# Designing Parallel Algorithms: Part 3

Editor's Note: This multi-part are on parallel algorithm design is based on the book Designing and Building Parallel Programs by Ian Foster. Designing and Building Parallel Programs promotes a view of parallel programming as an engineering discipline, in which programs are developed in a methodical fashion and both cost and performance are considered in a design. Part 1 focuses on the topics of Methodical Design and Partitioning. Subsequent installments will focus on Communication, Agglomeration, and Mapping, before finally examining case studies of parallel algorithms in action.

### Agglomeration

In the first two stages of the design process, we partitioned the computation to be performed into a set of tasks and introduced communication to provide data required by these tasks. The resulting algorithm is still abstract in the sense that it is not specialized for efficient execution on any particular parallel computer. In fact, it may be highly inefficient if, for example, it creates many more tasks than there are processors on the target computer and this computer is not designed for efficient execution of small tasks.

In the third stage, agglomeration, we move from the abstract toward the concrete. We revisit decisions made in the partitioning and communication phases with a view to obtaining an algorithm that will execute efficiently on some class of parallel computer. In particular, we consider whether it is useful to combine, or agglomerate, tasks identified by the partitioning phase, so as to provide a smaller number of tasks, each of greater size (Figure 11). We also determine whether it is worthwhile to replicate data and/or computation.

Figure 11: Examples of agglomeration. In (a), the size of tasks is increased by reducing the dimension of the decomposition from three to two. In (b), adjacent tasks are combined to yield a three-dimensional decomposition of higher granularity. In (c), subtrees in a divide-and-conquer structure are coalesced. In (d), nodes in a tree algorithm are combined.

The number of tasks yielded by the agglomeration phase, although reduced, may still be greater than the number of processors. In this case, our design remains somewhat abstract, since issues relating to the mapping of tasks to processors remain unresolved. Alternatively, we may choose during the agglomeration phase to reduce the number of tasks to exactly one per processor. We might do this, for example, because our target parallel computer or program development environment demands an SPMD program. In this case, our design is already largely complete, since in defining P tasks that will execute on P processors, we have also addressed the mapping problem. In this section, we focus on general issues that arise when increasing task granularity.

Three sometimes-conflicting goals guide decisions concerning agglomeration and replication: reducing communication costs by increasing computation and communication granularity, retaining flexibility with respect to scalability and mapping decisions, and reducing software engineering costs. These goals are discussed in the next three subsections.

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