Non-approximability of the Bulk Synchronous Task Scheduling Problem

  • Noriyuki Fujimoto
  • Kenichi Hagihara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2400)

Abstract

The mainstream architecture of a parallel machine with more than tens of processors is a distributed-memory machine. The bulk synchronous task scheduling problem (BSSP, for short) is an task scheduling problem for distributed-memory machines. This paper shows that there does not exist a ρ-approximation algorithm to solve the optimization counterpart of BSSP for any ρ > 6/5 unless \( \mathcal{P} = \mathcal{N}\mathcal{P} \).

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References

  1. 1.
    Bacon, D.F. and Graham, S.L. and Sharp, O.J.: Compiler Transformations for High-Performance Computing, ACM computing surveys, Vol. 26, No. 4 (1994) 345–420Google Scholar
  2. 2.
    Darbha, S. and Agrawal, D. P.: Optimal Scheduling Algorithm for Distributed-Memory Machines, IEEE Trans. on Parallel and Distributed Systems, Vol. 9, No. 1 (1998) 87–95CrossRefGoogle Scholar
  3. 3.
    El-Rewini, H. and Lewis, T.G. and Ali, H.H.: TASK SCHEDULING in PARALLEL and DISTRIBUTED SYSTEMS, PTR Prentice Hall (1994)Google Scholar
  4. 4.
    Fujimoto, N. and Baba, T. and Hashimoto, T. and Hagihara, K.: A Task Scheduling Algorithm to Package Messages on Distributed Memory Parallel Machines, Proc. of 1999 Int. Symposium on Parallel Architectures, Algorithms, and Networks (1999) 236–241Google Scholar
  5. 5.
    Fujimoto, N. and Hashimoto, T. and Mori, M. and Hagihara, K.: On the Performance Gap between a Task Schedule and Its Corresponding Parallel Program, Proc. of 1999 Int. Workshop on Parallel and Distributed Computing for Symbolic and Irregular Applications, World Scientific (2000) 271–287Google Scholar
  6. 6.
    Fujimoto, N. and Hagihara, K.: NP-Completeness of the Bulk Synchronous Task Scheduling Problem and Its Approximation Algorithm, Proc. of 2000 Int. Symposium on Parallel Architectures, Algorithms, and Networks (2000) 127–132Google Scholar
  7. 7.
    Fujimoto, N. and Baba, T. and Hashimoto, T. and Hagihara, K.: On Message Packaging in Task Scheduling for Distributed Memory Parallel Machines, The International Journal of Foundations of Computer Science, Vol. 12, No. 3 (2001) 285–306CrossRefGoogle Scholar
  8. 8.
    Kruatrachue, B., “Static task scheduling and packing in parallel processing systems”, Ph.D. diss., Department of Electrical and Computer Engineering, Oregon State University, Corvallis, 1987Google Scholar
  9. 9.
    Hoogeveen, J. A., Lenstra, J. K., and Veltman, B.: “Three, Four, Five, Six or the Complexity of Scheduling with Communication Delays”, Oper. Res. Lett. Vol. 16 (1994) 129–137MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Lenstra, J. K. and Rinnooy Kan, A. H. G.: Complexity of Scheduling under Precedence Constraints, Operations Research, Vol. 26 (1978) 22–35MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Lenstra, J.K. and Shmoys, D. B.: Computing Near-Optimal Schedules, Scheduling Theory and its Applications, John Wiley & Sons (1995) 1–14Google Scholar
  12. 12.
    Palis, M. A. and Liou, J. and Wei, D. S. L.: Task Clustering and Scheduling for Distributed Memory Parallel Architectures, IEEE Trans. on Parallel and Distributed Systems, Vol. 7, No. 1 (1996) 46–55CrossRefGoogle Scholar
  13. 13.
    Papadimitriou, C. H. and Yannakakis, M.: Towards An Architecture-Independent Analysis of Parallel Algorithms, SIAM J. Comput., Vol. 19, No. 2 (1990) 322–328MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Thurimella, R. and Yesha, Y.: A scheduling principle for precedence graphs with communication delay, Int. Conf. on Parallel Processing, Vol. 3 (1992) 229–236Google Scholar
  15. 15.
    Valiant, L.G.: A Bridging Model for Parallel Computation, Communications of the ACM, Vol. 33, No. 8 (1990) 103–111CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Noriyuki Fujimoto
    • 1
  • Kenichi Hagihara
    • 1
  1. 1.Graduate School of Information Science and TechnologyOsaka UniversityOsakaJapan

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