Rabin karp string matcher
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The document discusses the Rabin-Karp algorithm for string matching. It defines Rabin-Karp as a string search algorithm that compares hash values of strings rather than the strings themselves. It explains that Rabin-Karp works by calculating a hash value for the pattern and text subsequences to compare, and only does a brute force comparison when hash values match. The worst-case complexity is O(n-m+1)m but the average case is O(n+m) plus processing spurious hits. Real-life applications include bioinformatics to find protein similarities.
Rabin karp string matcher
- 1. String Matching Using The Rabin-Karp Algorithm Dr. AMIT KUMAR @JUET
- 2. Outline • Definition of the Rabin-Karp algorithm • How Rabin-Karp works • A Rabin-Karp example • Complexity • Real Life applications Dr. AMIT KUMAR @JUET
- 3. String Matching Problem • The idea of the string matching problem is that we want to find all occurrences of the pattern P in the given text T. • We could use the brute force method for string matching, which utilizes iteration over T. At each letter, we compare the sequence against P until all letters match of until the end of the alphabet is reached. • The worst case scenario can reach O(N*M) Dr. AMIT KUMAR @JUET
- 4. Definition of Rabin-Karp • A string search algorithm which compares a string's hash values, rather than the strings themselves. For efficiency, the hash value of the next position in the text is easily computed from the hash value of the current position. Dr. AMIT KUMAR @JUET
- 5. How Rabin-Karp works • Let characters in both arrays T and P be digits in radix-S notation. (S = (0,1,...,9) • Let p be the value of the characters in P • Choose a prime number q such that fits within a computer word to speed computations. • Compute (p mod q) – The value of p mod q is what we will be using to find all matches of the pattern P in T. Dr. AMIT KUMAR @JUET
- 6. How Rabin-Karp works (continued) • The Rabin-Karp string searching algorithm calculates a hash value for the pattern, and for each M-character subsequence of text to be compared. • If the hash values are unequal, the algorithm will calculate the hash value for next M-character sequence. • If the hash values are equal, the algorithm will do a Brute Force comparison between the pattern and the M-character sequence. • In this way, there is only one comparison per text subsequence, and Brute Force is only needed when hash values match. Dr. AMIT KUMAR @JUET
- 7. A Rabin-Karp example • Given T = 31415926535 and P = 26 • We choose q = 11 • P mod q = 26 mod 11 = 4 13 14 95 62 35 5 13 14 95 62 35 5 14 mod 11 = 3 not equal to 4 31 mod 11 = 9 not equal to 4 13 14 95 62 35 5 41 mod 11 = 8 not equal to 4Dr. AMIT KUMAR @JUET
- 8. Rabin-Karp example continued 13 14 95 62 35 5 15 mod 11 = 4 equal to 4 -> spurious hit 13 14 95 62 35 5 59 mod 11 = 4 equal to 4 -> spurious hit 13 14 95 62 35 5 92 mod 11 = 4 equal to 4 -> spurious hit 13 14 95 62 35 5 26 mod 11 = 4 equal to 4 -> an exact match!! 13 14 95 62 35 5 65 mod 11 = 10 not equal to 4 Dr. AMIT KUMAR @JUET
- 9. Rabin-Karp example continued As we can see, when a match is found, further testing is done to insure that a match has indeed been found. 13 14 95 62 35 5 53 mod 11 = 9 not equal to 4 13 14 95 62 35 5 35 mod 11 = 2 not equal to 4 Dr. AMIT KUMAR @JUET
- 10. Rabin-Karp example (Alphabets) • Let’s say that our alphabet consists of 10 letters. • our alphabet = a, b, c, d, e, f, g, h, i, j • Let’s say that “a” corresponds to 1, “b” corresponds to 2 and so on. The hash value for string “cah” would be ... 3*100 + 1*10 + 8*1 = 318 Dr. AMIT KUMAR @JUET
- 11. Complexity • The running time of the Rabin-Karp algorithm in the worst-case scenario is O(n-m+1)m but it has a good average-case running time. • If a sufficiently large prime number is used for the hash function, the hashed values of two different patterns will usually be distinct. • If the expected number of valid shifts is small O(1) then the Rabin-Karp algorithm can be expected to run in time O(n+m) plus the time to required to process spurious hits. Dr. AMIT KUMAR @JUET
- 12. Applications • Bioinformatics – Used in looking for similarities of two or more proteins; i.e. high sequence similarity usually implies significant structural or functional similarity. Dr. AMIT KUMAR @JUET