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:..aaa aac.

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 EXAMP LE …

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 patlen th 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

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-POINT

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

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

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 : else,5; 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 : ;

Ex: we compute j=5 j= Pat: e d b c a b c e d b c a b c 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.