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Parallel Processing and Applied Mathematics pp 101–110Cite as

Accelerating the Min-Min Heuristic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9574))

Abstract

Min-Min is a classical heuristic for scheduling tasks to heterogeneous computational resources, which has been applied either directly or as part of more sophisticated heuristics. The time complexity of the direct implementation of Min-Min is \(O(mn^2)\) for scheduling n tasks on m machines. This has motivated the use of simpler heuristics and parallel implementations of Min-Min for the sake of acceptable runtimes in large scenarios. Recently, we have proposed an efficient algorithm for computing Min-Min, whose time complexity is O(mn). In this work, we study mult-many core versions of this new algorithm. The experimental evaluation of our proposal shows important runtime reductions compared to the sequential version.

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Notes

  1. 1.

    The time complexity is O(mn) for fixed numeric precision implementations.

  2. 2.

    The real available free memory is 4.92 GB.

References

  1. Baxter, S.: Modern gpu. http://nvlabs.github.io/moderngpu/. Accessed April 2015

  2. Braun, T.D., Siegel, H.J., Beck, N., Bölöni, L.L., Maheswaran, M., Reuther, A.I., Robertson, J.P., Theys, M.D., Yao, B., Hensgen, D., Freund, R.F.: A comparison of eleven static heuristics for mapping a class of independent tasks onto heterogeneous distributed computing systems. J. Parallel Distrib. Comput. 61(6), 810–837 (2001)

    Article  MATH  Google Scholar 

  3. Canabé, M., Nesmachnow, S.: Parallel implementations of the MinMin heterogeneous computing scheduler in GPU. In: V Latin American Symposium on High Performance Computing. HPCLatam (2012). www.clei.cl/cleiej/papers/v15i3p8.pdf

  4. Diaz, C.O., Guzek, M., Pecero, J.E., Danoy, G., Bouvry, P., Khan, S.U.: Energy-aware fast scheduling heuristics in heterogeneous computing systems. In: Proceedings of the 2011 International Conference on High Performance Computing & Simulation (HPCS 2011), pp. 478–484 (2011)

    Google Scholar 

  5. Ezzatti, P., Pedemonte, M., Martín, A.: An efficient implementation of the min-min heuristic. Comput. Oper. Res. 40(11), 2670–2676 (2013)

    Article  MathSciNet  Google Scholar 

  6. Fernandez-Baca, D.: Allocating modules to processors in a distributed system. IEEE Trans. Softw. Eng. 15(11), 1427–1436 (1989)

    Article  Google Scholar 

  7. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  8. Giersch, A., Robert, Y., Vivien, F.: Scheduling tasks sharing files on heterogeneous master-slave platforms. J. Syst. Archit. 52(2), 88–104 (2006)

    Article  Google Scholar 

  9. Herf, M.: Radix tricks. http://stereopsis.com/radix.html. Accessed April 2015

  10. Hildebrandt, P., Isbitz, H.: Radix exchange-an internal sorting method for digital computers. J. ACM 6(2), 156–163 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ibarra, O.H., Kim, C.E.: Heuristic algorithms for scheduling independent tasks on nonidentical processors. J. ACM 24(2), 280–289 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  12. Knuth, D.E.: The Art of Computer Programming, Sorting and Searching, vol. 3, 2nd edn. Addison Wesley Longman Publishing Co., Inc., Redwood City (1998)

    MATH  Google Scholar 

  13. Luo, P., Lü, K., Shi, Z.: A revisit of fast greedy heuristics for mapping a class of independent tasks onto heterogeneous computing systems. J. Parallel Distrib. Comput. 67(6), 695–714 (2007)

    Article  MATH  Google Scholar 

  14. Mathworks: Multicore matlab. http://www.mathworks.com/discovery/multicore-matlab.html. Accessed April 2015

  15. McCool, M.D., Robison, A.D., Reinders, J.: Structured Parallel Programming: Patterns for Efficient Computation. Morgan Kaufmann, Burlington (2012)

    Google Scholar 

  16. Haberman, N.: Parallel neighbor sort (or the glory of the induction principle). Technical report 2087, Computer Science Department, Carnegie Mellon University (1972)

    Google Scholar 

  17. Nvidia Corporation: CUDA C Programming Guide Version 5.5. Nvidia Corporation (2013)

    Google Scholar 

  18. Pinel, F., Dorronsoro, B., Pecero, J., Bouvry, P., Khan, S.: A two-phase heuristic for the energy-efficient scheduling of independent tasks on computational grids. Cluster Comput. 16, 1–13 (2012)

    Google Scholar 

  19. Pinel, F., Dorronsoro, B., Bouvry, P.: Solving very large instances of the scheduling of independent tasks problem on the GPU. J. Parallel Distrib. Comput. 73(1), 101–110 (2013)

    Article  Google Scholar 

  20. Ritchie, G., Levine, J.: A fast, effective local search for scheduling independent jobs in heterogeneous computing environments. In: PLANSIG 2003: Proceedings of the 22nd Workshop of the UK Planning and Scheduling Special Interest Group, pp. 178–183, December 2003

    Google Scholar 

  21. Tabak, E., Cambazoglu, B., Aykanat, C.: Improving the performance of independent task assignment heuristics minmin, maxmin and sufferage. IEEE Trans. Parallel Distrib. Syst. 25(5), 1244–1256 (2013)

    Article  Google Scholar 

  22. Valiant, L.G.: Parallelism in comparison problems. SIAM J. Comput. 4(3), 348–355 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  23. Wu, M.Y., Shu, W., Zhang, H.: Segmented min-min: A static mapping algorithm for meta-tasks on heterogeneous computing systems. In: Proceedings of the 9th Heterogeneous Computing Workshop, HCW 2000, pp. 375–385. IEEE Computer Society, Washington, DC (2000)

    Google Scholar 

  24. Xhafa, F., Abraham, A.: Computational models and heuristic methods for grid scheduling problems. Future Gener. Comput. Syst. 26(4), 608–621 (2010)

    Article  Google Scholar 

  25. Xhafa, F., Alba, E., Dorronsoro, B., Duran, B.: Efficient batch job scheduling in grids using cellular memetic algorithms. J. Math. Model. Algorithms 7, 217–236 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Xhafa, F., Barolli, L., Durresi, A.: Batch mode scheduling in grid systems. Int. J. Web Grid Serv. 3(1), 19–37 (2007)

    Article  Google Scholar 

  27. Xhafa, F., Carretero, J., Dorronsoro, B., Alba, E.: A TABU search algorithm for scheduling independent jobs in computational grids. Comput. Artif. Intell. 28(2), 237–250 (2009)

    Google Scholar 

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Acknowledgment

The authors acknowledge support from Programa de Desarrollo de las Ciencias Básicas, Uruguay, and Sistema Nacional de Investigadores, Uruguay.

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Authors and Affiliations

  1. Instituto de Computación, Universidad de la República, 11.300, Montevideo, Uruguay

    Martín Pedemonte, Pablo Ezzatti & Álvaro Martín

Authors
  1. Martín Pedemonte
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  2. Pablo Ezzatti
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  3. Álvaro Martín
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Corresponding author

Correspondence to Martín Pedemonte .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Pedemonte, M., Ezzatti, P., Martín, Á. (2016). Accelerating the Min-Min Heuristic. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. Lecture Notes in Computer Science(), vol 9574. Springer, Cham. https://doi.org/10.1007/978-3-319-32152-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-32152-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32151-6

  • Online ISBN: 978-3-319-32152-3

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