1. Advanced Data Structure: Bioinformatics
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First week: Algorithms for exact string matching.
Second week: Approximate search and alignment
of short sequences.
Third week: Dealing with long sequences. 1

2. Advanced Data Structure:bibliography
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Bioinformatics, Sequence and Genome Analysis
David W. Mount
Flexible Pattern Matching in Strings (2002)
Gonzalo Navarro and Mathieu Raffinot 2

3. First week First week: algorithms for exact string matching:
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First week: algorithms for exact string matching:
One pattern: The algorithm depends on |p| and |
k patterns: The algorithm depends on k, |p| and ||
Second week: approximate search and alignment
of short sequences.
Third week: dealing with long sequences. 3

4. Exact string matching for one pattern
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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

5. Exact string matching: Brute force algorithm
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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

6. The window is shifted only one cell
Exact string matching: Brute force algorithm
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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

7. Exact string matching: one pattern
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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

8. BNDM : Backward Nondeterministic Dawg Matching
Exact string matching for one pattern
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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 e 8

9. Horspool algorithm How the comparison is made?
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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

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

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

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

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

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

15. Horspool algorithm : example
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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

16. Horspool algorithm: example
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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

17. Some questions about Horspool algorithm
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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

18. BNDM : Backward Nondeterministic Dawg Matching
Exact string matching for one pattern
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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

19. BNDM algorithm How the comparison is made?
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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

20. BNDM algorithm: example
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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

21. BNDM algorithm: example of window shift
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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 = ( ) & ( * * * * * ) = ( )
Found 21

22. BNDM algorithm: example
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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

23. Extended string matching
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Classes of characters: when in some DNA files or patterns there are new characters as N or R that means N={A,C,G,T} and R={G,A}.
Bounded length gaps: we find pattern as ATx(2,3)TA where x(2,3) means any 2 or 3 characters.
Optional characters: we find pattern as AC?ACT?T?A where C? means that C may or may not appear in the text.
Wild cards: we find pattern as AT*TA where * means an arbitrary long string.
Repeatable characters: we find pattern as AT[TA]*AT where [TA]* means that TA can appear zero or more times..
As you have seen this morning .... 23

24. BNDM : Backward Nondeterministic Dawg Matching
Exact string matching for one pattern
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Algorismes més eficients (Navarro & Raffinot)
BNDM : Backward Nondeterministic Dawg Matching
| |
BOM : Backward Oracle Matching 64 32 16
Horspool 8
BOM
BNDM 4 2
Long. pattern w

25. Autòmata Factor Oracle: propietats
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Factor Oracle of word G T A T G T A G A T
All states are accepting states.
Recognizes all factors … but more, which?
As you have seen this morning ....
If a word is rejected, it isn't a factor, then 25

26. BOM algorithm (Backward Oracle Matching)
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How many cells are shifted?
How the comparison is made?
Text :
Pattern :
Automata: Factor Oracle
Checks from right to left a
If the a isn't into the automaton
As you have seen this morning ....
If we reach the last stat of the automaton with the a a 26

27. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
A T G T A T G
As you have seen this morning .... 27

28. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
A T G T A T G
A T G T A T G
As you have seen this morning .... 28

29. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
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 .... 29

30. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
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 .... 30

31. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
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 .... 31

32. BOM algorithm: example
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How the comparison is made?
The automaton of the inverse patterns is built: given the pattern ATGTATG G A T
And the search is :
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 G A...
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 .... 32

33. Automata Factor Oracle
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Given the pattern GTATA, in which state the factors are accepted? G A T GT
GTA TA
When the new T is read, 4 factors should be accepted GTAT
TAT AT
T, how it can be reached?
GTAT
TAT AT T G A GT
GTA TA
When the new A is read, 5 factors should be accepted GTATA
TATA
ATA TA
A, how it can be reached?
As you have seen this morning .... 33

34. Automata Factor Oracle
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GTATA
TATA
ATA TA A
GTAT
TAT AT T G GT
GTA
When the new G is read, 6 factors should be accepted
GTATAG
TATAG
ATAG
TAG AG G G
GTATAG
TATAG
ATAG
TAG AG G
As you have seen this morning .... 34

35. ? Automaton Factor Oracle: linear algorithm 24/02/15 24/02/15
As you have seen this morning .... 35

36. Autòmata Factor Oracle: algorisme
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If there is a T transition ... T
As you have seen this morning .... 36

37. Autòmata Factor Oracle: algorisme
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But if there isn't a T transition ... T T
As you have seen this morning ....
… and recursively continue ... 37