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**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

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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.

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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.

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**Rule 2-2: 1-Suffix Rule (A Special Version of Rule 2)**

Consider the 1-suffix x. We may apply Rule 2-2 now.

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**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

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**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.

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**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

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**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.

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**Tuned Boyer Moore Preprocessing Table**

Example： P=AGCAGAC A C G T bmBC 1 4 2 7

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C

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**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

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C →

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**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

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C →

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T match A G C

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**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

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C →

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T match A G C

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**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

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C →

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**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

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**Example Text string T=GCGAGCAGACGTGCGAGTACG Pattern string P=AGCAGAC G**

tbmBC 1 4 2 7 G C A T A G C →

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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.

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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

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