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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 n 1 ×n 2 table Fill in table Top-left to bottom-right

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longest common subsequence

Longest Common Subsequence

Chris Carpenter

Charles Cobb

Lance Hymel

problem
Problem
  • Given two strings, find the longest subsequences (LCS) shared by both strings.
dynamic programming solution
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
Hirschberg Solution (cont)
  • Recursively scan
    • Still runs in linear time
    • Uses O(min(string1, string2)) memory
real world implementations
Real-World Implementations
  • File comparison
    • Source-code control
      • Insertion, Deletion, Merging
  • Bioinformatics
    • Sequence analysis
    • Comparative genomics
slide7

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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