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Suffix Trees

Suffix Trees. ALGGEN: Algorithmics and genetics group Dep. Llenguatges i Sistemes Informàtics Universitat Politècnica de Catalunya. Dr. Xavier Messeguer. http://www.lsi.upc.es/~alggen. Suffix trees. 7: s. s,7. 6: as. s,6. 5: aas. a. a. as,5. as,3. as,3. ba. ba. baas,1.

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Suffix Trees

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  1. Suffix Trees ALGGEN: Algorithmics and genetics group Dep. Llenguatges i Sistemes Informàtics Universitat Politècnica de Catalunya Dr. Xavier Messeguer http://www.lsi.upc.es/~alggen

  2. Suffix trees 7: s s,7 6: as s,6 5: aas a a as,5 as,3 as,3 ba ba baas,1 baas,1 ba ba as,4 as,4 baas,2 baas,2 s,7 s,6 as,5 Given string ababaas: Suffixes: 3: abaas 1: ababaas 4: baas 2: babaas What kind of queries?

  3. Queries on Suffix trees a ba baas,1 ba as,3 baas,2 as,4 s,7 s,6 as,5 • Does the sequence ababaas contain any ocurrence of patterns abab, aab, and ab? ………………………… • Find repeats within the sequence ababaas. …………………………

  4. Insertion algorithm: invariant properties   and the suffix-tree  …... Given the string …………………………...... P1: the leaves of suffixes from have been inserted P2: the string  is the longest string that can be spelt through the tree.

  5. Insertion algorithm: example   ababb...,5 a ababb...,3 ba baababb...,1 ba ababb...,4 baababb...,2 Given the string ababaababb...

  6. Insertion algorithm: example  Given the string ababaababb... 6 7...  ababb...,5 a ababb...,3 ba baababb...,1 ba ababb...,4 baababb...,2

  7. Insertion algorithm: example  Given the string ababaababb... 6 7 8...  ababb...,5 a ababb...,3 ba baababb...,1 ababb...,4 ba baababb...,2

  8. Insertion algorithm: example  Given the string ababaababb... 6 7 8...  ababb...,5 a ababb...,3 ba ababb...,1 b baababb...,1 baababb...,1 ababb...,4 ba b...,6 baababb...,2

  9. Insertion algorithm: example  Given the string ababaababb... 7 8...  ababb...,5 a ababb...,3 ba ababb...,1 b ababb...,4 ba b...,6 baababb...,2

  10. Insertion algorithm: example  Given the string ababaababb... 7 8…  ababb...,5 a ababb...,3 ba ababb...,1 b ababb...,4 ba b...,6 aababb...,2 b baababb...,2 baababb...,2 b...,7

  11. Insertion algorithm: example a ababb...,1 b b...,6 aababb...,2 b b...,7  Given the string ababaababb... 8…  ababb...,5 ababb...,3 ba ababb...,4 ba

  12. Insertion algorithm: improving time  Resume: Given the string ababaababb... 6 7 8...  a ababb...,5 ababb...,3 ba baababb...,1 ba ababb...,4 baababb...,2 we have pointed to the following nodes

  13. Insertion algorithm: improving time  Resume: Given the string ababaababb... 6 7 8...  ababb...,5 a ababb...,3 ba baababb...,1 ababb...,4 ba baababb...,2 we have pointed to the following nodes ba baababb...,1 ba baababb...,2

  14. Suffix tree implementation:suffix-links a ba baas,1 ba as,3 baas,2 as,4 s,7 s,6 as,5 Given sequence ababaas  a

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