A Fast String Matching Algorithm

1
A Fast String Matching Algorithm

• The Boyer Moore Algorithm

2
The obvious search algorithm

• Considers each character position of str and
  determines whether the successive patlen
  characters of str matches pat.
• In worst case, the number of comparisons is in
  the order of .
• Ex. pat aab str ..aaaaac .

3
Knuth-Pratt-Morris Algoritm

• Linear search algorithm.
• Preprocesses pat in time linear in
  and searches str in time linear in
  .
• EXAMPLE
• HERE IS A SIMPLE EXAMPLE

EXAMPLE
EXAMPLE
EXAMPLE
4
Characteristics of Boyer Moore Algorithm

• Basic idea string matches the pattern from the
  right rather than from the left.
• Preprocessing pat and compute two tables
• for shifting pat
  the pointer of str.
• Ex. pat AT-THAT str WHICH-FINALLY-HALTS
  .AT-THAT-POINT

5
Informal Description

• Compare the last char of the pat with the
  patlenth char of str
• AT-THAT
• WHICH-FINALLY-HALTS.AT-THAT-POINT
• Observation 1 char is not to occur in pat, skip
  
• chars of str.

AT-THAT
6
Informal Description

• Observation 2 char is in pat, slide pat down
• positions so that char is aligned to the
  corresponding character in pat.
• if char not occur in
  pat,then else
• , where j is the maximum
  integer such that
• .

AT-THAT WHICH-FINALLY-HALTS.--AT-THAT-P
OINT
7
Informal Description

• Observation 3a str matches the last m chars of
  pat, and came to a mismatch at some new char.
  Move strptr by .(pat shifted by
  )
• AT-THAT
• FINALLY-HALTS.--AT-THAT-POINT

AT-THAT
8
Informal Description

• Observation 3b the final m chars of pat (a
  subpat) is matched, find the right most plausible
  reoccurrence of the subpat, align it with the
  matched m chars of str (slide pat
  positions).
• AT-THAT
• FINALLY-HALTS.AT-THAT-POINT

AT-THAT
AT-THAT
9
The delta1 delta2 tables

• The delta1 table has as many entries as there are
  chars in the alphabet.
• Ex. pat a b c d e a t t h a t
• 4 3 2 1 0 else,5 1 0 4 0 2 1 0
  else,7
• The delta2 table has as many entries as there are
  chars in pat.
• Ex. pat a b c d e a t - t h a t
• 9 8 7 6 1 11 10 9 8 7 8 1

10

• Ex we compute j5
• j 1 2 3 4 5 6 7
• Pat e d b c a b c
• e d b c a b c
• -2 -1 0 1 2 3 4 5 6 7
• Then

11
The algorithm

• stringlen length of string.
• i patlen.
• top if i gt stringlen then return false.
• j patlen.
• loop if j0 then return i1.
• if string(i)pat(j)
• then
• j j-1
• i i-1
• goto loop.
• close
• i i max( delta1(sting(i)) , delta2(j))
• goto top.

12
Implementation Consideration
13
Loops fast, undo, slow

• Fastscans down string, effectively looking for
  the last character in pat,
  skipping according to .
• 80 time spent in it.
• Undodecides whether this situation arose because
  all of string has been scanned or because
  was hit.
• Slowbacks up checking for matches.
• It is easy to implement on a byte addressable
  machine
• Char lt- string (i), etc

14
Measured the cost of each search

• Three stringsbinary alphabet, English, random
  alphabet.
• Fig.1the number of references made to string.
• Fig.2the total number of machine instruction
  that actually got executed.

15
Performance (empirical evidence)
16
Boyer Moore V.S. Knuth, Morris, and Pratt
algorithm

• for English text.
• Boyer Moore
• every reference to string passes about 4
  characters for a pattern of length 5.
• For sufficiently large alphabets and sufficiently
  long patterns executes fewer than 1 instruction
  per character passed.
• K.M.P.
• Search reference string about 1.1 times per
  character.
• a character can be expected to be at least 3.3
  instructions.

17
Conclusion

• Require fewer CPU cycle.
• Most efficiently on a byte-addressable machine.
• Unadvisableto find the first of several possible
  substrings or to identify a location in string
  defined by a regular expression.
• Aho and Corasick is more suitable.

18
Conclusion

• Improveby fetching larger bytes in the fast loop
  and using a hash array to encode the extended
  .
• Exponentially increases the effective size of the
  alphabet and reduces the frequency of common
  characters.