The pattern language is organized into four design spaces.  Generally one starts at the top in the Finding Concurrency design space and works down through the other design spaces in order until a detailed design for a parallel program is obtained.

Click on a design space name in the figure or list for more details.

Before starting to work with the patterns in this design space, the algorithm designer must first consider the problem to be solved and make sure the effort to create a parallel program will be justified: Is the problem sufficiently large, and the results sufficiently significant, to justify expending effort to solve it faster? If so, the next step is to make sure the key features and data elements within the problem are well understood. Finally, the designer needs to understand which parts of the problem are most computationally intensive, since it is on those parts of the problem that the effort to parallelize the problem should be focused.

Once this analysis is complete, the patterns in the Finding Concurrency  design space can be used to start designing a parallel algorithm. The patterns in this design space can be organized into three groups as shown in the figure.

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Nominally, the patterns are applied in this order. In practice, however, it is often necessary to work back and forth between them, or possibly even revisit the decomposition patterns.

After analyzing the concurrency in a problem, perhaps by using the patterns in the Finding Concurrency design space, the next task is to  refine the design and move it closer to a program that can execute tasks concurrently by mapping the concurrency onto multiple units of execution (UEs) running on a parallel computer.

Of the countless ways to define an algorithm structure, most follow one of six basic design patterns. These patterns make up the Algorithm Structure  design space.  The figure shows the patterns in the designs space and the relationship to the other spaces.

The key issue at this stage is to decide which pattern or patterns are most appropriate for the problem.  In making this decision, various forces such as simplicity, portability, scalability, and efficiency may pull the design in different directions.  The features of the target platform must also be taken into account.

There is usually a major organizing principle implied by the concurrency that helps choose a pattern. This usually falls into one of three categories:

The most effective parallel algorithm design may make use of multiple algorithm structures (combined hierarchically, compositionally, or in sequence). For example, it often happens that the very top level of the design is a sequential composition of one or more Algorithm Structure patterns. Other designs may be organized hierarchically, with one pattern used to organize the interaction of the major task groups and other patterns used to organize tasks within the groups -- for example, an instance of Pipeline in which individual stages are instances of Task Parallelism.

https://www.cise.ufl.edu/research/ParallelPatterns/overview.htm