By Victor Malyshkin
This publication constitutes the court cases of the thirteenth foreign convention on Parallel Computing applied sciences, PaCT 2015, held in Petrozavodsk, Russia, in the course of August / September 2015. The 37 complete papers and 14 brief papers awarded have been conscientiously reviewed and chosen from 87 submissions. The papers are prepared in topical sections on parallel types, algorithms and programming equipment; unconventional computing; mobile automata; dispensed computing; precise processors programming concepts; applications.
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Additional info for Parallel Computing Technologies: 13th International Conference, PaCT 2015, Petrozavodsk, Russia, August 31-September 4, 2015, Proceedings
This approach has been successfully applied to the most popular parallel matrix multiplication algorithm, SUMMA, and the state-of-the-art MPI broadcast algorithms, demonstrating signiﬁcant multi-fold performance gains, especially for large-scale HPC systems. In this paper, we apply this approach to optimization of the MPI reduce operation. Theoretical analysis and experimental results on a cluster of Grid’5000 platform are presented. Keywords: MPI 1 · Reduce · Grid’5000 · Communication · Hierarchy Introduction Reduce is important and commonly used collective operation in the Message Passing Interface (MPI) .
Then, the operation continues groups happen between G between G groups. The cost of the reduce operations inside groups and between p − 1)×(α + m×β + m×γ) groups will be (G − 1)×(α + m×β + m×γ) and ( G respectively. Thus, the overall run time can be seen as a function of G: p (8) F (G) = G + − 2 × (α + m×β + m×γ) G The derivative of the function is (1 − Gp2 )×(α + m×β + m×γ), it can be shown √ that p = G is the minimum point of the function in the interval (1, p). Then the optimal value of the function will be as follows: √ √ (9) F ( p) = (2 p − 2) × (α + m×β + m×γ) 26 K.
An important condition for the high performance computing consists in the matching the arithmetic calculations and data communications between the subdomains by using MPI unblocked send-receive means. Moreover, the volume of the data transfer is very small as only the short vectors corresponding to the number of grid ponits on mutual boundary between the subdomains should be exchasnged. Let us note that for the examined grid boundary value problems, a twodimensional balanced domain decomposition into subdomains is considered, when for an approximately equal number of nodes NS ≈ N/P in every subdomain the macrogrid daimeter √ d (for a macrogrid composed of subdomains) is equal, approximately, to P .