# Decomposition techniques of parallel algorithm

Decomposition techniques are used to break down a problem into smaller, independent subproblems that can be solved concurrently in a parallel algorithm. Here are some common decomposition techniques used in parallel algorithm design:

1. Task Decomposition: In task decomposition, a problem is divided into a set of independent tasks that can be executed in parallel. Each task is assigned to a processor, and the results are combined to obtain the final solution. This technique is suitable for problems that can be naturally partitioned into independent subtasks.

2. Data Decomposition: In data decomposition, the problem is divided into subsets of data that can be processed independently and in parallel. Each processor is assigned a subset of data, and the results are combined to obtain the final solution. This technique is suitable for problems where the data can be partitioned into independent subsets.

3. Domain Decomposition: In domain decomposition, the problem is divided into smaller subdomains that can be processed independently in parallel. Each subdomain is assigned to a processor, and the results are combined to obtain the final solution. This technique is suitable for problems where the solution can be computed independently in different regions of the problem domain.

4. Function Decomposition: In function decomposition, the problem is divided into a set of functions that can be executed in parallel. Each function is assigned to a processor, and the results are combined to obtain the final solution. This technique is suitable for problems where the computations can be partitioned into independent functions.

5. Hybrid Decomposition: Hybrid decomposition involves combining multiple decomposition techniques to solve a problem in parallel. For example, task decomposition can be used to break down a problem into smaller tasks, and data decomposition can be used to partition the data within each task.

These decomposition techniques can be combined or modified to suit the specific requirements of the problem and the available parallel computing resources. The key to designing an efficient parallel algorithm is to select the appropriate decomposition technique and optimize it for the specific hardware architecture.