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Recuperació de la informació

Recuperació de la informació. Modern Information Retrieval (1999) Ricardo-Baeza Yates and Berthier Ribeiro-Neto Flexible Pattern Matching in Strings (2002) Gonzalo Navarro and Mathieu Raffinot Algorithms on strings (2001) M. Crochemore, C. Hancart and T. Lecroq

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Recuperació de la informació

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  1. Recuperació de la informació • Modern Information Retrieval (1999) • Ricardo-Baeza Yates and Berthier Ribeiro-Neto • Flexible Pattern Matching in Strings (2002) • Gonzalo Navarro and Mathieu Raffinot • Algorithms on strings (2001) • M. Crochemore, C. Hancart and T. Lecroq • http://www-igm.univ-mlv.fr/~lecroq/string/index.html

  2. String Matching String matching: definition of the problem (text,pattern) depends on what we have: text or patterns • Exact matching: • The patterns ---> Data structures for the patterns • 1 pattern ---> The algorithm depends on |p| and || • k patterns ---> The algorithm depends on k, |p| and || • Extensions • Regular Expressions • The text ----> Data structure for the text (suffix tree, ...) • Approximate matching: • Dynamic programming • Sequence alignment (pairwise and multiple) • Sequence assembly: hash algorithm • Probabilistic search: Hidden Markov Models

  3. String matching: one pattern Text : Pattern : How does the matching algorithms made the search? There is a sliding window along the text against which the pattern is compared: At each step the comparison is made and the window is shifted to the right. Which are the facts that differentiate the algorithms? • How the comparison is made. • The length of the shift.

  4. Alg. Cerca exacta d’un patró (text on-line) Algorismes més eficients (Navarro & Raffinot) BNDM : Backward Nondeterministic Dawg Matching | | BOM : Backward Oracle Matching 64 32 16 Horspool 8 BOM BNDM 4 Long. patró 2 w 2 4 8 16 32 64 128 256

  5. Automaton Given a pattern p, we find for an automaton A that verifies the properties: A is acyclic. A recognizes at least the factors of p. A has the fewer states as possible. A has a linear number of transitions according to the length of p. … and at the end of the last century …

  6. Automaton Factor Oracle: properties G T A G T T A G T A G T A G T T A G T A This state recognizes all the factors that ends in the fourth letter that have not been accepted before: GTAT, TAT, AT (note that T had been recognized before). All the factors of the first four letters have been recognized. Given the word G T A T G T A All states are accepting states ==> Recognize all the factors …. and more Hip: recognize all factors of GTA

  7. Automaton Factor Oracle: algorithm ? Algorithm: for i=1 to p do Add those transitions that recognize the new factors that end in letter i;

  8. Automaton Factor Oracle: algorithm T T What happens if the transition is in the automaton?

  9. Automaton Factor Oracle: algorithm T T What happens if transition isn’t in the automaton?

  10. Automaton Factor Oracle and BOM. G T A G T T A G T A This automaton recognizes words that are not factors of GTATGTA like GTGTA => the affirmative answer is not informative, …. but The negative answer ==> the word isn’t a factor! Is the strategy of the BOM algorithm.

  11. Algorithm BOM (Backward Oracle Matching) • How the comparison is made? Text : Pattern : Autòmaton Factor Oracle of the reverse pattern Check if the suffix is a factor of the pattern. • Which is the next position of the window? a • If some letter is not found • If the pattern is found:

  12. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A... • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern: A T G T A T G

  13. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A T G T A T G • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern A T G T A T G

  14. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A T G T A T G A T G T A T G • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern A T G T A T G

  15. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G A T G T A T G A T G T A T G A T G T A T G • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern A T G T A T G

  16. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G ... A T G T A T G A T G T A T G A T G T A T G A T G T A T G • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern A T G T A T G

  17. BOM algorithm G T A G T T A G T A • And the search phase : G T A C T A G A A T G T G T A G A C A T G T A T G G T G ... A T G T A T G A T G T A T G A T G T A T G A T G T A T G A T G T A T G • How the comparison is made? • Given the pattern ATGTATG we construct the automaton of the reverse pattern A T G T A T G

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