Abstract
In this paper, we present a new and efficient algorithm for solving the LCS problem for two strings. Our algorithm runs in \(O(\mathcal R\log\log n + n)\) time, where \(\mathcal R\) is the total number of ordered pairs of positions at which the two strings match.
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References
Arlazarov, V.L., Dinic, E.A., Kronrod, M.A., Faradzev, I.A.: On economic construction of the transitive closure of a directed graph (english translation). Soviet Math. Dokl. 11, 1209–1210 (1975)
Arslan, A.N., Egecioglu, Ö.: Algorithms for the constrained longest common subsequence problems. Int. J. Found. Comput. Sci. 16(6), 1099–1109 (2005)
Bender, M.A., Farach-Colton, M.: The lca problem revisited. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 88–94. Springer, Heidelberg (2000)
Bergroth, L., Hakonen, H., Raita, T.: A survey of longest common subsequence algorithms. In: SPIRE, pp. 39–48 (2000)
Crochemore, M., Landau, G.M., Ziv-Ukelson, M.: A sub-quadratic sequence alignment algorithm for unrestricted cost matrices. In: Symposium of Discrete Algorithms (SODA), pp. 679–688 (2002)
Gabow, H., Bentley, J., Tarjan, R.: Scaling and related techniques for geometry problems. In: STOC, pp. 135–143 (1984)
Hadlock, F.: Minimum detour methods for string or sequence comparison. Congressus Numerantium 61, 263–274 (1988)
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 subsequences. Commun. ACM 20(5), 350–353 (1977)
Jiang, T., Li, M.: On the approximation of shortest common supersequences and longest common subsequences. SIAM Journal of Computing 24(5), 1122–1139 (1995)
Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Problems in Information Transmission 1, 8–17 (1965)
Ma, B., Zhang, K.: On the longest common rigid subsequence problem. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 11–20. Springer, Heidelberg (2005)
Maier, D.: The complexity of some problems on subsequences and supersequences. Journal of the ACM 25(2), 322–336 (1978)
Masek, W.J., Paterson, M.: A faster algorithm computing string edit distances. J. Comput. Syst. Sci. 20(1), 18–31 (1980)
Myers, E.W.: An o(nd) difference algorithm and its variations. Algorithmica 1(2), 251–266 (1986)
Nakatsu, N., Kambayashi, Y., Yajima, S.: A longest common subsequence algorithm suitable for similar text strings. Acta Inf. 18, 171–179 (1982)
Rahman, M.S., Iliopoulos, C.S.: Algorithms for computing variants of the longest common subsequence problem. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 399–408. Springer, Heidelberg (2006)
Tsai, Y.-T.: The constrained longest common subsequence problem. Inf. Process. Lett. 88(4), 173–176 (2003)
van Emde Boas, P.: Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters 6, 80–82 (1977)
Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)
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Rahman, M.S., Iliopoulos, C.S. (2007). A New Efficient Algorithm for Computing the Longest Common Subsequence. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_8
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DOI: https://doi.org/10.1007/978-3-540-72870-2_8
Publisher Name: Springer, Berlin, Heidelberg
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