Advisor: Prof. R. C. T. Lee Speaker: T. H. Ku Skip Search algorithm Very Fast String Matching Algorithm for Small Alphabets and Long Patterns, Christian, C., Thierry, L. and Joseph, D.P., Lecture Notes in Computer Science, Vol. 1448, 1998, pp. 55-64 Advisor: Prof. R. C. T. Lee Speaker: T. H. Ku

Skip Search algorithm is an algorithm which solves the string matching problems. Input: a text string T of length n and a pattern string P of length m. Output: all occurrences of P in T.

The Skip Search algorithm consists two phases which are Processing and searching. The Skip Search algorithm uses Rule 4(Two window rule) and Rule 2-2 (1-Suffix Rule) to do the string matching.

the buckets for all characters of the alphabet Preprocessing The Preprocessing phase of the Skip Search algorithm preprocesses the pattern by computing the buckets for all characters of the alphabet. Example: Text string T=GCATCGCAGAGAGTATACAGTACG 0 12 3 4 5 6 7 Pattern string P=GCAGAGAG the buckets for all characters of the alphabet A C G T (6,4,2) (1) (7,5,3,0) φ

Search phase The search phase checks what is the km-th symbol in the text string, where 1≦k ≦n/m. According the symbol to align every identical symbol in the pattern and executes matching. Note that the bucket record every symbols’ location in the pattern. Example: Text string T=aabcdbdabcabc Pattern string P=abcabc, m=6 The 6-th symbol in T is b. Then we align it by the 5-th symbol and executes matching. Then we align it by the 2-th symbol and executes matching. T=aabcdbdabcabc abcabc

the buckets for all characters of the alphabet Full Example Text string T=GCATCGCAGAGAGTATACAGTACG 0 12 34 5 6 7 Pattern string P=GCAGAGAG the buckets for all characters of the alphabet A C G T (6,4,2) (1) (7,5,3,0) Φ

GCATCGCAGAGAGTATACAGTACG 0 1 2 3 4 5 6 7 8 9 1011 12 131415161718 19 20 212223 GCATCGCAGAGAGTATACAGTACG A C G T (6,4,2) (1) (7,5,3,0) φ GCAGAGAG mismatch GCAGAGAG mismatch GCAGAGAG exact match Then we check T[15]=T. Since there is no “T” in the pattern, we check T[23]=G. Then we shift pattern to align T[16…23]. GCAGAGAG

Time Complexity The space and time complexity of the preprocessing phase is O(m+σ)(σ is the number of alphabet.) The Skip Search algorithm has a quadratic worst case time complexity but the expected number of text character inspections is O(n).

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