1. Tècniques i Eines Bioinformàtiques
23/04/2019
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

2. Algorismes i estructures eficients de cerca
23/04/2019
String matching: definition of the problem (text,pattern)
Exact matching:
depends on what we have: text or patterns
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
23/04/2019
How does the string algorithms made the search?
For instance, given the sequence
CTACTACTACGTCTATACTGATCGTAGCTACTACATGC
search for the pattern ACTGA.
and for the pattern TACTACGGTATGACTAA
As you have seen this morning ....

4. Exact string matching: Brute force algorithm
23/04/2019
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 ...
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
As you have seen this morning ....

5. Exact string matching: Brute force algorithm
23/04/2019
Which is the next position of the window?
How the comparison is made?
Text :
Pattern :
From left to right: prefix
Text :
Pattern :
As you have seen this morning ....
The window is shifted only one cell

6. Exact string matching: one pattern
23/04/2019
How does the matching algorithms made the search?
There is a sliding window along the text
against which the pattern is compared:
Pattern :
Text :
At each step the comparison is made and
the window is shifted to the right.
As you have seen this morning ....
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)
23/04/2019
Experimental efficiency (Navarro & Raffinot)
BNDM : Backward Nondeterministic Dawg Matching
| |
BOM : Backward Oracle Matching 64 32 16
Horspool 8
BOM
BNDM 4 2
Long. pattern w

8. Horspool algorithm How the comparison is made?
23/04/2019
Which is the next position of the window?
How the comparison is made?
Text :
Pattern :
Sufix search
Pattern :
Text : a
As you have seen this morning ....
Shift until the next ocurrence of “a” in the pattern: a
We need a preprocessing phase to construct the shift table.

9. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is: A C G T
As you have seen this morning ....

10. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4 C G T
As you have seen this morning ....

11. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4
C 5 G T
As you have seen this morning ....

12. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4
C 5
G 2 T
As you have seen this morning ....

13. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4
C 5
G 2
T 1
As you have seen this morning ....

14. Horspool algorithm : example
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4
C 5
G 2
T 1
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
As you have seen this morning ....

15. Exemple algorisme de Horspool
23/04/2019
Given the pattern ATGTA
The shift table is:
A 4
C 5
G 2
T 1
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
As you have seen this morning ....
A T G T A

16. Qüestions sobre l’algorisme de Horspool
23/04/2019
Given the pattern ATGTA, the shift table is
A 4
C 5
G 2
T 1
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.
As you have seen this morning ....
3.- Determine the expected number of comparisons
in the suffix search phase

17. Exact string matching: one pattern (text on-line)
23/04/2019
Experimental efficiency (Navarro & Raffinot)
BNDM : Backward Nondeterministic Dawg Matching
| |
BOM : Backward Oracle Matching 64 32 16
Horspool 8
BOM
BNDM 4 2
Long. pattern w

18. BNDM algorithm How the comparison is made?
23/04/2019
Which is the next position of the window ?
How the comparison is made?
Text :
Pattern :
Search for suffixes of T that are factors of
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) = ( )
D = ( ) & ( ) = ( ) x
That is denoted as
D2 =
Depends on the value of the leftmost bit of D
As you have seen this morning ....

19. BNDM algorithm: exaple
23/04/2019
Given the pattern ATGTA
The mask of characters is:
B(A) = ( )
B(C) = ( )
B(G) = ( )
B(T) = ( )
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
D1 = ( )
D2 = ( ) & ( ) = ( )
D1 = ( )
D2 = ( ) & ( ) = ( )
As you have seen this morning ....
D1 = ( )
D2 = ( ) & ( ) = ( )
D3 = ( ) & ( ) = ( )
D4 = ( ) & ( ) = ( )

20. Exemple algorisme BNDM
23/04/2019
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
B(A) = ( )
B(C) = ( )
B(G) = ( )
B(T) = ( )
D1 = ( )
A T G T A
D2 = ( ) & ( ) = ( )
D3 = ( ) & ( ) = ( )
D4 = ( ) & ( ) = ( )
D5 = ( ) & ( ) = ( )
As you have seen this morning ....
D6 = ( ) & ( * * * * * ) = ( )
Trobat!

21. Exemple algorisme BNDM
23/04/2019
Given the pattern ATGTA
The mask of characters is :
B(A) = ( )
B(C) = ( )
B(G) = ( )
B(T) = ( )
How the shif is determined?
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
D1 = ( )
D2 = ( ) & ( ) = ( )
As you have seen this morning ....
D1 = ( )
D2 = ( ) & ( ) = ( )
D3 = ( ) & ( ) = ( )

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 2
Long. patró w

23. Autòmata Factor Oracle: propietats
23/04/2019
Factor Oracle del mot G T A T G T A G A T
Tots els estats són finals ==> Reconeix tots els factors …. i més G A T
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.
As you have seen this morning ....
Hip: reconeix tots factors
de GTA
Reconeix tots els factors de de les primeres 4 lletres

24. Autòmata Factor Oracle: algorisme
23/04/2019
Algorisme: per a i=1 fins p fer
Afegir transicions que reconeguin factors acabats a i; ?
As you have seen this morning ....

25. Autòmata Factor Oracle: algorisme
23/04/2019
Que passa si el següent caràcter existeix? T
As you have seen this morning ....

26. Autòmata Factor Oracle: algorisme
23/04/2019
Que passa si el següent caràcter no existeix? T T
As you have seen this morning ....

27. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019 G A T
i reconeix mots que no són factors com GTGTA.
Però, si no el reconeix ==> no és factor!
As you have seen this morning ....
Es l’estratègia de l’algorisme BOM

28. Algorisme BOM (Backward Oracle Matching)
23/04/2019
Com es determina la següent posició de la finestra?
Com fa la comparació?
Text :
Patró :
Autòmata: Factor Oracle
Comproba si el sufix és factor del patró a
Si la a no s’ha trobat
As you have seen this morning ....
Si arriben a l’estat final de l’autòmat amb la a a

29. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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...
A T G T A T G
As you have seen this morning ....

30. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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
As you have seen this morning ....

31. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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
As you have seen this morning ....

32. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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
As you have seen this morning ....

33. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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
As you have seen this morning ....

34. Autòmata Factor Oracle: exemple d’algorisme
23/04/2019
Com fa la comparació?
Es construeix l’autòmata del patró invers: Suposem que el patró és ATGTATG G A T
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
A T G T A T G
As you have seen this morning ....