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Pattern Matching Longest Common Subsequence

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Pattern Matching Longest Common Subsequence. Bill Robertson Zac Livingston John Garvin Bradley Wagner Nick Becker. Agenda. Introduction Pattern Matching String Matching Dynamic Programming Longest Common Subsequence Application 1 Application 2 Application n Future Areas of Interest.

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Pattern Matching Longest Common Subsequence

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  1. Pattern MatchingLongest Common Subsequence Bill Robertson Zac Livingston John Garvin Bradley Wagner Nick Becker

  2. Agenda • Introduction • Pattern Matching • String Matching • Dynamic Programming • Longest Common Subsequence • Application 1 • Application 2 • Application n • Future Areas of Interest

  3. Introduction • Present real-world scenario or interesting application • Grab audience

  4. Pattern Matching • Main objective • Issues to be solved • Basic overview

  5. History • Timeline preferable • History of problems solved by pattern matching

  6. Areas of Application • Application areas • Types of pattern matching

  7. String Matching • History • Overview • Highlight various algorithms with respective applications • Mention LCS problem briefly but need background on dynamic programming in order to fully understand

  8. Dynamic Programming • Overview • Motivation of Area • Key requirements • Alternatives (greedy algorithms)

  9. Longest Common Subsequence • Algorithm intro • Analysis • Correctness? …proofs, etc. • Walk through pseudocode • Step through example

  10. LCS algorithm, step one LCS(X=“All your base”, Y=“are belong to us”)

  11. LCS algorithm, step one Len(Y) “A” + LCS(X=“ll your base”, Y=“re belong to us”) Len(X) LCS(X=“All your base”, Y=“are belong to us”) ‘A’=’a’

  12. LCS algorithm, step one Len(Y) LCS(X=“ll your base”, Y=“are belong to us”) max Len(X) LCS(X=“All your base”, Y=“re belong to us”) LCS(X=“All your base”, Y=“are belong to us”) ‘A’≠’a’

  13. LCS algorithm, step one Len(Y) LCS(“ll your base”, “are belong to us”) “A” + LCS(“ll your base”, “re belong to us”) Len(X) LCS(X=“All your base”, Y=“are belong to us”) LCS(“All your base”, “re belong to us”)

  14. LCS algorithm--building table LCS-Length: len[0,length(X)]  0 len[length(Y),0]  0 for i  1 to length(X): for j  1 to length(Y): if X[i] = Y[j]: len[i,j]  len[i-1,j-1] dir[i,j]  “” else if len[i-1,j]  len[i,j-1]: len[i,j]  len[i-1,j] dir[i,j]  “” else: len[i,j]  len[i,j-1] dir[i,j]  “” 0 0 0 0 0 0 1 1 1 1 0 0 0

  15. LCS algorithm--finding length LCS-find: ... ... ... 0 0 0 0 0 0 1 1 1 1 0 0 0

  16. Asymptotic complexity LCS-length: ... O(?) ... O(?) ... O(?) Total: O(mn)

  17. Asymptotic complexity LCS-find: ... O(?) ... O(?) ... Total: O(m+n)

  18. Correctness • Proof sketch

  19. Applications • Application 1 • Application 2 • Application n • Bioinformatics • Sequence alignment • Secondary protein structure comparison/prediction • DNA microarrays (if we have time during presentation. would be good idea) • Relevance of work and how related to LCS

  20. Future Areas of Interest • Current areas of research and possible directions for work • Future of field and extensions of algorithm • Theoretical lower bound of LCS

  21. Conclusion • Summarize what the audience should have learned

  22. Bibliography

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