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Boyer–Moore string search algorithm

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short introduction to Boyer–Moore string search algorithm

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Boyer–Moore string search algorithm

  1. 1. BOYER–MOORE STRING SEARCH ALGORITHM SeyedHamid Shekarforoush Bowling Green State University
  2. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 28. SECOND RULE: GOOD SUFFIX RULE (GSR)  It used when we have some successful matches  Reusing the already matched string
  29. 29. SECOND RULE: GOOD SUFFIX RULE (GSR) 6 shifts
  30. 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. 31. BOTH RULES TOGETHER Letter T C G * BCR 2 3 1 10  BCR = 2 shifts  GSR = 6 shifts
  32. 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. 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).

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