1. 1 Turbo-BM Algorithm Adviser: R. C. T. Lee Speaker: H. M. Chen Deux méthodes pour accélérer l'algorithme de Boyer-Moore, Théorie des Automates et Applications., 589-600, 1992. CROCHEMORE, M., CZUMAJ, A., GASIENIEC, L., JAROMINEK, S., LECROQ, T., PLANDOWSKI, W. and RYTTER, W.

2. 2 The Turbo-BM algorithm is an amelioration of the Boyer-Moore algorithm. It needs no extra preprocessing and requires only a constant extra space with respect to the original Boyer- Moore algorithm. It improves the worst-case complexity of Boyer-Moore algorithm. Turbo-BM

3. 3 S1S1 S1S1 Text Pattern S1S1 S1S1 Text Pattern S1S1 S1S1 S1S1 Text Pattern S1S1 Good Suffix Rule 1 of the BM Algorithm.

4. 4 S2S2 S2S2 Text Pattern Another matching: S1S1 S1S1 But, remember that S 1 is a suffix of P. S2S2 S2S2 Text Pattern S1S1 S1S1 Thus, S2S2 S2S2 Text Pattern S2S2 S2S2 S1S1 S1S1 S1S1 S1S1

5. 5 S2S2 S1S1 Text Pattern S2S2 y x S2S2 x S1S1 S2S2 x S2S2 S2S2 Text Pattern S2S2 S2S2 S1S1 S1S1 S1S1 S1S1

6. 6 If we move only one step S2S2 S1S1 Text Pattern S2S2 y x S2S2 x S2S2 x y After this one step move S2S2 S1S1 Text Pattern S2S2 y x S2S2 x S1S1 S2S2 x y y S1S1 y S1S1 For a successful matching. Impossible for matching.

7. 7 Conclude : We must move at least |S 1 | - | S 2 | steps. Condition : (1) In the pervious step, Good Suffix Rule 1 (BM) was used. Thus S 1 is long and not unique. This means that there is a period. (2)In the pervious step, S 2 is contained in S 1. S1S1 S2S2 S1S1

8. 8 We compare the pattern and the text from right to left. Turbo-BM skips the memory part which has been matched in preceding attempt. Text = Pattern = memory match Turbo-skip

9. 9 bbaabbbbbbabababaaababab bbabababaaababab Text = Pattern = bbaabbbbbbabababaaababab bbabababaaababab Text = Pattern = Example memory match

10. 10 bbaabcabaccaadabaabaaada bbabaaaba Text = Pattern = bbabaaaba Shift by using Good Suffix Rule 1 Full Example memory

11. 11 bbaabcabaccaadabaabaaada Text = Pattern = bbabaaaba memory bbabaaaba Turbo-shift= |aba| - |a| = 2 Shift by Turbo-shift bbaabcabaccaadabaabaaada Text = Pattern = bbabaaaba Shift by Good Suffix Rule 1 bbabaaaba We select the maximal number of shift between Good Suffix Rule 1 and Turbo-shift. Full Example

12. 12 bbaabcabaccaadabaabaaada Text = Pattern = bbabaaaba bbabaaaba memory Shift by using Good Suffix Rule 1 Full Example

13. 13 bbaabcabaccaadababbabaaa Text = Pattern = bbabaaaba memory match is aba, but memory is a. when |match| > |memory|, we shift pattern by using Good Suffix Rule 1 only. Turbo-skip bbaabcabaccaadababbabaaa Text = Pattern = bbabaaaba bbabaaaba Shift by Good Suffix Rule 1 Full Example

14. 14 The preprocessing phase in O(m+Σ) time and space complexity and searching phase in O(n) time complexity. Time Complexity

15. 15 References Off-line serial exact string searching, CROCHEMORE, M., Oxford University Press, Chapter 1, 1997, pp. 1-53. Deux méthodes pour accélérer l'algorithme de Boyer-Moore, CROCHEMORE, M., CZUMAJ, A., GASIENIEC, L., JAROMINEK, S., LECROQ, T., PLANDOWSKI, W. and RYTTER W., Rouen France, 1991, pp. 45-63. Speeding up two string matching algorithms, CROCHEMORE, M., CZUMAJ, A., GASIENIEC, L., JAROMINEK, S., LECROQ, T., PLANDOWSKI, W. and RYTTER, W., Algorithmica, Vol 12, 1994, pp. 247-267. Text Algorithms, CROCHEMORE, M. and RYTTER, W., Oxford University Press, 1994. Recherches de mot, LECROQ, T., University of Orléans, France, 1992. Experimental results on string matching algorithms, LECROQ, T., Software - Practice & Experience, Vol 25, 1995, pp.727-765.

16. 16 THANK YOU