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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 http://www-igm.univ-mlv.fr/~lecroq/string/index.html. Algorismes de:

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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 • http://www-igm.univ-mlv.fr/~lecroq/string/index.html Algorismes de: Cerca de patrons (exacta i aproximada) (String matching i Pattern matching) Indexació de textos: Suffix trees, Suffix arrays

  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. Exact string matching: one pattern (text on-line) Experimental efficiency (Navarro & Raffinot) BNDM : Backward Nondeterministic Dawg Matching | | BOM : Backward Oracle Matching 64 32 16 Horspool 8 BOM BNDM 4 Long. pattern 2 w 2 4 8 16 32 64 128 256

  4. Multiple string matching 8 | | (5 strings) Wu-Manber 4 SBOM lmin 2 5 10 15 20 25 30 35 40 45 8 Wu-Manber (10 strings) (100 strings) 4 SBOM 8 Wu-Manber Ad AC 2 SBOM 4 5 10 15 20 25 30 35 40 45 Ad AC 2 5 10 15 20 25 30 35 40 45 Wu-Manber 8 (1000 strings) SBOM 4 Ad AC 2 5 10 15 20 25 30 35 40 45

  5. Trie Construct the trie of GTATGTA,GTAT,TAATA,GTGTA

  6. Trie G T A T A T G Construct the trie of GTATGTA,GTAT,TAATA,GTGTA

  7. Trie G T A T A T G Construct the trie of GTATGTA,GTAT,TAATA,GTGTA

  8. Trie Construct the trie of GTATGTA,GTAT,TAATA,GTGTA G T A T A T G T A A T A A

  9. Trie Construct the trie of GTATGTA,GTAT,TAATA,GTGTA G T A T A T G G T A T A A T A Which is the cost?

  10. Set Horspool algorithm • How the comparison is made? By suffixes Text : Patterns: Trie of all inverse patterns • Which is the next position of the window? a We shift until a is aligned with the first a in the trie not longer than lmin,or lmin

  11. Set Horspool algorithm 1. Construct the trie of GTATGTA, GTAT, TAATA i GTGTA G T A T A T G G T A T A A T A Search for ATGTATG,TATG,ATAAT,ATGTG 2. Determine lmin=

  12. Set Horspool algorithm 1. Construct the trie of GTATGTA, GTAT, TAATA i GTGTA G T A T A T G G T A T A A T A A 1 C 4 (lmin) G T 3. Determine the shift table Search for ATGTATG,TATG,ATAAT,ATGTG 2. Determine lmin=4

  13. Set Horspool algorithm 1. Construct the trie of GTATGTA, GTAT, TAATA i GTGTA G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 3. Determine the shift table Search for ATGTATG,TATG,ATAAT,ATGTG 2. Determine lmin=4

  14. Set Horspool algorithm 1. Construct the trie of GTATGTA, GTAT, TAATA i GTGTA G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 3. Determine the shift table Search for ATGTATG,TATG,ATAAT,ATGTG 2. Determine lmin=4 4. Find the patterns

  15. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  16. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  17. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  18. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  19. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  20. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA…

  21. Set Horspool algorithm G T A T A T G G T A T A A T A A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA… …

  22. Set Horspool algorithm G T A T A T G G T A T A A T A As more patterns we search for, shorter shifts we do! A 1 C 4 (lmin) G 2 T 1 Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACA… … Is the expected length of the shifts related with the number of patterns?

  23. Set Horspool algorithm Wu-Manber algorithm 1 símbol 2 símbols AA 1 AC 3 (LMIN-L+1) AG AT CA CC CG … A 1 C 4 (lmin) G 2 T 1 How the length of shifts can be increased? By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG

  24. Set Horspool algorithm Wu-Manber algorithm 1 símbol 2 símbols AA 1 AC 3 (LMIN-L+1) AG AT CA CC CG … A 1 C 4 (lmin) G 2 T 1 How the length of shifts can be increased? By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG 3

  25. Set Horspool algorithm Wu-Manber algorithm 1 símbol 2 símbols AA 1 AC 3 (LMIN-L+1) AG AT CA CC CG … A 1 C 4 (lmin) G 2 T 1 How the length of shifts can be increased? By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG 3 1

  26. Set Horspool algorithm Wu-Manber algorithm 1 símbol 2 símbols AA 1 AC 3 (LMIN-L+1) AG AT 1 CA CC CG … A 1 C 4 (lmin) G 2 T 1 How the length of shifts can be increased? By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG 3 3 3 3

  27. Set Horspool algorithm Wu-Manber algorithm 1 símbol 2 símbols AA 1 AC 3 (LMIN-L+1) AG 3 AT 1 CA 3 CC 3 CG 3 … AA 1 AT 1 GT 1 TA 2 TG 2 A 1 C 4 (lmin) G 2 T 1 How the length of shifts can be increased? By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG

  28. Wu-Manber algorithm G T A T A T G G T A AA 1 AT 1 GT 1 TA 2 TG 2 T A A T A A Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACATAATA

  29. Wu-Manber algorithm G T A T A T G G T A AA 1 AT 1 GT 1 TA 2 TG 2 T A A T A A Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACATAATA

  30. Wu-Manber algorithm G T A T A T G G T A AA 1 AT 1 GT 1 TA 2 TG 2 T A A T A A Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACATAATA

  31. Wu-Manber algorithm G T A T A T G G T A AA 1 AT 1 GT 1 TA 2 TG 2 T A A T A A Search for ATGTATG,TATG,ATAAT,ATGTG text: ACATGCTATGTGACATAATA But given k patterns, how many symbols we should take ? … log|Σ| 2*lmin*k

  32. Multiple string matching 8 | | (5 strings) Wu-Manber 4 SBOM lmin 2 5 10 15 20 25 30 35 40 45 8 Wu-Manber (10 strings) (100 strings) 4 SBOM 8 Wu-Manber Ad AC 2 SBOM 4 5 10 15 20 25 30 35 40 45 Ad AC 2 5 10 15 20 25 30 35 40 45 Wu-Manber 8 (1000 strings) SBOM 4 Ad AC 2 5 10 15 20 25 30 35 40 45

  33. BOM algorithm (Backward Oracle Matching) • How the comparison is made? Text : Pattern : Automata: Factor Oracle Check if the suffix is a factor of any pattern • Which is the next position of the window? The position determined by the last character of the text with a transition in the automata

  34. Factor Oracle of k strings A How can we build the Factor Oracle of GTATGTA, GTAA, TAATA i GTGTA ? G T A G T A T G T 1,4 A A T A 3 2

  35. Factor Oracle of k strings T Given the Factor Oracle of GTATGTA G

  36. Factor Oracle of k strings A Given the Factor Oracle of GTATGTA G T T

  37. Factor Oracle of k strings T Given the Factor Oracle of GTATGTA G T A T A

  38. Factor Oracle of k strings G Given the Factor Oracle of GTATGTA G T A T T A

  39. Factor Oracle of k strings T Given the Factor Oracle of GTATGTA G T A G T G T A

  40. Factor Oracle of k strings A 1 Given the Factor Oracle of GTATGTA G T A G T T G T A … we insert GTAA

  41. Factor Oracle of k strings A 2 …inserting GTAA G T A G T A T G T 1 A

  42. Factor Oracle of k strings Given the AFO of GTATGTA and GTAA G T A G T A T G T 1 A A 2 … we insert TAATA

  43. Factor Oracle of k strings A T A 3 … inserting TAATA G T A G T A T G T 1 A A 2

  44. Factor Oracle of k strings A Given the AFO of GTATGTA, GTAA and TAATA G T A G T A T G T 1 A A T A 3 2 …we insert GTGTA

  45. Factor Oracle of k strings A …inserting GTGTA G T A G T A T G T 1 A A T A 3 2

  46. Factor Oracle of k strings A G T A G T A T G T 1,4 A A T A 3 2 This is the Automata Factor Oracle of GTATGTA, GTAA, TAATA and GTGTA

  47. SBOM algorithm • How the comparison is made? Text : Pattern : Automata: Factor Oracle (Inverse patterns of length lmin) Check if the suffix is a factor of any pattern • Which is the next position of the window? The position determined by the last character of the text with a transition in the automata

  48. SBOM algorithm: example A We search for the patterns ATGTATG, TAATG,TAATAAT i AATGTG … the we build the Automata Factor Oracle of GTATG, GTAAT, TAATA and GTGTA of length lmin=5 G T A G T T A 1 4 A G T A A T 2 3

  49. SBOM algorithm: example Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A G T T A 1 4 A G T A A A T 2 3 text: ACATGCTAGCTATAATAATGTATG

  50. SBOM algorithm: example Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A G T T A 1 4 A G T A A A T 2 3 text: ACATGCTAGCTATAATAATGTATG

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