1 / 34

Tècniques i Eines Bioinformàtiques

Tècniques i Eines Bioinformàtiques. Bioinformatics, Sequence and Genome Analysis David W. Mount Flexible Pattern Matching in Strings (2002) Gonzalo Navarro and Mathieu Raffinot Algorithms on strings (2001) M. Crochemore, C. Hancart and T. Lecroq

doane
Download Presentation

Tècniques i Eines Bioinformàtiques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Tècniques i Eines Bioinformàtiques • Bioinformatics, Sequence and Genome Analysis • David W. Mount • 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. Algorismes i estructures eficients de cerca 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 || • The text ----> Data structure for the text (suffix tree, ...)

  3. Exact string matching: one pattern How does the string algorithms made the search? For instance, given the sequence CTACTACTACGTCTATACTGATCGTAGCTACTACATGC search for the pattern ACTGA. and for the pattern TACTACGGTATGACTAA

  4. Exact string matching: Brute force algorithm A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A Example: Given the pattern ATGTA, the search is G T A C T A G A G G A C G T A T G T A C T G ...

  5. Exact string matching: Brute force algorithm • How the comparison is made? From left to right: prefix • Which is the next position of the window? The window is shifted only one cell Text : Pattern : Text : Pattern :

  6. Exact 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.

  7. 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

  8. Horspool algorithm • How the comparison is made? Text : Pattern : Sufix search • Which is the next position of the window? a Text : Pattern : Shift until the next ocurrence of “a” in the pattern: a a a a a a We need a preprocessing phase to construct the shift table.

  9. Horspool algorithm : example Given the pattern ATGTA A C G T • The shift table is:

  10. Horspool algorithm : example Given the pattern ATGTA A 4 C G T • The shift table is:

  11. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G T • The shift table is:

  12. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T • The shift table is:

  13. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is:

  14. Horspool algorithm : example Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A

  15. Exemple algorisme de Horspool Given the pattern ATGTA A 4 C 5 G 2 T 1 • The shift table is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A A T G T A

  16. Qüestions sobre l’algorisme de Horspool A 4 C 5 G 2 T 1 Given the pattern ATGTA, the shift table is Given a random text over an equally likely probability distribution (EPD): 1.- Determine the expected shift of the window. And, if the PD is not equally likely? 2.- Determine the expected number of shifts assuming a text of length n. 3.- Determine the expected number of comparisons in the suffix search phase

  17. 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

  18. BNDM algorithm • How the comparison is made? Search for suffixes of T that are factors of x Text : Pattern : That is denoted as D2 = 1 0 0 0 1 0 0 Once the next character x is read D3 = D2<<1 & B(x) B(x): mask of x in the pattern P. For instance, if B(x) = ( 0 0 1 1 0 0 0) D = (0 0 0 1 0 0 0) & (0 0 1 1 0 0 0 ) = (0 0 0 1 0 0 0 ) • Which is the next position of the window? Depends on the value of the leftmost bit of D

  19. BNDM algorithm: exaple B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • The mask of characters is: • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A A T G T A A T G T A Given the pattern ATGTA D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 0 0 0 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 0 0 1 0 0 ) D2 = ( 0 1 0 0 0 ) & ( 0 0 1 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 1 0 0 0 1 ) D2 = ( 0 0 0 1 0 ) & ( 0 1 0 1 0 ) = ( 0 0 0 1 0 ) D3 = ( 0 0 1 0 0 ) & ( 0 0 1 0 0) = ( 0 0 1 0 0 ) D4 = ( 0 1 0 0 0 ) & ( 0 0 0 0 0) = ( 0 0 0 0 0 )

  20. Exemple algorisme BNDM B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • Given the pattern ATGTA • The mask of characters is : • The searching phase: G T A C T A G A G G A C G T A T G T A C T G ... A T G T A A T G T A D1 = ( 1 0 0 0 1 ) D2 = ( 0 0 0 1 0 ) & ( 0 1 0 1 0 ) = ( 0 0 0 1 0 ) D3 = ( 0 0 1 0 0 ) & ( 0 0 1 0 0 ) = ( 0 0 1 0 0 ) D4 = ( 0 1 0 0 0 ) & ( 0 1 0 1 0 ) = ( 0 1 0 0 0 ) D5 = ( 1 0 0 0 0 ) & ( 1 0 0 0 1 ) = ( 1 0 0 0 0 ) D6 = ( 0 0 0 0 0 ) & ( * * * * * ) = ( 0 0 0 0 0 ) Trobat!

  21. Exemple algorisme BNDM B(A) = ( 1 0 0 0 1 ) B(C) = ( 0 0 0 0 0 ) B(G) = ( 0 0 1 0 0 ) B(T) = ( 0 1 0 1 0 ) • The mask of characters is : • The searching phase: G T A C T A G A A T A C G T A T G T A C T G ... A T G T A A T G T A A T G T A Given the pattern ATGTA How the shif is determined? D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 0 0 0 0 0 ) = ( 0 0 0 0 0 ) D1 = ( 0 1 0 1 0 ) D2 = ( 1 0 1 0 0 ) & ( 1 0 0 0 1 ) = ( 1 0 0 0 0 ) D3 = ( 0 0 0 0 0 ) & ( 1 0 0 0 1 ) = ( 0 0 0 0 0 )

  22. 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

  23. Autòmata Factor Oracle: propietats G T A G T T A G T A G T A G T T A G T A L’estat reconeix tots els factors que acaben a la quarta lletra T que no eren reconeguts: GTAT, TAT, AT perque T ja ho era. Reconeix tots els factors de de les primeres 4 lletres Factor Oracle del mot G T A T G T A Tots els estats són finals ==> Reconeix tots els factors …. i més Hip: reconeix tots factors de GTA

  24. Autòmata Factor Oracle: algorisme ? Algorisme: per a i=1 fins p fer Afegir transicions que reconeguin factors acabats a i;

  25. Autòmata Factor Oracle: algorisme T T Que passa si el següent caràcter existeix?

  26. Autòmata Factor Oracle: algorisme T T Que passa si el següent caràcter no existeix?

  27. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A i reconeix mots que no són factors com GTGTA. Però, si no el reconeix ==> no és factor! Es l’estratègia de l’algorisme BOM

  28. Algorisme BOM (Backward Oracle Matching) • Com fa la comparació? Text : Patró : Autòmata: Factor Oracle Comproba si el sufix és factor del patró • Com es determina la següent posició de la finestra? a • Si la a no s’ha trobat a • Si arriben a l’estat final de l’autòmat amb la a

  29. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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... • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

  30. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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 • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

  31. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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 • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

  32. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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 • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

  33. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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 • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

  34. Autòmata Factor Oracle: exemple d’algorisme G T A G T T A G T A • I la cerca sobre el text : 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 • Com fa la comparació? • Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG A T G T A T G

More Related