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String Distances and Uniformities

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5495))

Abstract

The Levenstein or edit distance was developed as a metric for calculating distances between character strings. We are looking at weighting the different edit operations (insertion, deletion, substitution) to obtain different types of classifications of sets of strings. As a more general and less constrained approach we introduce topological notions and in particular uniformities.

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References

  1. Levenshtein, V.I.: Binary codes capable of correcting deletions, insertions, and reversals. Doklady Akademii Nauk SSSR 163(4), 845–848 (1965)

    MathSciNet  MATH  Google Scholar 

  2. Kelley, J.L.: General Topology. D. Van Nostrand (1955)

    Google Scholar 

  3. James, I.M.: Topologies and Uniformities. Springer, Heidelberg (1999)

    Book  Google Scholar 

  4. Howes, N.R.: Modern Analysis and Topology. Springer, Heidelberg (1995)

    Book  MATH  Google Scholar 

  5. Willard, S.: General Topology. Addison-Wesley, Reading (1970)

    MATH  Google Scholar 

  6. Wagner, R., Fisher, M.: The string-to-string correction problem. Journal of the ACM 21, 168–178 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Crochemore, M., Hancart, C., Lecroq, T.: Algorithms on Strings. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  8. Gusfield, D.: Algorithms on Strings, Trees, and Sequences - Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  9. Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Cambridge University Press, Cambridge (1998)

    Book  MATH  Google Scholar 

  10. Amengual, J.C., Sanchis, A., Vidal, E., Benedí, J.M.: Language simplification through error-correcting and grammatical inference techniques. Machine Learning Journal 44(1-2), 143–159 (2001)

    Article  MATH  Google Scholar 

  11. Dupont, P.E., Amengual, J.-C.: Smoothing probabilistic automata: An error-correcting approach. In: Oliveira, A.L. (ed.) ICGI 2000. LNCS (LNAI), vol. 1891, pp. 51–64. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  12. Navarro, G.: A guided tour to approximate string matching. ACM Computing Surveys 33(1), 31–88 (2001)

    Article  Google Scholar 

  13. Chávez, E., Navarro, G., Baeza-Yates, R.A., Marroquín, J.L.: Searching in metric spaces. ACM Computing Surveys 33(3), 273–321 (2001)

    Article  Google Scholar 

  14. Becerra-Bonache, L., de la Higuera, C., Janodet, J.C., Tantini, F.: Learning balls of strings from edit corrections. Journal of Machine Learning Research 9, 1823–1852 (2008)

    MathSciNet  MATH  Google Scholar 

  15. Delhay, A., Miclet, L.: Analogical equations in sequences: Definition and resolution. In: Paliouras, G., Sakakibara, Y. (eds.) ICGI 2004. LNCS (LNAI), vol. 3264, pp. 127–138. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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© 2009 Springer-Verlag Berlin Heidelberg

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Pearson, D.W., Janodet, JC. (2009). String Distances and Uniformities. In: Kolehmainen, M., Toivanen, P., Beliczynski, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2009. Lecture Notes in Computer Science, vol 5495. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04921-7_34

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  • DOI: https://doi.org/10.1007/978-3-642-04921-7_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04920-0

  • Online ISBN: 978-3-642-04921-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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