Abstract
Two equal length strings s and s′, over alphabets Σ s and Σ s′, parameterize match if there exists a bijection π:Σ s → Σ s′, such that π (s)=s′, where π (s) is the renaming of each character of s via π. Approximate parameterized matching is the problem of finding for a pattern p, at each location of a text string t, a bijection π that maximizes the number of characters that are mapped from p to the appropriate |p|-length substring of t.
Our main result is an O(nk 1.5+mklog m) time algorithm for this problem where m=|p| and n = |t|.
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References
Church, K.W., Amir, A., Dar, E.: Separable attributes: a technique for solving the submatrices character count problem. In: Proc. 13th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 400–401 (2002)
Amir, A., Aumann, Y., Cole, R., Lewenstein, M., Porat, E.: Function matching: Algorithms, applications and a lower bound. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 929–942. Springer, Heidelberg (2003)
Amir, A., Benson, G., Farach, M.: An alphabet independent approach to two dimensional pattern matching. SIAM J. Comp. 23(2), 313–323 (1994)
Amir, A., Farach, M., Muthukrishnan, S.: Alphabet dependence in parameterized matching. Information Processing Letters 49, 111–115 (1994)
Apostolico, A., Erdös, P., Lewenstein, M.: Parameterized matching with mismatches (manuscript)
Baker, B.S.: A theory of parameterized pattern matching: algorithms and applications. In: Proc. 25th Annual ACM Symposium on the Theory of Computation, pp. 71–80 (1993)
Baker, B.S.: Parameterized string pattern matching. J. Comput. Systems Sci. 52 (1996)
Baker, B.S.: Parameterized duplication in strings: Algorithms and an application to software maintenance. SIAM J. on Computing 26 (1997)
Baker, B.S.: Parameterized diff. In: Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 854–855 (1999)
Cole, R., Hariharan, R.: Faster suffix tree construction with missing suffix links. In: Proc. 32nd ACM STOC, pp. 407–415 (2000)
Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their use in improved network optimizations algorithms. J. of the ACM 34(3), 596–615 (1987)
Gabow, H.N.: Scaling algorithms for network problems. J. of Computer and System Sciences 31, 148–168 (1985)
Gabow, H.N., Tarjan, R.E.: Faster scaling algorithms for network problems. SIAM J. on Computing 18, 1013–1036 (1989)
Galil, Z., Giancarlo, R.: Improved string matching with k mismatches. SIGACT News 17(4), 52–54 (1986)
Kosaraju, S.R.: Faster algorithms for the construction of parameterized suffix trees. In: Proc. 36th IEEE FOCS, pp. 631–637 (1995)
Landau, G.M., Vishkin, U.: Introducing efficient parallelism into approximate string matching. In: Proc. 18th ACM Symposium on Theory of Computing, pp. 220–230 (1986)
Landau, G.M., Vishkin, U.: Fast string matching with k differences. J. Comput. Syst. Sci. 37 (1988)
Levenshtein, V.I.: Binary codes capable of correcting, deletions, insertions and reversals. Soviet Phys. Dokl. 10, 707–710 (1966)
Mehtre, B.M., Babu, G.P., Kankanhalli, M.S.: Color indexing for efficient image retrieval. Multimedia Tools and Applications 1(4) (1995)
Sung, W.K., Kao, M.Y., Lam, T.W., Ting, H.F.: A decomposition theorem for maximum weight bipartite matching. SIAM J. on Computing 31(1), 18–26 (2001)
Swain, M., Ballard, D.: Color indexing. International Journal of Computer Vision 7(1), 11–32 (1991)
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Hazay, C., Lewenstein, M., Sokol, D. (2004). Approximate Parameterized Matching. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_38
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DOI: https://doi.org/10.1007/978-3-540-30140-0_38
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