12_LongestCommonSubsequence - Wednesday Dr Daniel Hughes...

CSC
30155
Wednesday 20/10/10
Dr. Daniel Hughes
[email protected]

Plan for Today
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Review of the LCS Problem 20 minutes
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A Dynamic LCS Algorithm 30 minutes
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LCS questions 40 minutes
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Feedback 10 minutes

CSC
30155
The Longest Common
Subsequence Problem
Dr. Daniel Hughes
[email protected]

Supporting Reading
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Optional reading:
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Cormen et al., Introduction to Algorithms , MIT
Press, 2001, Chapter 15: Longest Common
Subsequence Problem (15.4)

Problem Definition
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A subsequence of a given sequence is the given
sequence with zero or more elements left out.
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Given two sequences: X and Y, we say that a
sequence Z is a common subsequence of X and Y if
Z is a subsequence of both X and Y.
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In the longest common subsequence problem we
are given two sequences X and Y and wish to find a
maximum-length common subsequence (or LCS) of
both X and Y.

Comparing to the Longest
Common Substring Problem
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A string is a sequence of characters. However, a
substring is not synonymous with a subsequence.
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Substrings are consecutive parts of a string, while
subsequences may not be.
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From now on, when using the term LCS, we are
referring to the Longest Common Subsequence
Problem .

Example
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(b) is a substring and a subsequence of (a):
(a)
ba babc
(b)
babc
(c)
aabc
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(c) is a subsequence of (a) but not a substring:
(a)
b a b abc
(b)
babc
(c)
aabc
substring
subsequence

A Key Application:
Genetic Identification (1/2)
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DNA may be viewed as a text written in the alphabet
(A,C,G,T).
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Evolution occurs due to a combination of DNA
mutation and natural selection.
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Mutations include:
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Point mutations : replacement of a character.
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Insertion mutations : addition of some characters.
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Deletion mutations : deletion of some characters.

A Key Application:
Genetic Identification (2/2)
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So if we want to identify the closest genetic
relative of an unknown species, we can:
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Take a sample of its DNA.
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Run LCS against known species.
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The one with the longest LCS is probably the
closest relative.

Why we Need and Efficient
LCS Algorithm
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While computers grow more
powerful, the quantity of
information that we want to
work with also grows.
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The Human Genome has 3
billion base pairs while the
Wheat Genome has 17 billion
base pairs .
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If we want to use LCS to
identify a species of wheat,
our algorithm will have to be
very fast.

The Brute-Force Approach
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Yesterday you worked on a BRUTE-FORCE
algorithm to solve this problem.
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The algorithm took two strings as parameters
X and Y and:
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Enumerated all subsequences in X .
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Checked if each subsequence appears in Y .
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Returned the longest matching subsequence .

Lets Look at the Performance
of some implementations:
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Java implementations will be uploaded at the
end of the week.