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An Effective Grammar-Based Compression Algorithm for Tree Structured Data

  • Kazunori Yamagata
  • Tomoyuki Uchida
  • Takayoshi Shoudai
  • Yasuaki Nakamura
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2835)

Abstract

Many semistructured data such as HTML/XML files are represented by rooted trees t such that all children of each internal vertex of t are ordered and all edges of t have labels. Such data is called tree structured data. Analyzing large tree structured data is a time-consuming process in data mining. If we can reduce the size of input data without loss of information, we can speed up such a heavy process. In this paper, we consider a problem of effective compression of an ordered rooted tree, which represents given tree structured data, without loss of information. Firstly, in order to define this problem in a grammar-based compression scheme, we present a variable replacement grammar (VRG for short) over ordered rooted trees. The grammar-based compression problem for an ordered rooted tree T is defined as a problem of finding a VRG which generates only T and whose size is minimum. For the grammar-based compression problem for an ordered rooted tree, we show that there is no polynomial time algorithm with approximation ratio less than \(\frac{8593}{8592}\) unless P=NP. Secondly, based on this theoretical result, we present an effective compression algorithm for finding a VRG which generates only a given ordered rooted tree and whose size is as small as possible. Finally, in order to evaluate the performance of our grammar-based compression algorithm, we report some experimental results.

Keywords

Compression Ratio Rooted Tree Term Tree Compression Algorithm Graph Transformation 
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. 1.
    Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann, San Francisco (2000)Google Scholar
  2. 2.
    Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)zbMATHGoogle Scholar
  3. 3.
    Asai, T., Abe, K., Kawasoe, S., Arimura, H., Sakamoto, H., Arikawa, S.: Efficient substructure discovery from large semi-structured data. In: Proc. 2nd SIAM Int. Conf. Data Mining (SDM 2002), pp. 158–174 (2002)Google Scholar
  4. 4.
    Charikar, M., Lehman, E., Liu, D., Panigrahy, R.: Approximating the smallest grammar: Kolmogorov Complexity in natural models. In: Proc. 34th ACM STOC 2002, pp. 792–801 (2002)Google Scholar
  5. 5.
    Cook, D.J., Holder, L.B.: Graph-based data mining. IEEE Intelligent Systems 15, 32–41 (2000)CrossRefGoogle Scholar
  6. 6.
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. World Scientific Publishing, Singapore (1997)Google Scholar
  7. 7.
    Itokawa, Y., Uchida, T., Shoudai, T., Miyahara, T., Nakamura, Y.: Finding frequent subgraphs from graph structured data with geometric information and its application to lossless. In: Proc. PAKDD-2003. LNCS (LNAI), vol. 2637, pp. 582–594. Springer, Heidelberg (2003)Google Scholar
  8. 8.
    Kieffer, J.C., Yang, E.-h.: Grammar based codes: A new class of universal lossless source codes. IEEE Transactions on Information Theory 46, 737–754 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lehman, E., Shelat, A.: Approximations algorithms for grammar-based compression. In: Proc. SODA 2002, pp. 205–212 (2002)Google Scholar
  10. 10.
    Matsumoto, S., Shoudai, T., Miyahara, T., Uchida, T.: Learning of finite unions of tree patterns with internal structured variables from queries. In: McKay, B., Slaney, J.K. (eds.) Canadian AI 2002. LNCS (LNAI), vol. 2557, pp. 523–534. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Miyahara, T., Suzuki, Y., Shoudai, T., Uchida, T., Takahashi, K., Ueda, H.: Discovery of frequent tag tree patterns in semistructured web documents. In: Chen, M.-S., Yu, P.S., Liu, B. (eds.) PAKDD 2002. LNCS (LNAI), vol. 2336, pp. 341–355. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Nevill-Manning, C., Witten, I.: Compression and explanation using hierarchical grammars. Computer Journal 40(2/3), 103–116 (1997)CrossRefGoogle Scholar
  13. 13.
    Sakamoto, H.: A fully linear-time approximation algorithm for grammar-based compression. DOI Technical Report 214, Department of Informatics, Kyushu University (2003)Google Scholar
  14. 14.
    Suzuki, Y., Akanuma, R., Shoudai, T., Miyahara, T., Uchida, T.: Polynomial time inductive inference of ordered tree patterns with internal structured variables from positive data. In: Kivinen, J., Sloan, R.H. (eds.) COLT 2002. LNCS (LNAI), vol. 2375, pp. 169–184. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    Wang, K., Liu, H.: Discovering structural association of semistructured data. IEEE Trans. Knowledge and Data Engineering 12, 353–371 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kazunori Yamagata
    • 1
  • Tomoyuki Uchida
    • 1
  • Takayoshi Shoudai
    • 2
  • Yasuaki Nakamura
    • 1
  1. 1.Faculty of Information SciencesHiroshima City UniversityHiroshimaJapan
  2. 2.Department of InformaticsKyushu UniversityKasugaJapan

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