Smith Algorithm

1. Smith Algorithm Experiments with a very fast substring search algorithm, SMITH P.D., Software - Practice & Experience 21(10), 1991, pp. 1065-1074. 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 • takes the maximum of the Horspool shift function and the Quick Search shift function. • uses Rule 2-2: 1-Suffix Rule

6. Smith Algorithm • This algorithm is almost the same as Quick Search Algorithm except the last character of the window is also considered. If this will induce a better movement than the Quick Search Algorithm. This is used; otherwise the Quick Search is used.

7. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG

8. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG mismatch

9. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG hpBC[A]=1, qsBC[G]=1, shift=1 mismatch

10. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG

11. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG mismatch

12. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG hpBC[G]=2, qsBC[A]=2, shift=2 mismatch

13. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG

14. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG exact match

15. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG hpBC[G]=2, qsBC[T]=8, shift=8 exact match

16. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG

17. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG mismatch

18. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG hpBC[T]=7, qsBC[A]=2, shift=7 mismatch

19. Example • Text string T=GCGCAGAGAGTAGAGAGTACG • Pattern string P=CAGAGAG

20. 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.

21. 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. 1221-1248. [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. 173-177 . [R92] Tuning the Boyer-Moore-Horspool string searching algorithm, RAITA T., Software - Practice & Experience, 22(10) , 1992, pp. 879-884. [S94] On tuning the Boyer-Moore-Horspool string searching algorithms, SMITH, P.D., Software - Practice & Experience, 24(4) , 1994, pp. 435-436. [BR92] Average running time of the Boyer-Moore-Horspool algorithm, BAEZA-YATES, R.A., RÉGNIER, M., Theoretical Computer Science 92(1) , 1992, pp. 19-31. [H80] Practical fast searching in strings, HORSPOOL R.N., Software - Practice & Experience, 10(6) , 1980, pp. 501-506. [L95] Experimental results on string matching algorithms, LECROQ, T., Software - Practice & Experience 25(7) , 1995, pp. 727-765.

22. Thanks for your listening