# Subsequence

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 $\langle A,B,D\rangle$ is a subsequence of $\langle A,B,C,D,E,F\rangle$ . They should not be confused with substring which is a refinement of subsequence.

## Common subsequence

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

$X=\langle A,C,B,D,E,G,C,E,D,B,G\rangle$ and
$Y=\langle B,E,G,C,F,E,U,B,K\rangle$ then a common subsequence of X and Y could be

$G=\langle B,E,E\rangle .$ This would not be the longest common subsequence, since G only has length 3, and the common subsequence $\langle B,E,E,B\rangle$ has length 4. The longest common subsequence of X and Y is $\langle B,E,G,C,E,B\rangle$ .

## Applications

Subsequences have applications to computer science, especially in the discipline of bioinformatics, where computers are used to compare, analyze, and store DNA strands.

Take two strands of DNA, say:

ORG1 = ACGGTGTCGTGCTATGCTGATGCTGACTTATATGCTA
and
ORG2 = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA.

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