Model-Driven Approach for Supporting the Mapping of Parallel Algorithms to Parallel Computing Platforms

Abstract

Abstract. The trend from single processor to parallel computer architectures has increased the importance of parallel computing. To support parallel computing it is important to map parallel algorithms to a computing platform that consists of multiple parallel processing nodes. In general different alternative mappings can be defined that perform differently with respect to the quality requirements for power consumption, efficiency and memory usage. The mapping process can be carried out manually for platforms with a limited number of processing nodes. However, for exascale computing in which hundreds of thousands of processing nodes are applied, the mapping process soon becomes intractable. To assist the parallel computing engineer we provide a model-driven approach to analyze, model, and select feasible mappings. We describe the developed toolset that implements the corresponding approach together with the required metamodels and model transformations. We illustrate our approach for the well-known complete exchange algorithm in parallel computing.

Systematic approach for deriving feasible mappings of parallel algorithms to parallel computing platforms

“…Usually, the adopted problem is decomposed into multiple sub-problems that are then computed in parallel. In the first section, the subdivision matrix elements are multiplied (lines [2][3][4]. For different kinds of problems, different parallel algorithms have been defined that can be executed simultaneously on multiple nodes.…”

“…The concurrent execution of the problem usually leads to a better time performance compared with the serial computation of the problem. The second section is the recursive multiplication of each subsection (lines [5][6][7][8][9][10][11][12]. To illustrate the mapping of a parallel algorithm to a parallel computing platform, we will use the parallel matrix multiplication algorithm with subdivisions [22].…”

“…In the first section, the subdivision matrix elements are multiplied (lines [2][3][4]. The second section is the recursive multiplication of each subsection (lines [5][6][7][8][9][10][11][12]. The third section is the summation of the resulting subdivision matrices for the recursive multiplication (lines [13][14][15][16].…”

Architecture Framework for Modeling the Deployment of Parallel Applications on Parallel Computing Platforms

“…Typically, for the same physical configuration we can have many different logical configurations each of them indicating different communication and exchange patterns of data among the cores in the nodes. In our earlier paper we define an approach for deriving the feasible logical configurations with respect to speed-up and efficiency metrics [1]. In this paper we assume that a feasible logical configuration is selected.…”

“…For more details about the scaling process we refer to our earlier paper [1]. The number of cores should be equal to the processing units in the physical configuration The numbering of the cores should match the numbering in the physical configuration Notation Core n,p Dominating Core n -the id of the node in the physical configuration p -the id of the processing unit in the physical configuration n,p…”