A parallel approximation algorithm for resource constrained scheduling and bin packing

  • Anand Srivastav
  • Peter Stangier
Scheduling and Load Balancing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1253)


We consider the following classical resource constrained scheduling problem. Given m identical processors, s resources R1,⋯, R3 with upper bounds b1,⋯, b3, n independent jobs T1,⋯, Tn of unit length, where each job requires one processor and an amount Ri(j) ∈ 0,1 of resource Ri, 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.


resource constrained scheduling multidimensional bin packing derandomization logcn-wise independence NC-approximation algorithm 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [ABI86]
    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. [ASE92]
    N. Alon, J. Spencer, P. Erdós; The probabilistic method. John Wiley & Sons, Inc. 1992.Google Scholar
  3. [AnVa79]
    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. [BeRo91]
    B. Berger, J. Rompel; Simulating (log cn)-wise independence in NC. JACM, 38 (4), (1991), 1026–1046.Google Scholar
  5. [BESW93]
    J. Blazewicz, K. Ecker, G. Schmidt, J. Weglarz; Scheduling in computer and maufacturing systems. Springer-Verlag, Berlin (1993).Google Scholar
  6. [Bol85]
    B. Bollobàs; Random Graphs. Academic Press, Orlando (1985).Google Scholar
  7. [GGJY76]
    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. [GaJo79]
    M. R. Garey, D. S. Johnson; Computers and Intractability. W. H. Freeman and Company, New York (1979).Google Scholar
  9. [GLS88]
    M. Grötschel, L. Lovász, A. Schrijver; Geometrie algorithms and combinatorial optimization. Springer-Verlag (1988).Google Scholar
  10. [Hol81]
    I. Holyer; The N P-completeness of edge coloring. SIAM J. Comp., 10 (4), (1981), 718–720.Google Scholar
  11. [Li82]
    J. H. van Lint; Introduction to Coding Theory. Springer Verlag New York, Heidelberg, Berlin (1982).Google Scholar
  12. [McSo77]
    F.J. MacWilliams, N.J.A. Sloane; The theory of error correcting codes. North Holland, Amsterdam, (1977).Google Scholar
  13. [MNN89]
    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. [Ra88]
    P. Raghavan; Probabilistic construction of deterministic algorithms: approximating packing integer programs. J. Comp. Sys. Sci., 37, (1988), 130–143.Google Scholar
  15. [RT87]
    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. [RS83]
    H. Röck, G. Schmidt; Machine aggregation heuristics in shop scheduling. Math. Oper. Res. 45 (1983) 303–314.Google Scholar
  17. [SrSt96]
    A. Srivastav, P. Stangier; Algorithmic Chernoff-Hoeffding inequalties in integer programming. Random Structures & Algorithms, Vol. 8, No. 1, (1996), 27–58.Google Scholar
  18. [SrSt97]
    A. Srivastav, P. Stangier; Tight aproximation for resource constrained scheduling and bin packing. To appear in Discrete Applied Math. 1997.Google Scholar
  19. [Sriv95]
    A. Srivastav; Derandomized algorithms in combinatorial optimization. Habilitation thesis, Insitut für Informatik, Freie Universität Berlin, (1995), 180 pages.Google Scholar
  20. [VeLu81]
    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. [Viz64]
    V. G. Vizing; On an estimate of the chromatic class of a p-graph. (Russian), Diskret. Analiz. 3 (1964), 25–30.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Anand Srivastav
    • 1
  • Peter Stangier
    • 2
  1. 1.Institut für InformatikHumboldt Universität zu BerlinBerlinGermany
  2. 2.Zentrum für Paralleles Rechnen (ZPR)Universität zu KölnKölnGermany

Personalised recommendations