Can a Single Program Like Merge Sort Be Utilized on Multiple Processors?

Merge sort is a well-known and efficient sorting algorithm that is used in a variety of applications. It is a divide-and-conquer algorithm that recursively splits the input array into smaller parts, sorts them, and then merges them back together. Many developers and researchers often wonder if merge sort can be adapted for use in multi-processor systems. This article will explore the feasibility of utilizing merge sort on multiple processors and provide some clues on how this can be achieved.

Understanding Merge Sort

Merge sort operates by recursively dividing the input array into two halves until the smallest subarrays are obtained. These subarrays are then merged back together in a sorted order. The time complexity of merge sort is O(n log n), making it an ideal choice for large datasets. However, the traditional merge sort algorithm is single-threaded and, as such, may not be fully leveraged in multi-core or multi-processor environments.

Parallel Processing in Multi-Processor Systems

In many modern computing environments, multiple processors or cores are available. These processors can independently execute tasks and can perform operations in parallel, significantly improving performance. Utilizing parallel processing involves dividing the workload among multiple processors, allowing them to work on different parts of the input data simultaneously. This can significantly speed up the execution of the algorithm.

Adapting Merge Sort for Multi-Processor Utilization

Adapting merge sort to multi-processor systems involves several key steps. The first step is to divide the input array into subarrays that can be processed in parallel. Each subarray can be sorted independently using a single-threaded merge sort algorithm. Once sorted, these subarrays can be merged together. The merge step is where the challenge lies, as it requires synchronization to ensure that the results are combined correctly.

Dividing the Workload

One common approach to dividing the workload is to use a divide-and-conquer strategy, similar to the traditional merge sort. The input array is recursively divided into smaller subarrays until the size of the subarrays is small enough to be efficiently sorted by a single thread. This can involve using a divide factor based on the number of available processors.

Sorting Subarrays in Parallel

Each subarray is then sorted independently using a single-threaded merge sort algorithm. This can be achieved by dividing the sorting task among multiple threads or processes. Each thread or process is responsible for sorting a portion of the input array. This step can be parallelized using thread pools or process pools, depending on the multi-processor system in use.

Merging Subarrays in Parallel

Once all subarrays have been sorted, they need to be merged back together. The challenge here is that the merge step requires synchronization to ensure that the results are combined in the correct order. This can be achieved using parallel merge algorithms, such as the parallel merge algorithm described in the research paper by Aggarwal and Varghese (1997). These algorithms use a divide-and-conquer strategy to merge the subarrays in parallel, while ensuring that the results are correctly combined.

Example Implementation

To illustrate the adaptation of merge sort for multi-processor systems, we can refer to the github repository mentioned in the prompt. This implementation showcases how merge sort can be adapted to utilize multiple processors. The repository provides a clear example of how the input array is divided, sorted subarrays are processed, and the results are merged together.

Conclusion

In conclusion, it is indeed possible to adapt the merge sort algorithm for use in multi-processor systems. While it requires careful management of the workload division and synchronization during the merge step, the benefits of parallel processing can lead to significant improvements in performance. The example repository provided gives a practical demonstration of this concept, and can serve as a starting point for further exploration.

References

Aggarwal, A., Varghese, G. (1997). Parallel Merge: A Persistent Problem. Proceedings of the ACM SIGMOD International Conference on Management of Data.