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Common Subsequence

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• Common subsequence
  • Common subsequence:

    C is a common subsequence of A and B iff: C is a subsequence of A           C is a subsequence of B

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• Examples: common subsequence
  • Example:

    String 1: X = ABCABCABC String 2: Y = BABACBAB Common subsequence 1: AAA X = ABCABCABC Y = BABACBAB Common subsequence 2: ABAA X = ABCABCABC Y = BABACBAB Common subsequence 3: ABABA X = ABCABCABC Y = BABACBAB Common subsequence 4: ABABAB X = ABCABCABC Y = BABACBAB

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• Longest Common Subsequence (LCS)
  • The LCS problem:

    Given 2 strings X and Y Find the longest common substring in X and Y

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• Applications
  • Gene similarity:

    When 2 gene sequences (strings) have a large (long) common subsequence, the genes are more alike The LCS algorithm will allow you to discover genes that are similar

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  • Text similarity testing:

    Given 2 text documents The longer their common substring, the better the match between the 2 text documents. The LCS algorithm will allow you to discover plagerized documents