Subsequence

In mathematics, a subsequence of a sequence X is a sequence formed from X by deleting some of the elements without disturbing the relative positions of the remaining elements. For example,

<math> < B,C,D,B > <math>

is a subsequence of

<math> < A,C,B,D,E,G,C,E,D,B,G > <math>,

with corresponding index sequence <3,7,9,10>.

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

<math> X = < A,C,B,D,E,G,C,E,D,B,G > <math> and

<math> Y = < B,E,G,C,F,E,U,B,K > <math>

then common subsequence of X and Y could be

<math> G = < B,E,E > <math>

This would not be the longest common subsequence, since G only has length 3, and the common subsequence < B,E,E,B > has length 4. The longest common subsequence of X and Y is < B,E,G,C,E,B >

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
ORG₂ = CGTTCGGCTATCGTACGTTCTATTCTATGATTTCTAA

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

See also: subsequential limits, limsup, liminf