Question
Answer and Explanation
In Message Passing Interface (MPI), block division is a common technique for distributing data across multiple processes. It's a method where a dataset is partitioned into contiguous blocks, and each process is assigned one or more of these blocks. Let's explore how MPI typically performs this block division:
1. Understanding the Concept:
- Block division aims to divide a larger dataset into roughly equal, contiguous chunks. Each MPI process then works on its assigned block(s) independently, fostering parallel computation. This is in contrast to other partitioning schemes like cyclic division where elements are assigned in a round-robin manner.
2. Basic Approach:
- When you're dividing an array or a dataset with a fixed size, you typically start by calculating the size of each block. Let's say you have an array of N elements and P processes. A basic block size can be calculated using: blockSize = N / P. However, when N is not perfectly divisible by P, you will have a remainder. MPI deals with remainders by giving the extra elements to a some of the processes.
- The general process involves determining the starting index of each block in the original data. Process 0 gets the first block, process 1 the second, and so on.
3. Handling Remainders:
- When the number of elements N is not exactly divisible by the number of processes P, there will be a remainder. A common method to distribute this is by adding one additional element to the block size of the first N % P processes. For example if N=10 and P=3. Then we do 10/3=3.33 which means every block should be around 3. But we have a remainder of 1. So, the first process will get 4 (3+1), and the others 3.
4. Implementation in MPI:
- While MPI doesn't offer a built-in function that performs block distribution automatically, many operations make use of these concepts and therefore provide the tools for you to implement it. The basic mechanism involves:
- Calculating the local data boundaries based on process rank and the overall data size using manual calculations as shown above.
- Using MPI functions like MPI_Scatter, MPI_Scatterv, or MPI_Allgather. These are common for gathering and sending subsets of data.
- For manual distribution, each process uses its calculated range to determine the start and end indices of its data subset.
5. Example using pseudocode:
N = total_data_size;
P = number_of_processes;
myRank = MPI.Comm_rank();
blockSize = N / P;
remainder = N % P;
if (myRank < remainder) {
myBlockSize = blockSize + 1;
myStart = myRank myBlockSize;
} else {
myBlockSize = blockSize;
myStart = remainder (blockSize + 1) + (myRank - remainder) blockSize;
}
myEnd = myStart + myBlockSize;
6. Use Cases:
- Block division is commonly used in parallel array computations, matrix operations, image processing, and many other scientific simulations where data locality is important.
7. Advantages of Block Division:
- Simple to implement and understand.
- Good data locality, as each process has a contiguous chunk of the data.
- Reduces the overhead of scattering data, particularly when dealing with very large datasets.
In essence, MPI does not provide a single operation for block division; you implement it using the knowledge of your process ID and the total number of processes to calculate the chunks, this allows you to send data with MPI operations, to each process. By ensuring that the data is distributed as needed and using the proper MPI calls.