Boyer–Moore string search algorithm

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



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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


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



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 7 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 7 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 7 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 4 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 7 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE 7 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

SC I ENCE1 shifts



Letter

s c i e n *

BCR 6 1 4 1 2 7

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)

https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_string_search_algorithm

https://en.wikipedia.org/wiki/Finite-state_machine

https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore_string_search_algorithm

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).

Software

Boyer–Moore string search algorithm