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1 10000 SFMOPT / / MOPT(Merge OPTimization) MOPT FMOPT(Fast MOPT) FMOPT SFMOPT(Subgrouping FMOPT) SFMOPT The Proposal and Evaluation of SFMOPT, a Task Mapping Method for Tasks Haruka Asano and Kenji Kise In recent years, computing systems which adopt mesh/torus network have appeared. Their communication time differs in where the positions of calculation tasks are located in such a direct network. Especially the positions of communicated tasks are important. The problem to determine the positions of all tasks is called a task mapping problem. The task mapping problem is complex because there are a lot of combinations. Therefore, it is difficult for the programmers to seek the best task mapping. We proposed a fast task mapping method MOPT (Merge OPTimization) before. In this paper, we propose FMOPT (Fast MOPT) which shortened the optimization time of MOPT using duplicate exclusions and parallelization. We also propose SFMOPT (Subgrouping FMOPT) which further accelerated FMOPT by introducing subgrouping. By using SFMOPT, we can optimize 8192 nodes in 31 seconds which had taken 2 hours before. 1. () / / Graduate School of Information Science and Engineering, Tokyo Institute of Technology 1), Jaguar 2) / () 1 ID MPI(Message Passing Interface) ID 2 3 / MPI c 2013 Information Processing Society of Japan 38

2 Iteration 0 Iteration 1 1 Iteration 2 Iteration 3 N N N! N 1 MOPT(Merge Optimization) 3) MOPT MOPT FMOPT FMOPT SFMOPT 2 MOPT 3 MOPT MOPT 2.1 / 1 (d) 2 (a) (b) MOPT (c) (f) 2.2 MOPT MOPT ( 2) MOPT 2 MOPT 2(a) 2(b) 0 2(c) c 2013 Information Processing Society of Japan 39

3 2 (1) G 1,G 2 s,t T raffic(s, t) s t Comm(G 1, G 2 ) = T raffic(s, t) (1) t G 2 s G 1 Eval Cost Eval Link 2 Eval Cost ( ) Eval Link XYZ Eval Cost MOPT MOPT mincost Eval Link MOPT MOPT minlink 2 2 X Y 3 X,Y,Z 3. MOPT 3.1 MOPT MOPT MOPT 8192 MOPT minlink 99.8% 98.5% 3.2 FMOPT MOPT FMOPT(Fast MOPT) FMOPT MOPT MOPT FMOPT MOPT MOPT 2 X,Y (3 X,Y,Z ) X Y (3 XY YZ ZX ) YZ X ZX Y XY Z MOPT 8 48 MOPT MOPT mincost Eval Cost 3 MOPT 3 3 ABC 3 abc A a X (1) Eval Cost (2) (8) (1) 90 (2) (4) (1) (4) Z (5) (8) (1) (2) (8) MOPT minlink MOPT mincost MOPT minlink XYZ XYZ c 2013 Information Processing Society of Japan 40

4 3 Eval Cost 4 Eval Link Eval Cost MOPT mincost 4 3 (1) Eval Link 3 (1) (8) (1) (6) (1)(6) Z (5)(2)Y (7)(4)Y Z (3)(8) A A A A A ( 1 ) A 2 2 (MOPT minlink ) ( 2 ) A 4 MOPT mincost 1/8MOPT minlink 1/4 3 MOPT 2 (G 1,G 2 ) X Y Z 1 MOPT mincost 2, MOPT minlink 3 MOPT mincost 6 1 G 1 G 2 X Y Z (FMOPT mincost) G 1 G 2 X /8 Y /4 Z /8 3 (FMOPT minlink) G 1 G 2 X /4 Y /4 Z /4 7 MOPT minlink 4 2 MOPT Z Z FMOPT 3.3 SFMOPT FMOPT MOPT FMOPT SFMOPT(Subgrouping MOPT) SFMOPT FMOPT SFMOPT 2 SFMOPT (1) c 2013 Information Processing Society of Japan 41

5 SFMOPT 2 3 SF- MOPT FMOPT SFMOPT FMOPT SFMOPT FMOPT SFMOPT D SFMOPT(D ) N 2 D O(1) O(1) O(N) O(N) FMOPT MOPT Intel Core i7 870 Linux gettimeofday() OpenMP MOPT MOPT MOPT( FMOPT) 6 6 FMOPT MOPT 2 3 FMOPT minlink 4 FMOPT mincost 5 8 FMOPT mincost MOPT FMOPT mincost FMOPT , c 2013 Information Processing Society of Japan 42

6 6 7 8 FMOPT Eval Link MOPT FMOPT SFMOPT SFMOPT 2 1 FMOPT 1 3 / XYZ XYZ None FMOPT FMOPT SFMOPT SFMOPT N FMOPT-half N FMOPT None FMOPT-half 2 1 FMOPT-half N N SFMOPT FMOPT-half 2 SFMOPT N SFMOPT FMOPT N FMOPT-half FMOPT 9 9 Eval Link FMOPT, SFMOPT, FMOPT-half FMOPT SFMOPT 9 9(512 ) FMOPT 547 SFMOPT 31 SFMOPT FMOPT-half FMOPT-half c 2013 Information Processing Society of Japan 43

7 9 10 (minlink) (mincost) SFMOPT 8192 SFMOPT FMOPT-half 1.1 FMOPT-half SFMOPT 10 Eval Cost FMOPT, SFMOPT, FMOPT-half Eval Link SF- MOPT FMOPT FMOPT-half Eval Cost Eval Link Eval Link Eval Link NAS Parallel Benchmark CGBT MGSP OpenNSIM 4) Eval Link 12 Eval Cost Eval Link 11 Eval Cost 12 XYZ Eval Link MG SFMOPT FMOPT XYZ SP FMOPT SFMOPT Eval Link 1 c 2013 Information Processing Society of Japan 44

8 MG FMOPTSFMOPT MG 3 XYZ XYZ MOPT 14 Eval Cost MG Eval Link FMOPT SFMOPT Eval Cost MG Eval Link XYZ 1 Eval Link 13 Eval Cost 14 MOPT MG 13 Eval Link MG FMOPTSFMOPTFMOPThalfNoneXYZ SFMOPT FMOPT-half SF- MOPT FMOPT 5% SFMOPT 14 Eval Cost SFMOPT FMOPT-halfNoneXYZ Eval Link CG SP SFMOPT FMOPT CG SP Eval Cost Eval Link Eval Link FMOPT SFMOPT (minlink) 14 (mincost) RMATT 5) RMATT BISEM Simulated annealing OPTIM BISEM SFMOPT BISEM SFMOPT BISEM SFMOPT 1 1 BISEM SFMOPT RMATT Simulated annealing RMATT RMATT 6) Simulated annealing 2 SFMOPT c 2013 Information Processing Society of Japan 45

9 RMATT BISEM SFMOPT 3 BlueGene/L 7) SFMOPT SFMOPT TAC3 8) RMATT Simulated annealing TAC3 SFMOPT 6. MOPT % SFMOPT MOPT 1% SFMOPT minlink 32%SF- MOPT mincost 67% MOPT FMOPT 512 SFMOPT minlink BluGene/Q 5 3 SFMOPT 2 3 MOPT (CREST) 1) Yokokawa, M., Shoji, F., Uno, A., Kurokawa, M. and Watanabe, T.: The K computer: Japanese next-generation supercomputer development project, International Symposium on Low Power Electronics and Design (ISLPED), pp (2011). 2) Bland, A. S., Kendall, R. A., Kothe, D. B., Rogers, J. H. and Shipman, G. M.: Jaguar: The world s most powerful computer, Cray User Group (2009). 3),, : /, D, Vol. J96-D, No. 2, pp (2013). 4),,,,,,,, : OpenNSIM, 2010-ARC-192(15), pp. 1 9 (2010). 5),,, : RMATT, SACSIS2011, pp (2011). 6),,,,,, : RMATT, 2012, pp (2012). 7) Bhanot, G., Gara, A., Heidelberger, P., Lawless, E., Sexton, J. and Walkup, R.: Optimizing task layout on the Blue Gene/L supercomputer, IBM Journal of Research and Development, Vol. 49, No. 2.3, pp (2005). 8), : /, 2013, pp (2013). c 2013 Information Processing Society of Japan 46

1., 1 COOKPAD 2, Web.,,,,,,.,, [1]., 5.,, [2].,,.,.,, 5, [3].,,,.,, [4], 33,.,,.,,.. 2.,, 3.., 4., 5., ,. 1.,,., 2.,. 1,,

1., 1 COOKPAD 2, Web.,,,,,,.,, [1]., 5.,, [2].,,.,.,, 5, [3].,,,.,, [4], 33,.,,.,,.. 2.,, 3.., 4., 5., ,. 1.,,., 2.,. 1,, THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE.,, 464 8601 470 0393 101 464 8601 E-mail: matsunagah@murase.m.is.nagoya-u.ac.jp, {ide,murase,hirayama}@is.nagoya-u.ac.jp,

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