Multilevel Algebraic Approach for Performance Analysis of Parallel Algorithms

Authors

  • Luisa D'Amore university of Naples Federico II, Naples
  • Valeria Mele Department of Mathematics and Applications R. Caccioppoli of University of Naples Federico II in Naples
  • Diego Romano Institute of High Performance Computing and Networking (ICAR), CNR, Naples
  • Giuliano Laccetti university of Naples Federico II, Naples

Keywords:

Complexity and performance of numerical algorithms, performance metrics, data decomposition, concurrency, parallel algorithms

Abstract

In order to solve a problem in parallel we need to undertake the fundamental step of splitting the computational tasks into parts, i.e. decomposing the problem solving. A whatever decomposition does not necessarily lead to a parallel algorithm with the highest performance. This topic is even more important when complex parallel algorithms must be developed for hybrid or heterogeneous architectures. We present an innovative approach which starts from a problem decomposition into parts (sub-problems). These parts will be regarded as elements of an algebraic structure and will be related to each other according to a suitably defined dependency relationship. The main outcome of such framework is to define a set of block matrices (dependency, decomposition, memory accesses and execution) which simply highlight fundamental characteristics of the corresponding algorithm, such as inherent parallelism and sources of overheads. We provide a mathematical formulation of this approach, and we perform a feasibility analysis for the performance of a parallel algorithm in terms of its time complexity and scalability. We compare our results with standard expressions of speed up, efficiency, overhead, and so on. Finally, we show how the multilevel structure of this framework eases the choice of the abstraction level (both for the problem decomposition and for the algorithm description) in order to determine the granularity of the tasks within the performance analysis. This feature is helpful to better understand the mapping of parallel algorithms on novel hybrid and heterogeneous architectures.

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Author Biographies

Luisa D'Amore, university of Naples Federico II, Naples

Professor of Numerical Computing Department of Mathematics and Applications R. Caccioppoli of University of Naples Federico II in Naples

Valeria Mele, Department of Mathematics and Applications R. Caccioppoli of University of Naples Federico II in Naples

Researcher at Department of Mathematics and Applications R. Caccioppoli of University of Naples Federico II in Naples

Diego Romano, Institute of High Performance Computing and Networking (ICAR), CNR, Naples

Researcher

Giuliano Laccetti, university of Naples Federico II, Naples

Professor of Computer Science Department of Mathematics and Applications R. Caccioppoli of University of Naples Federico II in Naples

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Published

2019-12-30

How to Cite

D’Amore, L., Mele, V., Romano, D., & Laccetti, G. (2019). Multilevel Algebraic Approach for Performance Analysis of Parallel Algorithms. COMPUTING AND INFORMATICS, 38(4), 817–850. Retrieved from http://www.cai.sk/ojs/index.php/cai/article/view/2019_4_817