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Longest Common Subsequence

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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Longest Common Subsequence

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  1. Longest Common Subsequence Chris Carpenter Charles Cobb Lance Hymel

  2. Problem • Given two strings, find the longest subsequences (LCS) shared by both strings.

  3. 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

  4. Hirschberg Solution

  5. Hirschberg Solution (cont) • Recursively scan • Still runs in linear time • Uses O(min(string1, string2)) memory

  6. Real-World Implementations • File comparison • Source-code control • Insertion, Deletion, Merging • Bioinformatics • Sequence analysis • Comparative genomics

  7. 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

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