Subsequence

A subsequence is a sequence which omits some members, for instance,

<math> Z_{yorick} = < B,C,D,B > </math>

is a subsequence of X where X is

<math> X = < 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.

Given X as above, and

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

A 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 sequence < B,E,E,B > has length 4.

It turns out the longest common subsequence of X and Y would be < 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.

A common problem in subsequences is the Longest-common subsequence problem, where we use dynamic programming to find a maximum length subsequence of two or more sequences.