Advertisement

Distances on Strings and Permutations

  • Michel Marie Deza
  • Elena Deza

Abstract

An alphabet is a finite set \(\mathcal{A}\), \(|\mathcal{A}| \ge 2\), elements of which are called characters (or symbols). A string (or word) is a sequence of characters over a given finite alphabet \(\mathcal{A}\). The set of all finite strings over the alphabet \(\mathcal{A}\) is denoted by \(W(\mathcal{A})\). Examples of real world applications, using distances and similarities of string pairs, are Speech Recognition, Bioinformatics, Information Retrieval, Machine Translation, Lexicography, Dialectology.

Keywords

Edit Distance Kolmogorov Complexity Editing Operation Minimal Total Cost Longe Common Subsequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [BGLVZ98]
    Bennet C.H., Gács P., Li M., Vitánai P.M.B. and Zurek W. Information Distance, IEEE Trans. Inf. Theory, Vol. 44-4, pp. 1407–1423, 1998. CrossRefGoogle Scholar
  2. [BCFS97]
    Block H.W., Chhetry D., Fang Z. and Sampson A.R. Metrics on Permutations Useful for Positive Dependence, J. Stat. Plan. Inference, Vol. 62, pp. 219–234, 1997. zbMATHCrossRefMathSciNetGoogle Scholar
  3. [Corm03]
    Cormode G. Sequence Distance Embedding, PhD Thesis, Univ. of Warwick, 2003. Google Scholar
  4. [DiGa07]
    Ding L. and Gao S. Graev Metric Groups and Polishable Subgroups, Adv. Math., Vol. 213, pp. 887–901, 2007. zbMATHCrossRefMathSciNetGoogle Scholar
  5. [EhHa88]
    Ehrenfeucht A. and Haussler D. A New Distance Metric on Strings Computable in Linear Time, Discrete Appl. Math., Vol. 20, pp. 191–203, 1988. zbMATHCrossRefMathSciNetGoogle Scholar
  6. [Goto82]
    Gotoh O. An Improved Algorithm for Matching Biological Sequences, J. Mol. Biol., Vol. 162, pp. 705–708, 1982. CrossRefGoogle Scholar
  7. [LCLMV04]
    Li M., Chen X., Li X., Ma B. and Vitányi P. The Similarity Metric, IEEE Trans. Inf. Theory, Vol. 50-12, pp. 3250–3264, 2004. CrossRefGoogle Scholar
  8. [Monj98]
    Monjardet B. On the Comparison of the Spearman and Kendall Metrics Between Linear Orders, Discrete Math., Vol. 192, pp. 281–292, 1998. zbMATHCrossRefMathSciNetGoogle Scholar
  9. [NeWu70]
    Needleman S.B. and Wunsh S.D. A General Method Applicable to the Search of the Similarities in the Amino Acids Sequences of Two Proteins, J. Mol. Biol., Vol. 48, pp. 443–453, 1970. CrossRefGoogle Scholar
  10. [Page65]
    Page E.S. On Monte-Carlo Methods in Congestion Problem. 1. Searching for an Optimum in Discrete Situations, J. Oper. Res., Vol. 13-2, pp. 291–299, 1965. MathSciNetGoogle Scholar
  11. [RiYi98]
    Ristad E. and Yianilos P. Learning String Edit Distance, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 20-5, pp. 522–532, 1998. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michel Marie Deza
    • 1
  • Elena Deza
    • 2
  1. 1.École Normale SupérieureParisFrance
  2. 2.Moscow State Pedagogical UniversityMoscowRussia

Personalised recommendations