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A parallel approximation algorithm for resource constrained scheduling and bin packing

  • Scheduling and Load Balancing
  • Conference paper
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Solving Irregularly Structured Problems in Parallel (IRREGULAR 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1253))

Abstract

We consider the following classical resource constrained scheduling problem. Given m identical processors, s resources R 1,⋯, R 3 with upper bounds b 1,⋯, b 3, n independent jobs T 1,⋯, T n of unit length, where each job requires one processor and an amount R i(j) ∈ 0,1 of resource R i, i=1,⋯, s, the optimization problem is to schedule the jobs at discrete times in 1,⋯, n subject to the processor and resource constraints so that the latest scheduling time is minimum. Note that multidimensional bin packing is a special case of this problem. We give for every fixed α>1 the first parallel 2α-factor approximation algorithm and show that there cannot exist a polynomial-time approximation algorithm achieving an approximation factor better than 4/3, unless P=N P.

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References

  1. N. Alon, L. Babai, A. Itai; A fast and simple randomized algorithm for the maximal independent set problem. J. Algo., 7 (1987), 567–583.

    Google Scholar 

  2. N. Alon, J. Spencer, P. Erdós; The probabilistic method. John Wiley & Sons, Inc. 1992.

    Google Scholar 

  3. D. Angluin, L.G. Valiant: Fast probabilistic algorithms for Hamiltonion circuits and matchings. J. Comp. Sys. Sci., Vol. 18, (1979), 155–193.

    Google Scholar 

  4. B. Berger, J. Rompel; Simulating (log cn)-wise independence in NC. JACM, 38 (4), (1991), 1026–1046.

    Google Scholar 

  5. J. Blazewicz, K. Ecker, G. Schmidt, J. Weglarz; Scheduling in computer and maufacturing systems. Springer-Verlag, Berlin (1993).

    Google Scholar 

  6. B. Bollobàs; Random Graphs. Academic Press, Orlando (1985).

    Google Scholar 

  7. M. R. Garey, R. L. Graham, D. S. Johnson, A.C.-C. Yao; Resource constrained scheduling as generalized bin packing. JCT Ser. A, 21 (1976), 257–298.

    Google Scholar 

  8. M. R. Garey, D. S. Johnson; Computers and Intractability. W. H. Freeman and Company, New York (1979).

    Google Scholar 

  9. M. Grötschel, L. Lovász, A. Schrijver; Geometrie algorithms and combinatorial optimization. Springer-Verlag (1988).

    Google Scholar 

  10. I. Holyer; The N P-completeness of edge coloring. SIAM J. Comp., 10 (4), (1981), 718–720.

    Google Scholar 

  11. J. H. van Lint; Introduction to Coding Theory. Springer Verlag New York, Heidelberg, Berlin (1982).

    Google Scholar 

  12. F.J. MacWilliams, N.J.A. Sloane; The theory of error correcting codes. North Holland, Amsterdam, (1977).

    Google Scholar 

  13. R. Motwani, J. Naor, M. Naor; The probabilistic method yields deterministic parallel algorithms. Proceedings 30the IEEE Conference on Foundation of Computer Science (FOCS'89), (1989), 8–13.

    Google Scholar 

  14. P. Raghavan; Probabilistic construction of deterministic algorithms: approximating packing integer programs. J. Comp. Sys. Sci., 37, (1988), 130–143.

    Google Scholar 

  15. P. Raghavan, C. D. Thompson; Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7 (4), (1987), 365–374.

    Google Scholar 

  16. H. Röck, G. Schmidt; Machine aggregation heuristics in shop scheduling. Math. Oper. Res. 45 (1983) 303–314.

    Google Scholar 

  17. A. Srivastav, P. Stangier; Algorithmic Chernoff-Hoeffding inequalties in integer programming. Random Structures & Algorithms, Vol. 8, No. 1, (1996), 27–58.

    Google Scholar 

  18. A. Srivastav, P. Stangier; Tight aproximation for resource constrained scheduling and bin packing. To appear in Discrete Applied Math. 1997.

    Google Scholar 

  19. A. Srivastav; Derandomized algorithms in combinatorial optimization. Habilitation thesis, Insitut für Informatik, Freie Universität Berlin, (1995), 180 pages.

    Google Scholar 

  20. W. F. de la Vega, C. S. Lueker; Bin packing can be solved within 1+∈ in linear time. Combinatorica, 1 (1981), 349–355.

    Google Scholar 

  21. V. G. Vizing; On an estimate of the chromatic class of a p-graph. (Russian), Diskret. Analiz. 3 (1964), 25–30.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Informatik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Anand Srivastav

  2. Zentrum für Paralleles Rechnen (ZPR), Universität zu Köln, Weyertal 80, 50931, Köln, Germany

    Peter Stangier

Authors
  1. Anand Srivastav
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  2. Peter Stangier
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Editor information

Gianfranco Bilardi Afonso Ferreira Reinhard Lüling José Rolim

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© 1997 Springer-Verlag Berlin Heidelberg

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Srivastav, A., Stangier, P. (1997). A parallel approximation algorithm for resource constrained scheduling and bin packing. In: Bilardi, G., Ferreira, A., Lüling, R., Rolim, J. (eds) Solving Irregularly Structured Problems in Parallel. IRREGULAR 1997. Lecture Notes in Computer Science, vol 1253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63138-0_14

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  • DOI: https://doi.org/10.1007/3-540-63138-0_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63138-5

  • Online ISBN: 978-3-540-69157-0

  • eBook Packages: Springer Book Archive

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