Mathematica Model and Parallel Merge Sort Algorithms

The parallel computing is a currently revisited area due to the easy access to fast and inexpensive computing system and the emerging new commercial computing platform as Amazon EC2. Parallel algorithms are now in an increase use. Sorting parallel algorithms as Quick Sort, Merge Sort, and Inception sort are frequently used in many applications. Parallel Merger Sort has been studied in parallel computation but it has used in a common way distribution using a half partition strategy (n/2). This research developed a new technique to distribute the job in a considerable reduced number of processors. A mathematical model for the run-time was developed including computation cost. This model was used to create a tool to get the right balance between run-time vs numbers of processors. This model allows determine the numbers of processors needed to perform the job efficiently and low-cost.