shoudai, T.: Polynomial time inductive inference of TTSP graph languages from positive data. IEICE Transactions 92-D(2), 181–190 (2009)Google Scholar
  12. 12.
    Uchida, T., Itokawa, Y., Shoudai, T., Miyahara, T., Nakamura, Y.: A new framework for discovering knowledge from two-dimensional structured data using layout formal graph system. In: Arimura, H., Sharma, A.K., Jain, S. (eds.) ALT 2000. LNCS (LNAI), vol. 1968, pp. 141–155. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Tutte, W.T.: A census of planar maps. Canadian Journal of Mathematics 15, 249–271 (1963)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Yamasaki, H., Sasaki, Y., Shoudai, T., Uchida, T., Suzuki, S.: Learning block-preserving graph patterns and its application to data mining. Machine Learning 76(1), 137–173 (2009)CrossRefGoogle Scholar
  15. 15.
    Yoshimura, Y., Shoudai, T., Suzuki, Y., Uchida, T., Miyahara, T.: Polynomial time inductive inference of cograph pattern languages from positive data. In: Muggleton, S.H., Tamaddoni-Nezhad, A., Lisi, F.A. (eds.) ILP 2011. LNCS, vol. 7207, pp. 389–404. Springer, Heidelberg (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Takahiro Hino
    • 1
  • Yusuke Suzuki
    • 1
  • Tomoyuki Uchida
    • 1
  • Yuko Itokawa
    • 2
  1. 1.Department of Intelligent SystemsHiroshima City UniversityJapan
  2. 2.Faculty of Psychological ScienceHiroshima International UniversityJapan

Personalised recommendations