Longest Common Subsequence

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# Longest Common Subsequence - PowerPoint PPT Presentation

Longest Common Subsequence. Chris Carpenter Charles Cobb Lance Hymel. Problem. Given two strings, find the longest subsequences (LCS) shared by both strings. Dynamic Programming Solution. Construct a n 1 ×n 2 table Fill in table Top-left to bottom-right

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## PowerPoint Slideshow about ' Longest Common Subsequence' - conlan

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### Longest Common Subsequence

Chris Carpenter

Charles Cobb

Lance Hymel

Problem
• Given two strings, find the longest subsequences (LCS) shared by both strings.
Dynamic Programming Solution
• Construct a n1×n2 table
• Fill in table
• Top-left to bottom-right
• Increment whenever match is found
• Bottom-right number is length of LCS
• Scan table bottom-right to top-left
• Locations where number decreases diagonally are included in LCS
Hirschberg Solution (cont)
• Recursively scan
• Still runs in linear time
• Uses O(min(string1, string2)) memory
Real-World Implementations
• File comparison
• Source-code control
• Insertion, Deletion, Merging
• Bioinformatics
• Sequence analysis
• Comparative genomics

Bioinformatics

• Sequence analysis is the process of subjecting a DNA, RNA or peptide sequence to any of a wide range of analytical methods
• The analytical methods include :
• Sequence Alignment
• Methodical biological database searches