Abstract
In this paper, we consider a generalized longest common subsequence problem with multiple substring exclusive constraints. For the two input sequences X and Y of lengths n and m, and a set of d constraints \(P=\{P_1,\cdots ,P_d\}\) of total length r, the problem is to find a common subsequence Z of X and Y excluding each of constraint string in P as a substring and the length of Z is maximized. A very simple dynamic programming algorithm to this problem is presented in this paper. The correctness of the new algorithm is demonstrated. The time and space complexities of the new algorithm are both O(nmr).
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References
Aho, A.V., Corasick, M.J.: Efficient string matching: an aid to bibliographic search. Commun. ACM 18(6), 333–340 (1975)
Ann, H.Y., Yang, C.B., Tseng, C.T., Hor, C.Y.: A fast and simple algorithm for computing the longest common subsequence of run-length encoded strings. Inform. Process Lett. 108(11), 360–364 (2008)
Ann, H.Y., Yang, C.B., Peng, Y.H., Liaw, B.C.: Efficient algorithms for the block edit problems. Inf. Comput. 208(3), 221–229 (2010)
Apostolico, A., Guerra, C.: The longest common subsequences problem revisited. Algorithmica 2(1), 315–336 (1987)
Arslan, A.N., Egecioglu, O.: Algorithms for the constrained longest common subsequence problems. Int. J. Found. Comput. Sci. 16(6), 1099–1109 (2005)
Blum, C., Blesa, M.J., Lpez-Ibnez, M.: Beam search for the longest common subsequence problem. Comput. Oper. Res. 36(12), 3178–3186 (2009)
Chen, Y.C., Chao, K.M.: On the generalized constrained longest common subsequence problems. J. Comb. Optim. 21(3), 383–392 (2011)
Chin, F.Y.L., Santis, A.D., Ferrara, A.L., Ho, N.L., Kim, S.K.: A simple algorithm for the constrained sequence problems. Inform. Process. Lett. 90(4), 175–179 (2004)
Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, Cambridge, UK (2007)
Deorowicz, S.: Quadratic-time algorithm for a string constrained LCS problem. Inform. Process. Lett. 112(11), 423–426 (2012)
Deorowicz, S., Obstoj, J.: Constrained longest common subsequence computing algorithms in practice. Comput. Inform. 29(3), 427–445 (2010)
Farhana, E., Ferdous, J., Moosa, T., Rahman, M.S.: Finite automata based algorithms for the generalized constrained longest common subsequence problems. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 243–249. Springer, Heidelberg (2010)
Gotthilf, Z., Hermelin, D., Lewenstein, M.: Constrained LCS: hardness and approximation. In: Ferragina, P., Landau, G.M. (eds.) CPM 2008. LNCS, vol. 5029, pp. 255–262. Springer, Heidelberg (2008)
Gotthilf, Z., Hermelin, D., Landau, G.M., Lewenstein, M.: Restricted LCS. In: Chavez, E., Lonardi, S. (eds.) SPIRE 2010. LNCS, vol. 6393, pp. 250–257. Springer, Heidelberg (2010)
Gusfield, D.: Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)
Hirschberg, D.S.: Algorithms for the longest common subsequence problem. J. ACM 24(4), 664–675 (1977)
Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest common subsequences. Commun. ACM 20(5), 350–353 (1977)
Iliopoulos, C.S., Rahman, M.S.: New efficient algorithms for the LCS and constrained LCS problems. Inform. Process. Lett. 106(1), 13–18 (2008)
Iliopoulos, C.S., Rahman, M.S.: A new efficient algorithm for computing the longest common subsequence. Theor. Comput. Sci. 45(2), 355–371 (2009)
Iliopoulos, C.S., Rahman, M.S., Rytter, W.: Algorithms for two versions of LCS problem for indeterminate strings. J. Comb. Math. Comb. Comput. 71, 155–172 (2009)
Iliopoulos, C.S., Rahman, M.S., Vorcek, M., Vagner, L.: Finite automata based algorithms on subsequences and supersequences of degenerate strings. J. Discrete Algorithm 8(2), 117–130 (2010)
Knuth, D.E., Morris, J.H., Pratt, V.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)
Maier, D.: The complexity of some problems on subsequences and supersequences. J. ACM 25, 322–336 (1978)
Peng, Y.H., Yang, C.B., Huang, K.S., Tseng, K.T.: An algorithm and applications to sequence alignment with weighted constraints. Int. J. Found. Comput. Sci. 21(1), 51–59 (2010)
Shyu, S.J., Tsai, C.Y.: Finding the longest common subsequence for multiple biological sequences by ant colony optimization. Comput. Oper. Res. 36(1), 73–91 (2009)
Tang, C.Y., Lu, C.L.: Constrained multiple sequence alignment tool development and its application to RNase family alignment. J. Bioinform. Comput. Biol. 1, 267–287 (2003)
Tsai, Y.T.: The constrained longest common subsequence problem. Inform. Process. Lett. 88(4), 173–176 (2003)
Tseng, C.T., Yang, C.B., Ann, H.Y.: Efficient algorithms for the longest common subsequence problem with sequential substring constraints. J. Complex. 29, 44–52 (2013)
Wagner, R., Fischer, M.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)
Wang, L., Wang, X., Wu, Y., Zhu, D.: A dynamic programming solution to a generalized LCS problem. Inform. Process. Lett. 113(1), 723–728 (2013)
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Wang, X., Wu, Y., Zhu, D. (2016). A Polynomial Time Algorithm for a Generalized Longest Common Subsequence Problem. In: Huang, X., Xiang, Y., Li, KC. (eds) Green, Pervasive, and Cloud Computing. Lecture Notes in Computer Science(), vol 9663. Springer, Cham. https://doi.org/10.1007/978-3-319-39077-2_2
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DOI: https://doi.org/10.1007/978-3-319-39077-2_2
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