1. Tuned Boyer Moore Algorithm
Fast string searching , HUME A. and SUNDAY D.M., Software - Practice & Experience 21(11), 1991, pp
Adviser: R. C. T. Lee
Speaker: C. W. Cheng
National Chi Nan University

2. Problem Definition
Input: a text string T with length n and a pattern string P with length m.
Output: all occurrences of P in T.

3. Definition
Ts : the first character of a string T aligns to a pattern P.
Pl : the first character of a pattern P aligns to a string T.
Tj : the character of the jth position of a string T.
Pi : the character of the ith position of a pattern P.
Pf : the last character of a pattern P.
n : The length of T.
m : The length of P.

4. Rule 2-2: 1-Suffix Rule (A Special Version of Rule 2)
Consider the 1-suffix x. We may apply Rule 2-2 now.

5. Introduction simplification of the Boyer-Moore algorithm.
uses only the bad-character shift.
easy to implement.
very fast in practice
uses Rule 2-2: 1-Suffix Rule

6. Tuned Boyer Moore Algorithm
In this algorithm, We always focus on the last character of the window of T and try to slide the pattern to match the last character of T.

7. Tuned Boyer Moore Algorithm Rule
Since Ts+m-1 ≠ Pf , we move the pattern P to right such that the largest position i in the right of Pi is equal to Ts+m. We can shift the pattern at least (m-i) positions right until Ts+m-1 = Pf. s
s+m-1 T x z y P z x y i f 1
Shift P z x y i f 1
Shift P z x y 1 i f

8. Tuned Boyer Moore Preprocessing Table
In this algorithm, we construct a table as follow. Let x be a character in the alphabet. We record the position of the last x, if it exists in P, we record the position of x from the second last position of P. If x does not exist in P1 to Pm-1, we record it as m.

9. Tuned Boyer Moore Preprocessing Table
Example：
P=AGCAGAC A C G T
bmBC 1 4 2 7

10. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C

11. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7
tbmBC[A]=1, shift=1 G C A T A G C

12. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C →

13. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7
tbmBC[G]=2, shift=2 G C A T A G C

14. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C →

15. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T
match A G C

16. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7
tbmBC[C]=4, shift=4 G C A T
exact match A G C

17. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C →

18. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T
match A G C

19. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7
tbmBC[C]=4, shift=4 G C A T
mismatch A G C

20. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C →

21. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7
tbmBC[T]=7, shift=7 G C A T A G C

22. Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G
tbmBC 1 4 2 7 G C A T A G C →

23. Time complexity
preprocessing phase in O(m+ σ) time and O(σ) space complexity, σ is the number of alphabets in pattern.
searching phase in O(mn) time complexity.

24. Reference
[KMP77] Fast pattern matching in strings, D. E. Knuth, J. H. Morris, Jr and V. B. Pratt, SIAM J. Computing, 6,
1977, pp. 323–350.
[BM77] A fast string search algorithm, R. S. Boyer and J. S. Moore, Comm. ACM, 20, 1977, pp. 762–772.
[S90] A very fast substring search algorithm, D. M. Sunday, Comm. ACM, 33, 1990, pp. 132–142.
[RR89] The Rand MH Message Handling system: User’s Manual (UCIVersion), M. T. Rose and J. L. Romine,
University of California, Irvine, 1989.
[S82] A comparison of three string matching algorithms, G. De V. Smith, Software—Practice and Experience,12,
1982, pp. 57–66.
[HS91] Fast string searching, HUME A. and SUNDAY D.M. , Software - Practice & Experience 21(11), 1991, pp.
[S94] String Searching Algorithms , Stephen, G.A., World Scientific, 1994.
[ZT87] On improving the average case of the Boyer-Moore string matching algorithm, ZHU, R.F. and
TAKAOKA, T., Journal of Information Processing 10(3) , 1987, pp
[R92] Tuning the Boyer-Moore-Horspool string searching algorithm, RAITA T., Software - Practice & Experience,
22(10) , 1992, pp
[S94] On tuning the Boyer-Moore-Horspool string searching algorithms, SMITH, P.D., Software - Practice &
Experience, 24(4) , 1994, pp
[BR92] Average running time of the Boyer-Moore-Horspool algorithm, BAEZA-YATES, R.A., RÉGNIER, M.,
Theoretical Computer Science 92(1) , 1992, pp
[H80] Practical fast searching in strings, HORSPOOL R.N., Software - Practice & Experience, 10(6) , 1980, pp.
[L95] Experimental results on string matching algorithms, LECROQ, T., Software - Practice & Experience 25(7) ,
1995, pp

25. Thanks for your listening