Rabin Karp - String Matching Algorithm

1. Yet another string matching algorithm
PRESENTED BY
P14-6011
P14-6016
Rabin Karp

2.  Proposed in 1987
 Michael O. Rabin
 Richard M. Karp
 Improved Naive String Matching
 By HASHING
 Average Running Time O(m+n)
Introduction

3.  Let text string be T of length N
 Pattern string be P of length M
 Example
 T=“hello world”; N=11;
 P=“llo”; M=3
 Application
 Keyword matching in large files
 Good for Plagiarism detection
Statement

4.  Calculate Hash of Pattern
 As well of M characters of text
 If hash is not equal
 Calculate hash of next M characters
 If hash is equal then
 Compare both character by character
Note: Only one comparison for sub sequence
Working

5. H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80
Example
tHash = Hash(“HEL”) = 10+20+30 = 60
pHash = Hash(“LLO”) = 30+30+40 = 100
tHash == pHash  FALSE
H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80
tHash = Hash(“ELL”) = 20+30+30 = 80
tHash == pHash  FALSE
H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80
tHash = Hash(“LLO”) = 30+30+40 = 100
tHash == pHash  TRUE

6. int RabinKarp(string t, string p) {
int pHash = Hash(p);
int limit = t.size() - p.size() + 1; // n – m + 1
for (int i = 0; i < limit; i++) {
string substr = t.substr(i, p.size());
int tHash = Hash(substr);
if (pHash == tHash && p == substr) return i;
}
return -1;
}
Implementation

7.  Hash to two string match then it is called Hit
 There is possibility
 Hash of “LLO” is 100
 Hash of “OLL” is 100
 This is called Hash Collision
 Minimize Collision by
 Scaling with index position
 30(3)+30(2)+40(1) = 190 | 40(3)+30(2)+30(1) = 210
 Taking mod with prime number
Hash Collision

8.  Hash of Pattern
 O(m)
 Hash Comparison
 O(n-m+1) = O(n) ; m < n
 Average Running Time
 O(m+n)
 Worst Case Running Time
 m comparison in each iteration
 O(mn)
Analysis

9. 1. CLRS – 2nd Edition, Page 911-916
2. slideshare.net/GajanandSharma1/rabin-karp-string-matching-algorithm
3. stoimen.com/blog/2012/04/02/computer-algorithms-rabin-karp-string-
searching/
4. en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm
5. cs.princeton.edu/courses/archive/fall04/cos226/lectures/string.4up.pdf
References