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Tuned Boyer Moore Algorithm Fast string searching, HUME A. and SUNDAY D.M., Software - Practice & Experience 21(11), 1991, pp. 1221-1248. Adviser: R. C.

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Presentation on theme: "Tuned Boyer Moore Algorithm Fast string searching, HUME A. and SUNDAY D.M., Software - Practice & Experience 21(11), 1991, pp. 1221-1248. Adviser: R. C."— Presentation transcript:

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 T s : the first character of a string T aligns to a pattern P. P l : the first character of a pattern P aligns to a string T. T j : the character of the jth position of a string T. P i : the character of the ith position of a pattern P. P f : 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 Txzy Since T s+m-1 P f, we move the pattern P to right such that the largest position i in the right of P i is equal to T s+m. We can shift the pattern at least (m-i) positions right until T s+m-1 = P f. Shift ss+m-1 Pzxy i1f Pzxy i 1 f Pzxy i 1 f Shift

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 P 1 to P m-1, we record it as m.

9 Tuned Boyer Moore Preprocessing Table Example P= AGCAGAC ACGT bmBC1427

10 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

11 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 tbmBC[A]=1, shift=1

12 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

13 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 tbmBC[G]=2, shift=2

14 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

15 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 match

16 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 exact match tbmBC[C]=4, shift=4

17 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

18 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 match

19 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 mismatch tbmBC[C]=4, shift=4

20 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

21 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427 tbmBC[T]=7, shift=7

22 Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC GCGAGCAGACGTGCGAGTACG AGCAGAC ACGT tbmBC1427

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: Users Manual (UCIVersion), M. T. Rose and J. L. Romine, University of California, Irvine, [S82] A comparison of three string matching algorithms, G. De V. Smith, SoftwarePractice 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, [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


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