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.
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References
Abiteboul, S., Buneman, P., Suciu, D.: Data on the Web: From Relations to Semistructured Data and XML. Morgan Kaufmann, San Francisco (2000)
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: Data Structures and Algorithms. Addison-Wesley, Reading (1983)
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)
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)
Cook, D.J., Holder, L.B.: Graph-based data mining. IEEE Intelligent Systems 15, 32–41 (2000)
Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformation, vol. 1. World Scientific Publishing, Singapore (1997)
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)
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)
Lehman, E., Shelat, A.: Approximations algorithms for grammar-based compression. In: Proc. SODA 2002, pp. 205–212 (2002)
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)
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)
Nevill-Manning, C., Witten, I.: Compression and explanation using hierarchical grammars. Computer Journal 40(2/3), 103–116 (1997)
Sakamoto, H.: A fully linear-time approximation algorithm for grammar-based compression. DOI Technical Report 214, Department of Informatics, Kyushu University (2003)
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)
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)
Wang, K., Liu, H.: Discovering structural association of semistructured data. IEEE Trans. Knowledge and Data Engineering 12, 353–371 (2000)
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Yamagata, K., Uchida, T., Shoudai, T., Nakamura, Y. (2003). An Effective Grammar-Based Compression Algorithm for Tree Structured Data. In: Horváth, T., Yamamoto, A. (eds) Inductive Logic Programming. ILP 2003. Lecture Notes in Computer Science(), vol 2835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39917-9_25
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DOI: https://doi.org/10.1007/978-3-540-39917-9_25
Publisher Name: Springer, Berlin, Heidelberg
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