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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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.
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.
Cormode G. Sequence Distance Embedding, PhD Thesis, Univ. of Warwick, 2003.
Ding L. and Gao S. Graev Metric Groups and Polishable Subgroups, Adv. Math., Vol. 213, pp. 887–901, 2007.
Ehrenfeucht A. and Haussler D. A New Distance Metric on Strings Computable in Linear Time, Discrete Appl. Math., Vol. 20, pp. 191–203, 1988.
Gotoh O. An Improved Algorithm for Matching Biological Sequences, J. Mol. Biol., Vol. 162, pp. 705–708, 1982.
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.
Monjardet B. On the Comparison of the Spearman and Kendall Metrics Between Linear Orders, Discrete Math., Vol. 192, pp. 281–292, 1998.
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.
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.
Ristad E. and Yianilos P. Learning String Edit Distance, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 20-5, pp. 522–532, 1998.
Author information
Authors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-3-642-30958-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30957-1
Online ISBN: 978-3-642-30958-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)