Abstract
A scalable pattern discovery by compression is proposed. A string is representable by a context-free grammar (CFG) deriving the string deterministically. In this framework of grammar-based compression, the aim of the algorithm is to output as small a CFG as possible. Beyond that, the optimization problem is approximately solvable. In such approximation algorithms, the compressor by Sakamoto et al. (2009) is especially suitable for detecting maximal common substrings as well as long frequent substrings. This is made possible thanks to the characteristics of edit-sensitive parsing (ESP) by Cormode and Muthukrishnan (2007), which was introduced to approximate a variant of edit distance. Based on ESP, we design a linear time algorithm to find all frequent patterns in a string approximately and prove a lower bound for the length of extracted frequent patterns. We also examine the performance of our algorithm by experiments in DNA sequences and other compressible real world texts. Compared to the practical algorithm developed by Uno (2008), our algorithm is faster with large and repetitive strings.
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References
Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic local alignment search tool. J. Mol. Biol. 215(3), 403–410 (1990)
Charikar, M., Lehman, E., Liu, D., Panigrahy, R., Prabhakaran, M., Sahai, A., Shelat, A.: The smallest grammar problem. IEEE Transactions on Information Theory 51(7), 2554–2576 (2005)
Cilibrasi, R., Vitanyi, P.M.B.: Clustering by compression. IEEE Transactions on Information Theory 51(4), 1523–1545 (2005)
Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves. ACM Trans. Algor. 3(1), Article 2 (2007)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences. Cambridge University Press, Cambridge (1997)
Karp, R.M., Miller, R.E., Rosenberg, A.L.: Rapid identification of repeated patterns in strings, trees and arrays. In: STOC 1972, pp. 125–136 (1972)
Kieffer, J.C., Yang, E.-H.: Grammar-based codes: A new class of universal lossless source codes. IEEE Transactions on Information Theory 46(3), 737–754 (2000)
Lehman, E., Shelat, A.: Approximation algorithms for grammar-based compression. In: SODA 2002, pp. 205–212 (2002)
Li, M., Chen, X., Li, X., Ma, B., Vitanyi, P.M.B.: The similarity metric. IEEE Transactions on Information Theory 50(12), 3250–3264 (2004)
Pearson, W.R.: Flexible sequence similarity searching with the fasta3 program package methods. Mol. Biol. 132, 185–219 (2000)
Rytter, W.: Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci. 302(1-3), 211–222 (2003)
Sadakane, K.: Compressed text databases with efficient query algorithms based on the compressed suffix array. In: Lee, D.T., Teng, S.-H. (eds.) ISAAC 2000. LNCS, vol. 1969, pp. 410–421. Springer, Heidelberg (2000)
Sakamoto, H.: A fully linear-time approximation algorithm for grammar-based compression. J. Discrete Algorithms 3(2-4), 416–430 (2005)
Sakamoto, H., Maruyama, S., Kida, T., Shimozono, S.: A space-saving approximation algorithm for grammar-based compression. IEICE Trans. on Information and Systems E92-D(2), 158–165 (2009)
Shapira, D., Storer, J.A.: Edit distance with move operations. J. Discrete Algorithms 5(2), 380–392 (2007)
Uno, T.: An efficient algorithm for finding similar short substrings from large scale string data. In: Washio, T., Suzuki, E., Ting, K.M., Inokuchi, A. (eds.) PAKDD 2008. LNCS (LNAI), vol. 5012, pp. 345–356. Springer, Heidelberg (2008)
Välimäki, N., Mäkinen, V., Gerlach, W., Dixit, K.: Engineering a compressed suffix tree implementation. ACM Journal of Experimental Algorithmics 14 (2009)
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Nakahara, M., Maruyama, S., Kuboyama, T., Sakamoto, H. (2011). Scalable Detection of Frequent Substrings by Grammar-Based Compression. In: Elomaa, T., Hollmén, J., Mannila, H. (eds) Discovery Science. DS 2011. Lecture Notes in Computer Science(), vol 6926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24477-3_20
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DOI: https://doi.org/10.1007/978-3-642-24477-3_20
Publisher Name: Springer, Berlin, Heidelberg
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