 Author: Ricardo A. Baeza-Yates, Gaston H. Gonnet  Publisher: 1992 Communications of the ACM  Presenter: Yuen-Shuo Li  Date: 2013/08/14 1

 String searching is a very important component of many problems, including text editing, bibliographic retrieval, and symbol manipulation.

T[a] = T[b] = T[c] = T[d] = cbaba T[a] = 11010

50301 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

0301 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

14020 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

14020 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

14020 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

4020 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

50301 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

04121 State cbbabababcaba… text T[a] = T[b] = T[c] = T[d] = 11111

 To update the state after reading a new character on the text, we must  Shift the vector state b bits to the left to reflect that we have advanced one position in the text.  Update the individual states according to the new character.

The number of mismatches

0 or 1 b = 1

Let {a, b, c, d} be the alphabet, and ababc the pattern. T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = 11111

 The initial state is State abdabababc text T[a] = T[b] = T[c] = T[d] = The match at the end of the text is indicated by the value 0 in the leftmost bit of the state

m: pattern size w: word size

T[a] = T[b] = T[c] = T[d] = 01101

 We allow up to k characters of the pattern to mismatch with the corresponding text. For example, if k = 2, the pattern mismatch: mismatch (match) dispatch (match) respatch (mismatch)

At each step we record the overflow bits in an overflow state, and we reset the overflow bits of all individual states.

 We want to search for all occurrences of ababc with at most 2 mismatch. Because the value of b is 3 for 2 mismatches, every position in the state is represented by a number in the range  Initial state:  Initial overflow: We report a match when the sum of the leftmost digits of the state and the overflow is less than 3

 Experimental results for searching 100 times for all possible matches of a pattern in a 50,000 character English text(a legal document)

BMH: Boyer-Moore, as suggested by Horspool

 The execution time while search 1,000 words chosen at random from the same English text