Smith Algorithm

1 / 22

# Smith Algorithm - PowerPoint PPT Presentation

Smith Algorithm. Experiments with a very fast substring search algorithm, SMITH P.D., Software - Practice &amp; Experience 21(10), 1991, pp. 1065-1074. . Adviser: R. C. T. Lee Speaker: C. W. Cheng National Chi Nan University. Problem Definition.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Smith Algorithm' - eros

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Smith Algorithm

Experiments with a very fast substring search algorithm, SMITH P.D., Software - Practice & Experience 21(10), 1991, pp. 1065-1074.

Speaker: C. W. Cheng

National Chi Nan University

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.

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.
Rule 2-2: 1-Suffix Rule (A Special Version of Rule 2)
• Consider the 1-suffix x. We may apply Rule 2-2 now.
Introduction
• takes the maximum of the Horspool shift function and the Quick Search shift function.
• uses Rule 2-2: 1-Suffix Rule
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.

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

hpBC[A]=1, qsBC[G]=1, shift=1

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

hpBC[G]=2, qsBC[A]=2, shift=2

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

exact match

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

hpBC[G]=2, qsBC[T]=8, shift=8

exact match

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

hpBC[T]=7, qsBC[A]=2, shift=7

mismatch

Example
• Text string T=GCGCAGAGAGTAGAGAGTACG
• Pattern string

P=CAGAGAG

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.
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.