Understanding the Rabin Karp Algorithm for Data, Patterns and String Matching

What is Rabin Karp's Algorithm?

The Rabin-Karp algorithm identifies and matches text patterns by using a hash function. It filters out characters that don't match before making comparisons. This is different from the Naive String-Matching Algorithm where each character has been gone over in the first phase.

The Rabin-Karp string matching method assigns hash values to the patterns and the M-character sequences of the pattern to be compared. If the values are not equal, the method will determine the hash value for the subsequent M-character sequence. The algorithm will look at the pattern and the M-character series if the hash values are equal.

How Does the Algorithm Work?

Here is a step-by-step understanding of the algorithm with examples:

1. Use a hash function to determine the pattern's hash value. After that, we go through the text character by character, beginning with the first character. We determine the hash value for the substring having the identical length as the pattern at every point in the text. In this instance, we would determine a hash value of the text "ABABDABA."
2. Match the substring's computed hash value with the pattern's hash value. If they do, we determine if they are identical by character-by-character comparing the substring and the pattern. Since the hash values in this instance do not match, we proceed to the next index, which is index 1 in the text, and compute the hash value of the string "BABDABA."
3. Every index is then put through the same procedure until a match is found. As a result, we will return index 10 as the beginning index of the pattern in the text. In this instance, we continue the process multiple times until we get text index 10, where we discover an overlap between the substring "ABABCABAB" and the sequence "ABABCABAB."
   

Applications of the algorithm

There are several applications of the Rabin Karp algorithm, some of which are discussed below:

1. Word processing: The rabin karp algorithm in data structure is used by many big search engines, to find the keywords and highlight them in bold letters.
2. Plagiarism detection: This algorithm is used to detect the copied text in a file and it instantly highlights the text that is copied and alerts the user for the presence of the copied text.
3. Data validation: Passwords, emails, and IP addresses can all be verified using string pattern-matching methods.
4. Bioinformatics: Variations in DNA sequences, which include genes or regulatory areas, can be found using string pattern matching techniques.
   

Rabin Karp: Complexity of Algorithm

Discussion on the time and space complexity of the Rabin Karp algorithm for string matching is as follows:

Time complexity:

• In the Rabin Karp algorithm, we calculate the hash value of the pattern with O(Np)times, and then for the hash value and to compare the corresponding hash value with that of the pattern O(Ns)times, we traverse the given string.
• So the time complexity of the Rabin Karp algorithm is O(Ns + Np), in which Ns and Np are the given string and patterns respectively.

Space complexity:

• In the Rabin Karp algorithm, there is constant space, therefore the space complexity is O(1).
  

Calculating the Hash Value in Rabin Karp

A hash value can be used to quickly see if a pattern matches any substrings in a longer text. A rolling hash function is used to generate the hash value. This function makes it possible to change the hash value for a new substring by quickly subtracting the old character's input and inserting the new character's contribution. This allows one to determine the hash value for every substring without having to recalculate the full hash by simply swiping the pattern over the text.

In Rabin Karp algorithm for pattern searching, the hash value is normally computed as follows:

Step 1: Select a modulus and the right base

The prime number p is selected as the modulus. This selection guarantees a good split of hash values and helps prevent overflow problems. Select a base "b," which is frequently the character set's size.

Step 2: Set the hash value to zero

The initial hash value "hash" should be set to 0.

Step 3: Determine the pattern's starting hash value

Proceed from left to right, iterating through every character in the pattern.

Determine the contribution of each character "c" at location "i" to the hash value using the formula "c * (bpattern_length – i – 1) % p" and add it to "hash." You now have the hash value for the complete pattern.

Step 4: Move the pattern across the text.

The hash code for the text's first substring that is exactly the same length as the pattern should be determined first.

Step 5: For each successive substring, change the hash value:

You remove the part of the leftmost element and add the new character's input on the right to change the sequence one position to the right. When going from location "i" to place "i+1," the hash value is updated using the following formula:

hash = (hash - (text[i - pattern_length] * (bpattern_length - 1)) % p) * b + text[i]

Step 6: Comparing hash values

A possible match occurs when the hash value of a subset in the text fits the hash value of the pattern. Because hash collisions can happen, you should verify the match character-by-character even if the hash values coincide.

Advantages

1. Best and most used algorithm used to find multiple patterns in the same text.
2. Works with different types of data like the same data in the common characters in the same input and the substrings.
3. For the detection of plagiarism in large datasets the Rabin Karp algorithm is used.
4. When used with the hash function, the Rabin Karp algorithm could easily be used for string matching.
   

Limitations

1. With the frequent hash collision, the Rabin Karp algorithm will have the worst time complexity.
2. The Rabin Karp algorithm is space-consuming, as it takes more space to store the hash value data.
3. Due to the predictability of the hash function being used in the Rabin Karp algorithm, it causes it to be a security concern.
4. Couldn’t be used by cryptography applications because of many security concerns.
5. The algorithms' worst-case complexity increases due to spurious hits. When the hash value of the pattern and the string are the same, but the string is different from the pattern, this is known as a bogus hit. To reduce spurious hits, we employ modulus.
   

Conclusion

The Rabin-Karp method is a string-matching technique that rapidly determines if a given pattern is found in a text by using a hash function. The primary benefit of the Rabin Karp algorithm is its ability to quickly determine whether a pattern occurs in a text without requiring the user to go through every possible location.

This makes it ideal for specific problem types, like scanning for plagiarism in a group of papers or finding a particular string in a large document.

FAQs

1. What is the Rabin-Karp algorithm in detail?

The Rabin-Karp algorithm works by calculating the hash value of a string that starts at that spot and has the same length as the pattern at each location in the text. A careful examination is made at that place if the hash value of this value and the pattern's hash value match.

2. What is the difference between the KMP and the Rabin-Karp algorithm?

Both KMP (Knuth-Morris-Pratt) and Rabin-Karp are string matching algorithms that use hash functions to find patterns in text. However, they differ in their implementation, reliability, and worst-case time complexity.

3. What is the difference between naive string matching and the Rabin-Karp algorithm?

The main difference between naive string matching and the Rabin-Karp algorithm is how they search for patterns in text. The naive algorithm uses a brute-force approach, comparing each character of the pattern to the corresponding text character. The Rabin-Karp algorithm uses a hash function to filter out characters that don't match before comparing characters.

4. What is the preprocessing of the Rabin-Karp algorithm?

Calculating hash(x) is the preprocessing step of the Karp-Rabin algorithm. It can be completed in O(m) time and constant space.

5. Why is the Rabin-Karp algorithm used?

Using a hash function is a string-matching technique that may quickly determine whether a given pattern appears in a text. The key benefit of the algorithm is that it can detect patterns in texts quickly and without the need to go over every location in the text.

6. Why is Rabin Karp used?

It's useful for problems like:

• Finding a string in a large document
• Detecting plagiarism in a set of papers
• Finding multiple patterns in the same text
• Working with multiple substrings

7. What is the limitation of the Rabin-Karp algorithm?

When hash collisions happen frequently, the Rabin-Karp algorithm may have the worst spatial complexity. When compared to other string-matching techniques, the complexity can reach O(M*N), which is not the ideal complexity. The hash value data is stored in excess space via the Rabin-Karp algorithm.

8. What are the advantages of the Rabin cryptosystem?

The main benefit of the Rabin cryptosystem is that should the codebreaker have the ability to calculate the public key n effectively, the entire ciphertext can be retrieved to a random plaintext. Stronger concepts of security are achieved with modifications to the Rabin cryptosystem.

9. What is the Rabin-Karp string-matching algorithm medium?

Matching the hashes of two strings can be completed in linear time and is significantly more effective than comparing each character of those strings to locate a match, Rabin-Karp improves on this idea.