Question
Answer and Explanation
The Knuth-Morris-Pratt (KMP) algorithm is a string-searching algorithm known for its efficiency in finding occurrences of a pattern within a text. However, the standard KMP algorithm is inherently sequential. To parallelize it using OpenMP, you need to identify which parts of the algorithm can be executed concurrently.
The core of the KMP algorithm involves two phases:
1. Prefix Table Generation (LPS Array): This step calculates the Longest Proper Prefix which is also a Suffix (LPS) array, which helps to avoid unnecessary comparisons during the search phase.
2. String Searching: This step utilizes the LPS array to efficiently search for the pattern within the text.
Parallelization of these phases:
1. Parallelizing Prefix Table Generation (LPS): Unfortunately, generating the LPS table is typically not parallelizable because the computation of each entry depends on the preceding entries. This phase must remain sequential. The standard KMP algorithm uses a single loop for building LPS array.
2. Parallelizing String Searching: The main search loop can be parallelized. The text can be divided into chunks, and each chunk can be searched by a separate thread. However, care must be taken to handle edge cases where a pattern occurrence may span across chunk boundaries. A simple, yet efficient approach is to use overlapping chunks for search.
Here is a conceptual overview of how the search phase can be parallelized using OpenMP:
#include <omp.h>
#include <iostream>
#include <vector>
#include <string>
// Function to compute the LPS array (sequential)
std::vector<int> computeLPS(const std::string& pattern) {
// ... LPS calculation code ...
return lps;
}
// Function to perform KMP search in a chunk of text
void kmpSearch(const std::string& text, const std::string& pattern, const std::vector<int>& lps, int start, int end, std::vector<int>& results) {
int n = text.length();
int m = pattern.length();
int i = start, j = 0;
while (i < end) {
if (pattern[j] == text[i]) {
j++;
i++;
}
if (j == m) {
results.push_back(i - j);
j = lps[j - 1];
} else if (i < end && pattern[j] != text[i]) {
if (j != 0) {
j = lps[j - 1];
} else {
i++;
}
}
}
}
int main() {
std::string text = "ABABDABACDABABCABAB";
std::string pattern = "ABABCABAB";
std::vector<int> lps = computeLPS(pattern);
int numThreads = 4; // Set the number of threads
int chunkSize = text.length() / numThreads; // size of each chunk
std::vector<std::vector<int>> threadResults(numThreads);
#pragma omp parallel num_threads(numThreads)
{
int threadId = omp_get_thread_num();
int start = threadId chunkSize; // Start index of chunk
int end = (threadId == numThreads - 1) ? text.length() : start + chunkSize + pattern.length() - 1; // End index of chunk considering pattern overlap.
kmpSearch(text, pattern, lps, start, end, threadResults[threadId]); // Execute search in each chunk
}
//Merge thread results into one output
std::vector<int> finalResults;
for (const auto& res : threadResults) {
finalResults.insert(finalResults.end(), res.begin(), res.end());
}
std::cout << "Pattern found at indices: ";
for (int index : finalResults) {
std::cout << index << " ";
}
std::cout << std::endl;
return 0;
}
Key Considerations:
Chunk Overlap: In the provided example, an overlap equal to the length of the pattern is included. This is important to find patterns spanning chunk boundaries. This might mean more work is done, but correct results must be ensured.
Thread Safety: The searching part is generally thread-safe because each thread works on its own section of the text. The output, however, needs careful merging or appending (see example).
Overhead: Using threads does introduce some overhead. The performance benefit comes when the size of the text is large enough to justify the thread creation and management costs.
In summary, while the LPS calculation in the KMP algorithm cannot be easily parallelized, the search process can be effectively parallelized using OpenMP by partitioning the text and having each thread perform the KMP search on its section, including handling edge-cases around search chunks.