1. Exact string matching: one pattern (text on-line)
24/02/15
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

2. Multiple string matching
24/02/15 8 4 2
| |
Wu-Manber
SBOM
lmin
(5 strings) 8 4 2
Wu-Manber
SBOM
(10 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(100 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(1000 strings)
Ad AC

3. Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
24/02/15
Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
As you have seen this morning ....

4. Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
24/02/15
Construct the trie of GTATGTA,GTAT,TAATA,GTGTA G A T
As you have seen this morning ....

5. Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
24/02/15
Construct the trie of GTATGTA,GTAT,TAATA,GTGTA G A T
As you have seen this morning ....

6. Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
24/02/15
Construct the trie of GTATGTA,GTAT,TAATA,GTGTA T G T A A T G T A A T A A
As you have seen this morning ....

7. Construct the trie of GTATGTA,GTAT,TAATA,GTGTA
24/02/15
Construct the trie of GTATGTA,GTAT,TAATA,GTGTA T G T A A T G G T A T A A T A
As you have seen this morning ....
Which is the cost?

8. Set Horspool algorithm
24/02/15
How the comparison is made?
By suffixes
Text :
Patterns:
Trie of all inverse patterns
Which is the next position of the window? a
As you have seen this morning ....
We shift until a is aligned with the first a in the trie not longer than lmin, or lmin

9. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
1. Construct the trie of GTATGTA,
GTAT, TAATA i GTGTA
2. Determine lmin=
As you have seen this morning ....

10. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
1. Construct the trie of GTATGTA,
GTAT, TAATA i GTGTA
2. Determine lmin=4
A 1
C 4 (lmin) G T
3. Determine the shift table
As you have seen this morning ....

11. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
1. Construct the trie of GTATGTA,
GTAT, TAATA i GTGTA
2. Determine lmin=4
A 1
C 4 (lmin)
G 2 T
3. Determine the shift table
As you have seen this morning ....

12. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
1. Construct the trie of GTATGTA,
GTAT, TAATA i GTGTA
2. Determine lmin=4
A 1
C 4 (lmin)
G 2
T 1
3. Determine the shift table
As you have seen this morning ....
4. Find the patterns

13. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

14. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

15. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

16. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

17. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

18. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning ....

19. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning .... …

20. Set Horspool algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
As more patterns we search for,
shorter shifts we do!
A 1
C 4 (lmin)
G 2
T 1
text: ACATGCTATGTGACA…
As you have seen this morning .... …
Is the expected length of the shifts related with the number of patterns?

21. Set Horspool algorithm Wu-Manber algorithm
24/02/15
How the length of shifts can be increased?
By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG
A 1
C 4 (lmin)
G 2
T 1
1 símbol
AA 1
AC (LMIN-L+1) AG AT CA CC CG …
2 símbols
As you have seen this morning ....

22. Set Horspool algorithm Wu-Manber algorithm
24/02/15
How the length of shifts can be increased?
By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG
A 1
C 4 (lmin)
G 2
T 1
1 símbol
AA 1
AC (LMIN-L+1) AG AT CA CC CG …
2 símbols 3
As you have seen this morning ....

23. Set Horspool algorithm Wu-Manber algorithm
24/02/15
How the length of shifts can be increased?
By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG
A 1
C 4 (lmin)
G 2
T 1
1 símbol
AA 1
AC (LMIN-L+1) AG AT CA CC CG …
2 símbols 3 1
As you have seen this morning ....

24. Set Horspool algorithm Wu-Manber algorithm
24/02/15
How the length of shifts can be increased?
By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG
A 1
C 4 (lmin)
G 2
T 1
1 símbol
AA 1
AC (LMIN-L+1) AG
AT 1 CA CC CG …
2 símbols 3 3
As you have seen this morning ....

25. Set Horspool algorithm Wu-Manber algorithm
24/02/15
How the length of shifts can be increased?
By reading blocks of symbols instead of only one! Given ATGTATG,TATG,ATAAT,ATGTG
A 1
C 4 (lmin)
G 2
T 1
1 símbol
AA 1
AC (LMIN-L+1)
AG 3
AT 1
CA 3
CC 3
CG 3 …
2 símbols
AA 1
AT 1
GT 1
TA 2
TG 2
As you have seen this morning ....

26. Search for ATGTATG,TATG,ATAAT,ATGTG
Wu-Manber algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
AA 1
AT 1
GT 1
TA 2
TG 2
text: ACATGCTATGTGACATAATA
As you have seen this morning ....

27. Search for ATGTATG,TATG,ATAAT,ATGTG
Wu-Manber algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
AA 1
AT 1
GT 1
TA 2
TG 2
text: ACATGCTATGTGACATAATA
As you have seen this morning ....

28. Search for ATGTATG,TATG,ATAAT,ATGTG
Wu-Manber algorithm
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
AA 1
AT 1
GT 1
TA 2
TG 2
text: ACATGCTATGTGACATAATA
As you have seen this morning ....

29. … Wu-Manber algorithm Search for ATGTATG,TATG,ATAAT,ATGTG
24/02/15
Search for ATGTATG,TATG,ATAAT,ATGTG T A G
AA 1
AT 1
GT 1
TA 2
TG 2
text: ACATGCTATGTGACATAATA
But given k patterns, how many symbols we should take ?
As you have seen this morning .... …
log|Σ| 2*lmin*k

30. Multiple string matching
24/02/15 8 4 2
| |
Wu-Manber
SBOM
lmin
(5 strings) 8 4 2
Wu-Manber
SBOM
(10 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(100 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(1000 strings)
Ad AC

31. BOM algorithm (Backward Oracle Matching)
24/02/15
Which is the next position of the window?
How the comparison is made?
Text :
Pattern :
Automata: Factor Oracle
Check if the suffix is a factor of any pattern
As you have seen this morning ....
The position determined by the last character of the text
with a transition in the automata

32. Factor Oracle of k strings
24/02/15
How can we build the Factor Oracle of
GTATGTA, GTAA, TAATA i GTGTA ? G T A T G T A T G A
1,4 A A T A
As you have seen this morning .... 3 2

33. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T
As you have seen this morning ....

34. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T A T
As you have seen this morning ....

35. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T A T T A
As you have seen this morning ....

36. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T A T G T A
As you have seen this morning ....

37. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T A T G T T G A
As you have seen this morning ....

38. Factor Oracle of k strings
24/02/15
Given the Factor Oracle of GTATGTA G T A T G T A 1 T G A
As you have seen this morning ....
… we insert GTAA

39. Factor Oracle of k strings
24/02/15
…inserting GTAA G T A T G T A T G A 2 1 A
As you have seen this morning ....

40. Factor Oracle of k strings
24/02/15
Given the AFO of GTATGTA and GTAA G T A T G T A T G 1 A A
As you have seen this morning .... 2
… we insert TAATA

41. Factor Oracle of k strings
24/02/15
… inserting TAATA G T A T G T A T G A 1 A A T A 3
As you have seen this morning .... 2

42. Factor Oracle of k strings
24/02/15
Given the AFO of GTATGTA, GTAA and TAATA G T A T G T A T G A 1 A A T A
As you have seen this morning .... 3 2
…we insert GTGTA

43. Factor Oracle of k strings
24/02/15
…inserting GTGTA G T A T G T A T G A 1 A A T A
As you have seen this morning .... 3 2

44. Factor Oracle of k strings
24/02/15 G T A T G T A T G A
1,4 A A T A 3 2
As you have seen this morning ....
This is the Automata Factor Oracle of
GTATGTA, GTAA, TAATA and GTGTA

45. SBOM algorithm How the comparison is made?
24/02/15
Which is the next position of the window?
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
As you have seen this morning ....
The position determined by the last character of the text
with a transition in the automata

46. SBOM algorithm: example
24/02/15
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 T G T A 1 4 A T G A
As you have seen this morning .... A T A 2 3

47. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

48. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

49. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

50. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

51. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

52. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

53. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGTATG
As you have seen this morning ....

54. SBOM algorithm: example
24/02/15
Search for ATGTATG, TAATG,TAATAAT i AATGTG G T A T G T A 1 4 A T G A A T A 2 3
text: ACATGCTAGCTATAATAATGT…
As you have seen this morning ....

55. Multiple string matching
24/02/15 8 4 2
| |
Wu-Manber
SBOM
lmin
(5 strings) 8 4 2
Wu-Manber
SBOM
(10 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(100 strings)
Ad AC 8 4 2
Wu-Manber
SBOM
(1000 strings)
Ad AC