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BOYER–MOORE STRING SEARCH ALGORITHM SeyedHamid ShekarforoushBowling Green State University
SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE 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
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C G A T
SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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SEARCHING A SPECIFIC PATTERN IN A TARGET TEXTTHE NAÏVE METHOD
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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
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
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 7 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 7 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 7 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 4 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 7 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE 7 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE1 shifts
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE
FIRST RULE: THE BAD CHARACTER RULE (BCR)
BOWL I NG GRE EN STAT E UN I VERS I TY COMPUT ER SC I ENCE
Letter
s c i e n *
BCR 6 1 4 1 2 7
SC I ENCE
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.
BUILDING BCR TABLE • Length – index – 1• Length = 7
index 0 1 2 3 4 5 6 7pattern 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?
BUILDING BCR TABLE • Length – index – 1• Length = 7
index 0 1 2 3 4 5 6 7pattern 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
SECOND RULE: GOOD SUFFIX RULE (GSR)
It used when we have some successful matches
Reusing the already matched string
SECOND RULE: GOOD SUFFIX RULE (GSR)
6 shifts
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
BOTH RULES TOGETHER
Letter
T C G *
BCR 2 3 1 10
BCR = 2 shifts GSR = 6 shifts
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)
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_search_algorithm&oldid=688111014 (accessed November 20, 2015).
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