CPM 2011: Combinatorial Pattern Matching pp 309-322 | Cite as
Faster Subsequence and Don’t-Care Pattern Matching on Compressed Texts
Abstract
Subsequence pattern matching problems on compressed text were first considered by Cégielski et al. (Window Subsequence Problems for Compressed Texts, Proc. CSR 2006, LNCS 3967, pp. 127–136), where the principal problem is: given a string T represented as a straight line program (SLP) \(\mathcal{T}\) of size n, a string P of size m, compute the number of minimal subsequence occurrences of P in T. We present an O(nm) time algorithm for solving all variations of the problem introduced by Cégielski et al.. This improves the previous best known algorithm of Tiskin (Towards approximate matching in compressed strings: Local subsequence recognition, Proc. CSR 2011), which runs in O(nmlogm) time. We further show that our algorithms can be modified to solve a wider range of problems in the same O(nm) time complexity, and present the first matching algorithms for patterns containing VLDC (variable length don’t care) symbols, as well as for patterns containing FLDC (fixed length don’t care) symbols, on SLP compressed texts.
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References
- 1.Baeza-Yates, R.A.: Searching subsequences. Theoretical Computer Science 78(2), 363–376 (1991)MathSciNetCrossRefMATHGoogle Scholar
- 2.Baturo, P., Rytter, W.: Compressed string-matching in standard sturmian words. Theoretical Computer Science 410(30–32), 2804–2810 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 3.Cégielski, P., Guessarian, I., Lifshits, Y., Matiyasevich, Y.: Window subsequence problems for compressed texts. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds.) CSR 2006. LNCS, vol. 3967, pp. 127–136. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 4.Claude, F., Navarro, G.: Self-indexed text compression using straight-line programs. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 235–246. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 5.Hermelin, D., Landau, G.M., Landau, S., Weimann, O.: A unified algorithm for accelerating edit-distance computation via text-compression. In: Proc. STACS 2009, pp. 529–540 (2009)Google Scholar
- 6.Karpinski, M., Rytter, W., Shinohara, A.: An efficient pattern-matching algorithm for strings with short descriptions. Nordic Journal of Computing 4, 172–186 (1997)MathSciNetMATHGoogle Scholar
- 7.Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)MathSciNetCrossRefMATHGoogle Scholar
- 8.Larsson, N.J., Moffat, A.: Offline dictionary-based compression. In: Proc. Data Compression Conference 1999, pp. 296–305. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
- 9.Lifshits, Y., Lohrey, M.: Querying and embedding compressed texts. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 681–692. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 10.Mannila, H., Toivonen, H., Verkamo, A.I.: Discovery of frequent episodes in event sequences. Data Mining and Knowledge Discovery 1(3), 259–289 (1997)CrossRefGoogle Scholar
- 11.Miyazaki, M., Shinohara, A., Takeda, M.: An improved pattern matching algorithm for strings in terms of straight-line programs. In: CPM 1997. LNCS, vol. 1264, pp. 1–11. Springer, Heidelberg (1997)CrossRefGoogle Scholar
- 12.Nevill-Manning, C.G., Witten, I.H., Maulsby, D.L.: Compression by induction of hierarchical grammars. In: Data Compression Conference 1994, pp. 244–253. IEEE Computer Society Press, Los Alamitos (1994)Google Scholar
- 13.Rytter, W.: Grammar compression, LZ-encodings, and string algorithms with implicit input. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 15–27. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 14.Tiskin, A.: Faster subsequence recognition in compressed strings. J. Math. Sci. 158(5), 759–769 (2009)MathSciNetCrossRefMATHGoogle Scholar
- 15.Tiskin, A.: Towards approximate matching in compressed strings: Local subsequence recognition. In: Proc. CSR 2011 (to appear, 2011)Google Scholar
- 16.Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Transactions on Information Theory IT-23(3), 337–349 (1977)MathSciNetCrossRefMATHGoogle Scholar
- 17.Ziv, J., Lempel, A.: Compression of individual sequences via variable-length coding. IEEE Transactions on Information Theory 24(5), 530–536 (1978)MathSciNetCrossRefMATHGoogle Scholar