A Parallel Skeleton for Divide-and-conquer Unbalanced and Deep Problems

Martínez, Millán A.; Fraguela, Basilio B.; Dominguez, Jessica A.

doi:10.1007/s10766-021-00709-y

Cited by 2 publications

(1 citation statement)

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“…For implicit execution, several optimizations have been proposed [46,47]. Optimizations based on techniques such as "work-stealing" were proposed, and they fit very well for of divide-and-conquer problems with a high degree of imbalance among the generated subproblems and/or a deep level of recurrence.…”

Section: Synchronization and Data Managementmentioning

confidence: 99%

On Generalizing Divide and Conquer Parallel Programming Pattern

Niculescu¹

2022

Mathematics

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(1) Background: Structuring is important in parallel programming in order to master its complexity, and this structuring could be achieved through programming patterns and skeletons. Divide-and-conquer computation is essentially defined by a recurrence relation that links the solution of a problem to the solutions of subproblems of the same type, but of smaller sizes. This pattern allows the specification of different types of computations, and so it is important to provide a general specification that comprises all its cases. We intend to prove that the divide-and-conquer pattern could be generalized such that to comprise many of the other parallel programming patterns, and in order to prove this, we provide a general formulation of it. (2) Methods: Starting from the proposed generalized specification of the divide-and-conquer pattern, the computation of the pattern is analyzed based on its stages: decomposition, base-case and composition. Examples are provided, and different execution models are analyzed. (3) Results: a general functional specification is provided for a divide-and-conquer pattern and based on it, and we prove that this general formulation could be specialized through parameters’ instantiating into other classical parallel programming patterns. Based on the specific stages of the divide-and-conquer, three classes of computations are emphasized. In this context, an equivalent efficient bottom-up computation is formally proved. Associated models of executions are emphasized and analyzed based on the three classes of divide-and-conquer computations. (4) Conclusion: A more general definition of the divide-and-conquer pattern is provided, and this includes an arity list for different decomposition degrees, a level of recursion, and also an alternative solution for the cases that are not trivial but allow other approaches (sequential or parallel) that could lead to better performance. Together with the associated analysis of patterns equivalence and optimized execution models, this provides a general formulation that is useful both at the semantic level and implementation level.

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Section: Synchronization and Data Managementmentioning

confidence: 99%

On Generalizing Divide and Conquer Parallel Programming Pattern

Niculescu¹

2022

Mathematics

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A highly optimized skeleton for unbalanced and deep divide-and-conquer algorithms on multi-core clusters

2022

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Efficiently implementing the divide-and-conquer pattern of parallelism in distributed memory systems is very relevant, given its ubiquity, and difficult, given its recursive nature and the need to exchange tasks and data among the processors. This task is noticeably further complicated in the presence of multi-core systems, where hybrid parallelism must be exploited to attain the best performance, and when unbalanced and deep workloads are considered, as additional measures must be taken to load balance and avoid deep recursion problems. In this manuscript a parallel skeleton that fulfills all these requirements while providing high levels of usability is presented. In fact, the evaluation shows that our proposal is on average 415.32% faster than MPI codes and 229.18% faster than MPI + OpenMP benchmarks, while offering an average improvement in the programmability metrics of 131.04% over MPI alternatives and 155.18% over MPI + OpenMP solutions.

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A Parallel Skeleton for Divide-and-conquer Unbalanced and Deep Problems

Cited by 2 publications

References 25 publications

On Generalizing Divide and Conquer Parallel Programming Pattern

On Generalizing Divide and Conquer Parallel Programming Pattern

A highly optimized skeleton for unbalanced and deep divide-and-conquer algorithms on multi-core clusters

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