Analyzing time-dimension communication characterizations for representative scientific applications on supercomputer systems

Abstract

Exascale computing is one of the major challenges of this decade, and several studies have shown that communications are becoming one of the bottlenecks for scaling parallel applications. The analysis on the characteristics of communications can effectively aid to improve the performance of scientific applications. In this paper, we focus on the statistical regularity in time-dimension communication characteristics for representative scientific applications on supercomputer systems, and then prove that the distribution of communication-event intervals has a power-law decay, which is common in scientific interests and human activities. We verify the distribution of communication-event intervals has really a power-lawdecay on the Tianhe-2 supercomputer, and also on the other six parallel systems with three different network topologies and two routing policies. In order to do a quantitative study on the power-law distribution, we exploit two groups of statistics: bursty vs. memory and periodicity vs. dispersion. Our results indicate that the communication events show a “strong-bursty and weak-memory” characteristic and the communication event intervals show the periodicity and the dispersion. Finally, our research provides an insight into the relationship between communication optimizations and time-dimension communication characteristics.

Keywords

power-law distributions / supercomputer systems / time-dimension communication characteristics / Tianhe-2

References

[1] Liao X K, Pang Z B, Wang K F, Lu Y T, Xie M, Xia J, Dong D Z, Suo G. High performance interconnect network for tianhe system. Journal of Computer Science and Technology, 2015, 30(2): 259–272

[2] Geist A, Lucas R. Major computer science challenges at exascale. The International Journal of High Performance Computing Applications, 2009, 23(4): 427–436

[3] Shao B B M, Rao H R. A parallel hypercube algorithm for discrete resource allocation problems. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2006, 36(1): 233–242

[4] Dongarra J J, Luszczek P, Petitet A. The linpack benchmark: past, present and future. Concurrency and Computation: Practice and Experience, 2003, 15(9): 803–820

[5] Li Y, Zhai J D, Li K Q. Communication analysis and performance prediction of parallel applications on large-scale machines. Innovative Research and Applications in Next-Generation High Performance Computing, 2016, 5: 80–105

[6] Yang X J, Du J, Wang Z Y. An effective speedup metric for measuring productivity in large-scale parallel computer systems. The Journal of Supercomputing, 2011, 56(2): 164–181

[7] Chen J, Tang Y H, Dong Y, Xue J L, Wang Z Y, and Zhou W H. Reducing static energy in supercomputer interconnection networks using topology-aware partitioning. IEEE Transactions on Computers, 2016, 65(8): 2588–2602

[8] Zhou W H, Chen J, Cui C, Wang Q, Dong D Z, Tang Y H. Detailed and clock-driven simulation for HPC interconnection network. Frontiers of Computer Science, 2016, 10(5): 797–811

[9] Raponi P G, Petrini F, Walkup R, Checconi F. Characterization of the communication patterns of scientific applications on blue gene/P. In: Proceedings of 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum. 2011, 1017–1024

[10] Almasi G, Asaad S, Bellofatto R E, Bickford H R, Blumrich M A, Brezzo B, Bright A A, Brunheroto J R, Castanos J G, Chen D. Overview of the IBM blue gene/p project. IBM Journal of Research and Development, 2008, 52(1–2): 199–220

[11] Landge A G, Levine J A, Bhatele A, Isaacs K E, Gamblin T, Schulz M, Langer S H, Bremer P T, Pascucci V. Visualizing network traffic to understand the performance of massively parallel simulations. IEEE Transactions on Visualization and Computer Graphics, 2012, 18(12): 2467–2476

[12] Yuan X, Mahapatra S, Lang M, Paki n S. LFTI: a new performance metric for assessing interconnect designs for extreme-scale HPC systems. In: Proceedings of the 28th International Parallel and Distributed Processing Symposium. 2014, 273–282

[13] Zhou W H, Chen J, Wang Z Y, Xu X H, Xu L Y, Tang Y H. Timedimension communication characterization of representative scientific applications on Tianhe-2. In: Proceedings of the 17th IEEE International Conference on High Performance Computing and Communications. 2015, 423–429

[14] Simon H A. On a class of skew distribution functions. Biometrika, 1955, 42(3/4): 425–440

[15] Mitzenmacher M. A brief history of generative models for power law and lognormal distributions. Internet Mathematics, 2004, 1(2): 226–251

[16] Newman M E J. Power laws, pareto distributions and Zipf’s law. Contemporary Physics, 2005, 46(5): 323–351

[17] Sornette D. Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools. Spnhger Science & Business Media, 2004

[18] Faloutsos M, Faloutsos P, Faloutsos C. On power-law relationships of the internet topology. ACM SIGCOMM Computer Communication Review, 1999, 29(4): 251–262

[19] Clauset A, Shalizi C R, Newman M E J. Power-law distributions in empirical data. SIAM Review, 2009, 51(4): 661–703

[20] Bailey D H, Barszcz E, Barton J T, Browning D S, Carter R L, Dagum L, Fatoohi R A, Frederickson P O, Lasinski T A, Schreiber R S, Simon H D, Venkatakrishnan V, Weeratunga S K. The nas parallel benchmarks. International Journal of High Performance Computing Applications, 1991, 5(3): 63–73

[21] Jasak H, Jemcov A, Tukovic Z. Openfoam: A C++ library for complex physics simulations. International Workshop on Coupled Methods in Numerical Dynamics, 2007, 1000: 1–20

[22] Accelerated Strategic Computing Initiative. The ASCI sweep3d benchmark code, 1995

[23] Kim J, Esler K, McMinis J, Clark B, Gergely J, Chiesa S, Delaney K, Vincent J, Ceperley D. QMCPACK simulation suite, 2014

[24] Plimpton S, Crozier P, Thompson A. Lammps-large-scale atomic/molecular massively parallel simulator. Sandia National Laboratories, 2007, 18: 43

[25] Berendsen H J C, van der Spoel D, van Drunen R. GROMACS: a message-passing parallel molecular dynamics implementation. Computer Physics Communications, 1995, 91(1): 43–56

[26] Zhai J D, Chen W G, Zheng W M. Phantom: predicting performance of parallel applications on large-scale parallel machines using a single node. ACM Sigplan Notices, 2010, 45(5): 305–314

[27] Gutenberg B, Richter C F. Frequency of earthquakes in california. Bulletin of the Seismological Society of America, 1944, 34(4): 185–188

[28] Neukum G, Ivanov B A. Crater size distributions and impact probabilities on earth from lunar, terrestrial-planet, and asteroid cratering data. Hazards due to Comets and Asteroids, 1994, 359–416

[29] Lu E T, Hamilton R J. Avalanches and the distribution of solar flares. The Astrophysical Journal, 1991, 380: L89–L92

[30] Roberts D C, Turcotte D L. Fractality and self-organized criticality of wars. Fractals, 1998, 6(4): 351–357

[31] Zipf G K. Human Behavior and The Principle of Least Effort. Addisonwesley Press, 1949, 1–721

[32] Estoup J B. Les Gammes StenographiquesInstitut Stenographique de France. Paris, 1916

[33] Zanette D H, Manrubia S C. Vertical transmission of culture and the distribution of family names. Physica A: Statistical Mechanics and its Applications, 2001, 295(1): 1–8

[34] Coile R C. Lotka’s frequency distribution of scientific productivity. Journal of the American Society for Information Science, 1977, 28(6): 366–370

[35] de Solla Price D J. Networks of scientific papers. Science, 1965, 149(3683): 510–515

[36] Cox R A K, Felton J M, Chung K H. The concentration of commercial success in popular music: an analysis of the distribution of gold records. Journal of Cultural Economics, 1995, 19(4): 333–340

[37] Kohli R, Sah R K. Market shares: some power law results and observations. Management Science, 2006, 52(11): 1792–1798

[38] Willis J C, Yule G U. Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature, 1922, 109(2728): 177–179

[39] Pareto V. Cours D’économie Politique. Librairie Droz, 1964, 1–429

[40] Adamic L A, Huberman B A. The nature of markets in the world wide Web. Quarterly Joural of Electronic Commerce, 2000, 1(1): 5–12

[41] Crovella M E, Bestavros A. Self-similarity in World Wide Web traffic: evidence and possible causes. IEEE/ACM Transactions on Networking, 1997, 5(6): 835–846

[42] Goh K I, Barabási A L. Burstiness and memory in complex systems. EPL (Europhysics Letters), 2008, 81(4): 48002

[43] Hidalgo R C A. Conditions for the emergence of scaling in the interevent time of uncorrelated and seasonal systems. Physica A: Statistical Mechanics and its Applications, 2006, 369(2): 877–883

[44] Zhou T, Zhao Z D, Yang Z M, Zhou C S. Relative clock verifies endogenous bursts of human dynamics. EPL (Europhysics Letters), 2012, 97(1): 18006

[45] Lee Rodgers J, Nicewander W A. Thirteen ways to look at the correlation coefficient. The American Statistician, 1988, 42(1): 59–66

[46] Legates D R, McCabe G J. Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation. Water Resources Research, 1999, 35(1): 233–241

[47] Engelen R V. Efficient symbolic analysis for optimizing compilers. In: Proceedings of the 10th International Conference on Compiler Construction. 2001, 118–132

[48] Kelefouras V, Kritikakou A, Goutis C. A methodology for speeding up loop kernels by exploiting the software information and the memory architecture. Computer Languages, Systems & Structure, 2015, 41: 21–41

[49] Liao X K, Xiao L Q, Yang C Q, Lu Y T. Milkyway-2 supercomputer: system and application. Frontiers of Computer Science, 2014, 8(3): 345–356

[50] Dally W J, Towles B P. Principles and Practices of Interconnection Networks. Elsevier, Amsterdam, 2004, 1–550

[51] Morgan J A, Tatar J F. Calculation of the residual sum of squares for all possible regressions. Technometrics, 1972, 14(2): 317–325

[52] Boccaletti S, Latora V, Moreno Y, Chavezf M, Hwang D U. Complex networks: structure and dynamics. Physics Reports, 2006, 424(4–5): 175–308

[53] Tabe T B, Stout Q F. The use of the MPI communication library in the NAS parallel benchmarks. Ann Arbor, 1999, 1001: 48109

[54] Malmgren R D, Stouffer D B, Motter A E, Amaral L A. A poissonian explanation for heavy tails in e-mail communication. Proceedings of the National Academy of Sciences, 2008, 105(47): 18153–18158.

[55] Kay S M, Marple Jr S L. Spectrum analysis — a modern perspective. Proceedings of the IEEE, 1981, 69(11): 1380–1419.

[56] Woodbury G. An Introduction to Statistics. Cengage Learning, 2001, 1–720

[57] Bland J M, Altman D G. Statistics notes: measurement error. Bmj, 1996, 313(7059): 744

[58] Gropp W, Lusk E, Skjellum A. Using MPI: Portable Parallel Programming with The Message-Passing Interface, Massachusetts: MIT press, 1999, 1–275

[59] Matsuda M, Kudoh T, Kodama Y, Takano R, Ishikawa Y. Efficient MPIcollective operations for clusters in long-and-fast networks. In: Proceedings of 2006 IEEE International Conference on Cluster Computing. 2006, 1–9

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