Eigenanalysis-based task mapping on parallel computers with cellular networks
HTML articles powered by AMS MathViewer
- by Peng Zhang, Yuxiang Gao, Janet Fierson and Yuefan Deng;
- Math. Comp. 83 (2014), 1727-1756
- DOI: https://doi.org/10.1090/S0025-5718-2013-02770-6
- Published electronically: December 16, 2013
- PDF | Request permission
Abstract:
Through eigenanalysis of communication matrices, we develop a new objective function formulation for mapping tasks to parallel computers with cellular networks. This new formulation significantly speeds up the solution process through consideration of the symmetries in the supply matrix of a network and a transformation of the demand matrix of any application. The extent of the speedup is not easily obtainable through analytical means for most production networks. However, numerical experiments of mapping wave equations on 2D mesh onto 3D torus networks by simulated annealing demonstrate a far superior convergence rate and quicker escape from local minima with our new formulation than with the standard graph theory-based one.References
- Michael Affenzeller and Rene Mayrhofer, Generic heuristics for combinatorial optimization problems, Proc. of the 9th International Conference on Operational Research 2002, 2002, pp. 83–92.
- T. Agarwal, Amit Sharma, A. Laxmikant, and Laxmikant V. Kala, Topology-aware task mapping for reducing communication contention on large parallel machines, 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Proceedings, 25-29 April 2006, Rhodes Island, Greece, IEEE, 2006.
- George Almasi, Siddhartha Chatterjee, Alan Gara, John A. Gunnels, Manish Gupta, Amy Henning, Josa E. Moreira, and Robert Walkup, Unlocking the performance of the bluegene/l supercomputer, Proceedings of the ACM/IEEE SC2004 Conference on High Performance Networking and Computing, 6-12 November 2004, Pittsburgh, PA, USA, CD-Rom, IEEE Computer Society, 2004, p. 57.
- Gyan Bhanot, Alan Gara, Philip Heidelberger, Eoin Lawless, James C. Sexton, and Robert Walkup, Optimizing task layout on the blue gene/l supercomputer, IBM Journal of Research and Development 49 (2005), no. 2-3, 489–500. *4\baselineskip
- Shahid H. Bokhari, On the mapping problem, IEEE Trans. Comput. 30 (1981), no. 3, 207–214. MR 608522, DOI 10.1109/TC.1981.1675756
- Yongzhi Chen and Yuefan Deng, Task mapping on supercomputers with cellular networks, Computer Physics Communications 179 (2008), no. 7, 479–485.
- M.A.M. de Aguiar and Y. Bar-Yam, Spectral analysis and the dynamic response of complex networks, Physical Review E 71(1) (2005), 016106.
- Gerd Finke, Rainer E. Burkard, and Franz Rendl, Quadratic assignment problems, Surveys in combinatorial optimization (Rio de Janeiro, 1985) North-Holland Math. Stud., vol. 132, North-Holland, Amsterdam, 1987, pp. 61–82. MR 878775, DOI 10.1016/S0304-0208(08)73232-8
- S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, Optimization by simulated annealing, Science 220 (1983), no. 4598, 671–680. MR 702485, DOI 10.1126/science.220.4598.671
- Panos M. Pardalos, Franz Rendl, and Henry Wolkowicz, The quadratic assignment problem: a survey and recent developments, Quadratic assignment and related problems (New Brunswick, NJ, 1993) DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 16, Amer. Math. Soc., Providence, RI, 1994, pp. 1–42. MR 1290345, DOI 10.1090/dimacs/016/01
- P. Sadayappan and Fikret Eraal, Nearest-neighbor mapping of finite element graphs onto processor meshes, IEEE Transactions on Computers 36 (1987), no. 12, 1408–1424.
- Peter Salamon, Paolo Sibani, and Richard Frost, Facts, conjectures, and improvements for simulated annealing, SIAM Monographs on Mathematical Modeling and Computation, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. MR 1945007, DOI 10.1137/1.9780898718300
- Oliver Sinnen, Task scheduling for parallel systems (Wiley series on parallel and distributed computing), Wiley-Interscience, 2007.
- Brian E. Smith and Brett Bode, Performance effects of node mappings on the IBM bluegene/l machine, Euro-Par 2005, Parallel Processing, 11th International Euro-Par Conference, Lisbon, Portugal, August 30 - September 2, 2005, Proceedings (Josa C. Cunha and Pedro D. Medeiros, eds.), Lecture Notes in Computer Science, vol. 3648, Springer, 2005, pp. 1005–1013.
- M. R. F. Smyth, A spectral theoretic proof of Perron-Frobenius, Math. Proc. R. Ir. Acad. 102A (2002), no. 1, 29–35. MR 1930810, DOI 10.3318/PRIA.2002.102.1.29
- Lee Soo-Young and J.K. Aggarwal, A mapping strategy for parallel processing, IEEE Transactions on Computers 36 (1987), 433–442.
- Hao Yu, I-Hsin Chung, and Josa E. Moreira, Blue gene system software - topology mapping for blue gene/l supercomputer, Proceedings of the ACM/IEEE SC2006 Conference on High Performance Networking and Computing, November 11-17, 2006, Tampa, FL, USA, ACM Press, 2006, p. 116.
Bibliographic Information
- Peng Zhang
- Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
- Email: Peng.Zhang@stonybrook.edu
- Yuxiang Gao
- Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
- Email: Yuxiang.Gao@stonybrook.edu
- Janet Fierson
- Affiliation: Department of Mathematics and Computer Science, La Salle University, Philadelphia, Pennsylvania 19141
- ORCID: 0000-0001-5138-6917
- Email: fierson@lasalle.edu
- Yuefan Deng
- Affiliation: Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794
- Email: Yuefan.Deng@stonybrook.edu
- Received by editor(s): October 18, 2010
- Received by editor(s) in revised form: August 26, 2011, and November 17, 2012
- Published electronically: December 16, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 83 (2014), 1727-1756
- MSC (2010): Primary 68M10, 90C06, 90C20, 90C35; Secondary 68M07, 90C90, 65B99, 15A63, 15A18
- DOI: https://doi.org/10.1090/S0025-5718-2013-02770-6
- MathSciNet review: 3194128