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Non-approximability Results for Scheduling Problems with Minsum Criteria

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Integer Programming and Combinatorial Optimization (IPCO 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1412))

Abstract

We provide several non-approximability results for determin- istic scheduling problems whose objective is to minimize the total job completion time. Unless P = NP, none of the problems under consid- eration can be approximated in polynomial time within arbitrarily good precision. Most of our results are derived by Max SNP hardness proofs. Among the investigated problems are: scheduling unrelated machines with some additional features like job release dates, deadlines and weights, scheduling flow shops, and scheduling open shops.

Supported by the START program Y43-MAT of the Austrian Ministry of Science.

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References

  1. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and hardness of approximation problems. Proceedings of the 33rd IEEE Symposium on the Foundations of Computer Science, pages 14–23, 1992.

    Google Scholar 

  2. P. Crescenzi and V. Kann. A compendium of NP-optimization problems. 1997. http://www.nada.kth.se/nada/theory/problemlist/html.

  3. M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.

    MATH  Google Scholar 

  4. R. L. Graham, E. L. Lawler, J. K. Lenstra, and A. H. G. Rinnooy Kan. Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5:287–326, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. A. Hoogeveen, J. K. Lenstra, and B. Veltman. Three, four, five, six, or the complexity of scheduling with communication delays. Operations Research Letters, 16:129–137, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  6. V. Kann. Maximum bounded 3-dimensional matching is MAX SNP-complete. Information Processing Letters, 37:27–35, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Kellerer, T. Tautenhahn, and G. J. Woeginger. Approximability and nonapproximability results for minimizing total flow time on a single machine. Proceedings of the 28th Annual ACM Symposium on the Theory of Computing, pages 418–426, 1996.

    Google Scholar 

  8. E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan, and D. B. Shmoys. Sequencing and scheduling: Algorithms and complexity. In S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, editors, Logistics of Production and Inventory. Handbooks in Operations Research and Management Science, Vol. 4, pages 445–522. North-Holland, Amsterdam, 1993.

    Google Scholar 

  9. J. K. Lenstra and A. H. G. Rinnooy Kan. Complexity of scheduling under precedence constraints. Operations Research, 26:22–35, 1978.

    MATH  MathSciNet  Google Scholar 

  10. J. K. Lenstra and D. B. Shmoys. Computing near-optimal schedules. In P. Chrétienne, E. G. Coffman Jr., J. K. Lenstra, and Z. Liu, editors, Scheduling Theory and its Applications, pages 1–14. Wiley, Chichester, 1995.

    Google Scholar 

  11. J. K. Lenstra, D. B. Shmoys, and É. Tardos. Approximation algorithms for scheduling unrelated parallel machines. Math. Programming, 46:259–271, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Leonardi and D. Raz. Approximating total flow time on parallel machines. Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, pages 110–119, 1997.

    Google Scholar 

  13. C. H. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  14. C. H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. Journal of Computer and System Sciences, 43:425–440, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  15. M. Skutella. Problem posed at the open problem session of the Dagstuhl Meeting on “Parallel Machine Scheduling”. Schloß Dagstuhl, Germany, July 14–18, 1997.

    Google Scholar 

  16. D. P. Williamson, L. A. Hall, J. A. Hoogeveen, C. A. J. Hurkens, J. K. Lenstra, S. V. Sevastianov, and D. B. Shmoys. Short shop schedules. Operations Research, 45:288–294, 1997.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Han Hoogeveen & Petra Schuurman

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Gerhard J. Woeginger

Authors
  1. Han Hoogeveen
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  2. Petra Schuurman
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  3. Gerhard J. Woeginger
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Editor information

Editors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6020 Annapolis, Houston, TX, 77005, USA

    Robert E. Bixby

  2. PROS Strategic Solutions, 3223 Smith Street, Houston, TX, 77006, USA

    E. Andrew Boyd

  3. Department of Industrial, Engineering, Texas A&M University, 1000 Country Place Dr. Apt. 69, Houston, TX, 77079, USA

    Roger Z. Ríos-Mercado

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© 1998 Springer-Verlag Berlin Heidelberg

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Hoogeveen, H., Schuurman, P., Woeginger, G.J. (1998). Non-approximability Results for Scheduling Problems with Minsum Criteria. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_27

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  • DOI: https://doi.org/10.1007/3-540-69346-7_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64590-0

  • Online ISBN: 978-3-540-69346-8

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