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In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence is a subsequence of obtained after removal of elements , , and . The relation of one sequence being the subsequence of another is a preorder.

The subsequence should not be confused with substring which can be derived from the above string by deleting substring . The substring is a refinement of the subsequence.

Common subsequence[edit]

Given two sequences X and Y, a sequence Z is said to be a common subsequence of X and Y, if Z is a subsequence of both X and Y. For example, if


then a common subsequence of X and Y could be

This would not be the longest common subsequence, since Z only has length 3, and the common subsequence has length 4. The longest common subsequence of X and Y is .


Subsequences have applications to computer science,[1] especially in the discipline of bioinformatics, where computers are used to compare, analyze, and store DNA, RNA, and protein sequences.

Take two sequences of DNA containing 37 elements, say:


The longest common subsequence of sequences 1 and 2 is:


This can be illustrated by highlighting the 27 elements of the longest common subsequence into the initial sequences:


Another way to show this is to align the two sequences, i.e., to position elements of the longest common subsequence in a same column (indicated by the vertical bar) and to introduce a special character (here, a dash) in one sequence when two elements in the same column differ:

        | || ||| ||||| |  | |  | || |  || | || |  |||

Subsequences are used to determine how similar the two strands of DNA are, using the DNA bases: adenine, guanine, cytosine and thymine.


See also[edit]


  1. ^ In computer science, string is often used as a synonym for sequence, but it is important to note that substring and subsequence are not synonyms. Substrings are consecutive parts of a string, while subsequences need not be. This means that a substring of a string is always a subsequence of the string, but a subsequence of a string is not always a substring of the string, see: Gusfield, Dan (1999) [1997]. Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. USA: Cambridge University Press. p. 4. ISBN 0-521-58519-8. 

This article incorporates material from subsequence on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.