# A Fast String Matching Algorithm by pptfiles

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```									  A Fast String Matching Algorithm

The Boyer Moore Algorithm
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 .
Knuth-Pratt-Morris Algoritm
Linear search algorithm.
Preprocesses pat in time linear in   and searches
str in time linear in         .

…               EXAMPLE
EXAMPLE
EXAMPLE
EXAMPLE
HERE IS A SIMPLE EXAMPLE
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
Informal Description
Compare the last char of the pat with the
patlenth char of str :
AT-THAT
AT-THAT
WHICH-FINALLY-HALTS.—AT-THAT-POINT

Observation 1: char is not to occur in pat, skip
chars of str.
Informal Description
Observation 2: char is in pat, slide pat down
positions so that char is aligned to the corresponding
character in pat.
AT-THAT
WHICH-FINALLY-HALTS.--AT-THAT-
POINT
= if char not occur in pat,then     ; else
, where j is the maximum integer such that
.
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
AT-THAT
…FINALLY-HALTS.--AT-THAT-POINT
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
AT-THAT
AT-THAT
…FINALLY-HALTS.—AT-THAT-POINT
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
Ex: we compute j=5
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
The algorithm
stringlen          length of string.
i       patlen.
top : if i > stringlen then return false.
j     patlen.
loop: if j=0 then return i+1.
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.
Implementation Consideration
Loops: fast, undo, slow
Fast：scans down string, effectively looking for the last
character           in pat, skipping according
to        .
– 80% time spent in it.
Undo：decides whether this situation arose because all
of string has been scanned or because
was hit.
Slow：backs up checking for matches.
It is easy to implement on a byte addressable machine
– Char <- string (i), etc
Measured the cost of each search

Three strings：binary alphabet, English, random
alphabet.

Fig.1：the number of references made to string.
Fig.2：the total number of machine instruction
that actually got executed.
Performance (empirical evidence)
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.
Conclusion

Require fewer CPU cycle.
Most efficiently on a byte-addressable machine.
Unadvisable：to 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.
Conclusion

Improve：by 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.

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