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International Congress on Mathematical Software

ICMS 2016: Mathematical Software – ICMS 2016 pp 265–274Cite as

Advanced Computing and Optimization Infrastructure for Extremely Large-Scale Graphs on Post Peta-Scale Supercomputers

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9725))

Abstract

In this talk, we present our ongoing research project. The objective of this project is to develop advanced computing and optimization infrastructures for extremely large-scale graphs on post peta-scale supercomputers. We explain our challenge to Graph 500 and Green Graph 500 benchmarks that are designed to measure the performance of a computer system for applications that require irregular memory and network access patterns. The 1st Graph500 list was released in November 2010. The Graph500 benchmark measures the performance of any supercomputer performing a BFS (Breadth-First Search) in terms of traversed edges per second (TEPS). In 2014 and 2015, our project team was a winner of the 8th, 10th, and 11th Graph500 and the 3rd to 6th Green Graph500 benchmarks, respectively. We also present our parallel implementation for large-scale SDP (SemiDefinite Programming) problem. The semidefinite programming (SDP) problem is a predominant problem in mathematical optimization. The primal-dual interior-point method (PDIPM) is one of the most powerful algorithms for solving SDP problems, and many research groups have employed it for developing software packages. We solved the largest SDP problem (which has over 2.33 million constraints), thereby creating a new world record. Our implementation also achieved 1.774 PFlops in double precision for large-scale Cholesky factorization using 2,720 CPUs and 4,080 GPUs on the TSUBAME 2.5 supercomputer.

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Notes

  1. 1.

    http://www.graph500.org.

  2. 2.

    http://green.graph500.org.

  3. 3.

    http://sdpa.sourceforge.net/.

References

  1. Beamer, S., Asanović, K., Patterson, D.A.:Searching for a parent instead of fighting over children: a fast breadth-first search implementation for Graph500. EECS Department, University of California, Berkeley, CA, UCB/EECS-2011-117 (2011)

    Google Scholar 

  2. Beamer, S., Asanović, K., Patterson, D.A.: Direction-optimizing breadth-first search. In: Proceedings of ACM/IEEE International Conference High Performance Computing, Networking, Storage and Analysis (SC12). IEEE Computer Society (2012)

    Google Scholar 

  3. Yoo, A., Chow, E., Henderson, K., McLendon, W., Hendrickson, B., Catalyurek, U.: A scalable distributed parallel breadth-first search algorithm on BlueGene/L. In: Proceedings of the 2005 ACM/IEEE Conference on Supercomputing, ser. SC 2005, pp. 25–43. IEEE Computer Society (2005)

    Google Scholar 

  4. Checconi, F., Petrini, F., Willcock, J., Lumsdaine, A., Choudhury, A.R., Sabharwal, Y.: Breaking the speed and scalability barriers for graph exploration on distributed-memory machines. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, ser. SC 2012, pp. 13:1–13:12. IEEE Computer Society Press (2012)

    Google Scholar 

  5. Satish, N., Kim, C., Chhugani, J., Dubey, P.: Large-scale energy efficient graph traversal: a path to efficient data-intensive supercomputing. In: Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis, ser. SC 2012, pp. 14:1–14:11. IEEE Computer Society Press (2012)

    Google Scholar 

  6. Checconi, F., Petrini, F.: Traversing trillions of edges in real time: graph exploration on large-scale parallel machines. In: Proceeding of IEEE 28th International Parallel and Distributed Processing Symposium, ser. IPDPS 2014, pp. 425–434. IEEE (2014)

    Google Scholar 

  7. Yamashita, M., Fujisawa, K., Kojima, M.: SDPARA: semidefinite programming algorithm parallel version. J. Parallel Comput. 29(8), 1053–1067 (2003)

    Article  MathSciNet  Google Scholar 

  8. Nakata, M., Fukuda, M., Fujisawa, K.: Variational approach to electronic structure calculations on second-order reduced density matrices and the \(N\)-representability problem. In: Siedentop, H. (ed.), Complex Quantum Systems - Analysis of Large Coulomb Systems, Institute of Mathematical Sciences, National University of Singapore, pp. 163–194 (2013)

    Google Scholar 

  9. Fujisawa, K., Endo, T., Sato, H., Yamashita, M., Matsuoka, S., Nakata, M.: High-performance general solver for extremely large-scale semidefinite programming problems. In: Proceedings of the 2012 ACM/IEEE Conference on Supercomputing, SC 2012 (2012)

    Google Scholar 

  10. Fujisawa, K., Endo, T., Sato, H., Yasui, Y., Matsuzawa, N., Waki, H.: Peta-scale general solver for semidefinite programming problems with over two million constraints. In: International Conference for High Performance Computing, Networking, Storage and Analysis 2013, SC 2013 Regular, Electronic, and Educational Poster (SC 2013) (2013)

    Google Scholar 

  11. Fujisawa, K., Endo, T., Yasui, Y., Sato, H., Matsuzawa, N., Matsuoka, S., Waki, H.: Peta-scale general solver for semidefinite programming problems with over two million constraints. In: The 28th IEEE International Parallel & Distributed Processing Symposium (IPDPS 2014) (2014)

    Google Scholar 

  12. Iwabuchi, K., Sato, H., Mizote, R., Yasui, Y., Fujisawa, K., Matsuoka, S.: Hybrid BFS approach using semi-external memory. In: International Workshop on High Performance Data Intensive Computing (HPDIC2014) in Conjunction with IEEE IPDPS 2014 (2014)

    Google Scholar 

  13. Iwabuchi, K., Sato, H., Yasui, Y., Fujisawa, K., Matsuoka, S.: NVM-based Hybrid BFS with memory efficient data structure. In: The Proceedings of the IEEE BigData2014 (2014)

    Google Scholar 

  14. Iwabuchi, K., Sato, H., Yasui, Y., Fujisawa, K.: Performance analysis of hybrid BFS approach using semi-external memory. In: International Conference for High Performance Computing, Networking, Storage and Analysis, SC 2013 Regular, Electronic, and Educational Poster (SC 2013) (2013)

    Google Scholar 

  15. Suzumura, T., Ueno, K., Sato, H., Fujisawa, K., Matsuoka, S.: A performance characteristics of Graph500 on large-scale distributed environment. In: The Proceedings of the 2011 IEEE International Symposium on Workload Characterization (2011)

    Google Scholar 

  16. Ueno, K., Suzumura, T.: Highly scalable graph search for the Graph500 benchmark. In: The 21st International ACM Symposium on High-Performance Parallel and Distributed Computing, HPDC 2012. Delft, Netherlands (2012)

    Google Scholar 

  17. Yamashita, M., Fujisawa, K., Fukuda, M., Kobayashi, K., Nakata, K., Nakata, M.: Latest developments in the SDPA family for solving large-scale SDPs. In: Anjos, M.F., Lasserre, J.B. (eds.) Handbook on Semidefinite, Conic and Polynomial Optimization, International Series in Operations Research & Management Science. Springer, Heidelberg (2011)

    Google Scholar 

  18. Yamashita, M., Fujisawa, K., Fukuda, M., Nakata, K., Nakata, M.: Parallel solver for semidefinite programming problem having sparse Schur complement matrix. The ACM Trans. Math. Softw. 39(12), 6 (2012)

    MathSciNet  MATH  Google Scholar 

  19. Yasui, Y., Fujisawa, K., Goto, K.: NUMA-optimized parallel breadth-first search on multicore single-node system. In: The Proceedings of the IEEE BigData2013 (2013)

    Google Scholar 

  20. Yasui, Y., Fujisawa, K., Goto, K., Kamiyama, N., Takamatsu, M.: NETAL: high-performance implementation of network analysis library considering computer memory hierarchy. J. Oper. Res. Soc. Jpn. 54(4), 259–280 (2011)

    MathSciNet  MATH  Google Scholar 

  21. Yasui, Y., Fujisawa, K., Sato, Y.: Fast and energy-efficient breadth-first search on a single NUMA system. In: Kunkel, J.M., Ludwig, T., Meuer, H.W. (eds.) ISC 2014. LNCS, vol. 8488, pp. 365–381. Springer, Heidelberg (2014)

    Google Scholar 

  22. Yasui, Y., Fujisawa, K.: Fast and scalable NUMA-based thread parallel breadth-first search. In: The 2015 International Conference on High Performance Computing & Simulation (HPCS 2015) (2015). doi:10.1109/HPCSim.2015.7237065

  23. Tsujita, Y., Endo, T., Fujisawa, K.: The scalable petascale data-driven approach for the cholesky factorization with multiple GPUs. In: First International Workshop on Extreme Scale Programming Models and Middleware. In Conjunction with International Conference for High Performance Computing, Networking, Storage and Analysis (SC 2015) (2015). doi:10.1145/2832241.2832245

  24. Fujisawa, K., et al.: Advanced computing & optimization infrastructure for extremely large-scale graphs on post peta-scale supercomputers. In: Fujisawa, K., Shinano, Y., Waki, H. (eds.) Optimization in the Real World: Toward Solving Real-World Optimization Problems. Mathematics for Industry. Springer, Heidelberg (2015). doi:10.1007/978-4-431-55420-2_1

    Google Scholar 

  25. Yasui, Y., Fujisawa, K.: NUMA-aware scalable graph traversal on SGI UV systems. In: The Proceedings of 1st High Performance Graph Processing Workshop. In Conjunction with The International ACM Symposium on High-Performance Parallel and Distributed Computing (HPDC 2016) (2016)

    Google Scholar 

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Acknowledgment

This research project was supported by the Japan Science and Technology Agency (JST), the Core Research of Evolutionary Science and Technology (CREST), the Center of Innovation Science and Technology based Radical Innovation and Entrepreneurship Program (COI Program), the TSUBAME 2.0 & 2.5 Supercomputer Grand Challenge Program at the Tokyo Institute of Technology, and “Advanced Computational Scientific Program” of Research Institute for Information Technology, Kyushu University.

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Authors and Affiliations

  1. The Institute of Mathematics for Industry, Kyushu University & JST CREST, Fukuoka, Japan

    Katsuki Fujisawa

  2. Global Scientific Information and Computing Center, Tokyo Institute of Technology & JST CREST, Tokyo, Japan

    Toshio Endo

  3. Center for Co-Evolutional Social Systems, Kyushu University & JST COI, Fukuoka, Japan

    Yuichiro Yasui

Authors
  1. Katsuki Fujisawa
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  2. Toshio Endo
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  3. Yuichiro Yasui
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Corresponding author

Correspondence to Katsuki Fujisawa .

Editor information

Editors and Affiliations

  1. Universität Kaiserslautern , Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Zuse Institute Berlin , Berlin, Germany

    Thorsten Koch

  3. Johannes Kepler University Linz , Hagenberg, Austria

    Peter Paule

  4. University of Notre Dame , Notre Dame, Indiana, USA

    Andrew Sommese

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Fujisawa, K., Endo, T., Yasui, Y. (2016). Advanced Computing and Optimization Infrastructure for Extremely Large-Scale Graphs on Post Peta-Scale Supercomputers. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_33

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  • DOI: https://doi.org/10.1007/978-3-319-42432-3_33

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  • Online ISBN: 978-3-319-42432-3

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