short introduction to Boyer–Moore string search algorithm

1. BOYER–MOORE STRING
SEARCH ALGORITHM
SeyedHamid Shekarforoush
Bowling Green State University

2. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
0
C G A T

3. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
1
C G A T

4. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
2
C G A T

5. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
3
C G A T

6. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
4
C G A T

7. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
5
C G A T

8. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
6
C G A T

9. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
7
C G A T

10. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
8
C G A T

11. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
9
C G A T

12. SEARCHING A SPECIFIC PATTERN IN A
TARGET TEXT
THE NAÏVE METHOD
G T T T A C G G T C T T C T T G G C C G A T T A
# comparisons
27
C G A T

13. BOYER–MOORE STRING SEARCH ALGORITHM
 developed by Robert S. Boyer and J Strother
Moore in 1977
 Smart naïve method
 tries to match the pattern with target text
 Use two rules to skip unnecessary matches
 Match from the end of pattern

14. FIRST RULE: THE BAD CHARACTER RULE (BCR)
 Text : bowling green state university computer science department
 Pattern : science
Letter s c i e n *
BCR 6 1 4 1 2 7

15. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E

16. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 7 shifts

17. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 7 shifts

18. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 7 shifts

19. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 4 shifts

20. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 7 shifts

21. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E 7 shifts

22. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E1 shifts

23. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E

24. FIRST RULE: THE BAD CHARACTER RULE (BCR)
B OW L I NG G R E E N S T A T E U N I V E R S I T Y C OMP U T E R S C I E N C E
Letter s c i e n *
BCR 6 1 4 1 2 7
S C I E N C E

25. BUILDING BCR TABLE
• Length – index – 1
• The BCR value can’t be less than 1
• If we have repeated letters we count the minimum BCR value, because it
should be the rightmost occurrence of the letter
• We use symbol “*” for any other letter that is not in the pattern and the BC
value is the length of the pattern, because we can skip the whole pattern
knowing that character “*” is not in the pattern.

26. BUILDING BCR TABLE • Length – index – 1
• Length = 7
index 0 1 2 3 4 5 6 7
pattern s c i e n c e *
BCR 6 5 4 3 2 1 0>>>1 7
•Length – index – 1
•7-0-1 =6
•The BCR value can’t be less than 1
•Why?

27. BUILDING BCR TABLE • Length – index – 1
• Length = 7
index 0 1 2 3 4 5 6 7
pattern s c i e n c e *
BCR 6 5 4 3 2 1 0>>>1 7
•Minimum BCR for repeated letters
Letter s c i e n *
BCR 6 1 4 1 2 7

28. SECOND RULE: GOOD SUFFIX RULE (GSR)
 It used when we have some
successful matches
 Reusing the already matched
string

29. SECOND RULE: GOOD SUFFIX RULE (GSR)
6 shifts

30. BOTH RULES TOGETHER
 At each step when we get a mismatch and we want to shift, the algorithm
use both rules and use the bigger shift

31. BOTH RULES TOGETHER
Letter T C G *
BCR 2 3 1 10
 BCR = 2 shifts  GSR = 6 shifts

32. PERFORMANCE
 The Boyer–Moore is work faster
and better with longer pattern
with less repeated characters
 Most of the time the BCR win
over the GSR
 many implementation don’t use
the GSR at all
Algorithm Preprocessing time Matching time
Naïve 0 (no preprocessing) Θ((n−m)m)
Rabin–Karp Θ(m) average Θ(n + m),
worst
Θ((n−m)m)
Finite-state Θ(mk) Θ(n)
Knuth–Morris–Pratt Θ(m) Θ(n)
Boyer–Moore Θ(m + k) best Ω(n/m), worst O(n)
Bitap Θ(m + k) O(mn)

33. REFRENCES
 [1] Robert S. Boyer and J. Strother Moore. 1977. A fast string searching
algorithm. Commun. ACM 20, 10 (October 1977), 762-772.
DOI=http://dx.doi.org/10.1145/359842.359859
 [2] Wikipedia contributors, "Boyer–Moore string search algorithm," Wikipedia,
The Free Encyclopedia,
https://en.wikipedia.org/w/index.php?title=Boyer%E2%80%93Moore_string_sear
ch_algorithm&oldid=688111014 (accessed November 20, 2015).