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An algorithm for approximate tandem repeats

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Combinatorial Pattern Matching (CPM 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 684))

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Abstract

A perfect tandem repeat within a string S is a substring r = r 1,... r2l of S, for which r 1 ... rl = rl+1 ... r2l. An approximate tandem repeat is a substring r = r 1,..., rl′,... rl, for which r 1,..., rl′ and r l′+1, ... rl are similar. In this paper we consider two criterions of similarity: the Hamming distance (k mismatches) and the edit distance (k differences). For a string S of length n and an integer k our algorithm reports all locally optimal approximate repeats, r = ūû, for which the Hamming distance of ū and û is at most k in O(nk log (n/k)) time, or all those for which the edit distance of ū and û is at most k, in O(nk log k log n) time.

Partially supported by the New York State Science and Technology Foundation Center for Advanced Technology.

Partially supported by NSF grant CCR-9110255 and the New York State Science and Technology Foundation Center for Advanced Technology.

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References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.

    Google Scholar 

  2. A. Apostolico (1992) “Fast Parallel Detection of Squares in Strings,” Algorithmica, Vol. 8, pp. 285–319.

    Google Scholar 

  3. S. K. Kannan and E. W. Myers (1993) “An algorithm for locating nonoverlapping regions of maximum alignment score,” these proceedings.

    Google Scholar 

  4. V. I. Levenshtein (1966) “Binary Codes Capable of Correcting Deletions, Insertions and Reversals,” Soviet Phys. Dokl, Vol. 10, pp. 707–710.

    Google Scholar 

  5. G.M. Landau and U. Vishkin (1988) “Fast string matching with k differences,” JCSS, Vol. 37, No. 1, pp. 63–78.

    Google Scholar 

  6. E. Myers (1986) “Incremental Alignment Algorithms and Their Applications,” Tech. Rep. 86-22, Dept. of Computer Science, U. of Arizona, Tucson, AZ 85721.

    Google Scholar 

  7. M.G. Main and R.J. Lorentz (1984) “An O(n log n) algorithm for finding all repetitions in a string,” J. of Algorithms, Vol. 5, pp. 422–432.

    Google Scholar 

  8. M.G. Main and R.J. Lorentz (1985) “Linear time recognition of square free strings,” A. Apostolico and Z. Galil (editors), Combinatorial Algorithms on Words, NATO ASI Series, Series F: Computer and System Sciences, Vol. 12, Springer-Verlag, pp. 272–278.

    Google Scholar 

  9. E. Ukkonen (1983) “On approximate string matching,” Proc. Int. Conf. Found. Comp. Theor., Lecture Notes in Computer Science 158, Springer-Verlag, pp. 487–495.

    Google Scholar 

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Alberto Apostolico Maxime Crochemore Zvi Galil Udi Manber

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© 1993 Springer-Verlag Berlin Heidelberg

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Landau, G.M., Schmidt, J.P. (1993). An algorithm for approximate tandem repeats. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1993. Lecture Notes in Computer Science, vol 684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029801

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  • DOI: https://doi.org/10.1007/BFb0029801

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56764-6

  • Online ISBN: 978-3-540-47732-7

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