Skip to main content

Distances on Strings and Permutations

  • Chapter
Book cover Encyclopedia of Distances
  • 2367 Accesses

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

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. 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.

    Article  Google Scholar 

  2. 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.

    Article  MATH  MathSciNet  Google Scholar 

  3. Cormode G. Sequence Distance Embedding, PhD Thesis, Univ. of Warwick, 2003.

    Google Scholar 

  4. Ding L. and Gao S. Graev Metric Groups and Polishable Subgroups, Adv. Math., Vol. 213, pp. 887–901, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  5. Ehrenfeucht A. and Haussler D. A New Distance Metric on Strings Computable in Linear Time, Discrete Appl. Math., Vol. 20, pp. 191–203, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gotoh O. An Improved Algorithm for Matching Biological Sequences, J. Mol. Biol., Vol. 162, pp. 705–708, 1982.

    Article  Google Scholar 

  7. 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.

    Article  Google Scholar 

  8. Monjardet B. On the Comparison of the Spearman and Kendall Metrics Between Linear Orders, Discrete Math., Vol. 192, pp. 281–292, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  9. 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.

    Article  Google Scholar 

  10. 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.

    MathSciNet  Google Scholar 

  11. Ristad E. and Yianilos P. Learning String Edit Distance, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 20-5, pp. 522–532, 1998.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Deza, M.M., Deza, E. (2013). Distances on Strings and Permutations. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30958-8_11

Download citation

Publish with us

Policies and ethics