is a sequence
which omits some members, for instance,
is a subsequence of X
- , with corresponding index sequence <3,7,9,10>
Given two sequences X
, a sequence G
is said to be a common subsequence
, if G
is a subsequence of both X
Given X as above, and
A common subsequence of X
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.