Skip to main content
SpringerLink
Log in

Unrelated parallel machine scheduling—perspectives and progress

  • Theoretical Article
  • Published:
OPSEARCH Aims and scope Submit manuscript

Abstract

Scheduling problems have been analyzed by several researchers for over forty years. Much progress has been made in the scheduling theory, approximate solutions, complexity aspects, and practical algorithms. The focus of this paper is on one class of scheduling problems known as unrelated parallel machines. We look at the progress made in this area since the author’s thesis (Suresh 1994) in the early 1990’s. Suggestions for further research is made with a discussion of some of the areas not explored in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Abrams, D.S., Lloyd, S.: Nonlinear quantum mechanics implies polynomial-time solution for np-complete and #p problems. Phys. Rev. Lett. 81(18), 3992–3995 (1998)

    Article  Google Scholar 

  2. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and hardness of approximation problems. Annual IEEE Symposium on Foundations of Computer Science, pp. 14–23 (1992)

  3. Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. J. ACM 45, 501–555 (1998)

    Article  Google Scholar 

  4. Arora, S., Safra, S.: Probabilistic checking of proofs: a new characterization of np. J. ACM 45, 70–122 (1998)

    Article  Google Scholar 

  5. Ausiello, G., Crescenzi, P., Gambosi, G., Marchetti-Spaccamela, A., Portasi, M.: Complexity and Approximation Combinatorial—Optimization Problems and Their Approximability Properties. Springer, Berlin (1999)

    Google Scholar 

  6. Azar, Y., Epstein, A.: Convex programming for scheduling unrelated parallel machines. In: Proceedings of the 37th Annual ACM Symposium on Theory of Computing, STOC ’05, pp. 331–337. ACM, New York (2005)

    Google Scholar 

  7. Azar, Y., Jain, K., Mirrokni, V.: (almost) optimal coordination mechanisms for unrelated machine scheduling. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’08, pp. 323–332. Society for Industrial and Applied Mathematics, Philadelphia (2008)

    Google Scholar 

  8. Benioff, P.: Quantum mechanical hamiltonian models of turing machines. J. Stat. Phys. 29, 515–546 (1982)

    Article  Google Scholar 

  9. Caragiannis, I.: Efficient coordination mechanisms for unrelated machine scheduling. In: Proceedings of the 20th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’09, pp. 815–824. Society for Industrial and Applied Mathematics, Philadelphia (2009)

    Google Scholar 

  10. Cerny, V.: A thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. J. Optim. Theory Appl. 45, 41–51 (1985)

    Article  Google Scholar 

  11. Christodoulou, G., Koutsoupias, E., Vidali, A.: A lower bound for scheduling mechanisms. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’07, pp. 1163–1170. Society for Industrial and Applied Mathematics, Philadelphia (2007)

    Google Scholar 

  12. Coffman, E.G., Garey, M.R., Johnson, D.S.: An application of bin-packing to multiprocessor scheduling. SIAM J. Comput. 7(1), 1–17 (1978). doi:10.1137/0207001, URL: http://link.aip.org/link/?SMJ/7/1/1

    Article  Google Scholar 

  13. Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of the 3rd Annual ACM Symposium on Theory of Computing, STOC ’71, pp. 151–158. ACM, New York (1971)

    Chapter  Google Scholar 

  14. Davis, E., Jaffe, J.M.: Algorithms for scheduling tasks on unrelated processors. J. ACM 28, 721–736 (1981)

    Article  Google Scholar 

  15. Davis, L.: Job shop scheduling with genetic algorithms. In: Proceedings of the 1st International Conference on Genetic Algorithms, pp. 136–140. L. Erlbaum Associates Inc., Hillsdale (1985)

    Google Scholar 

  16. Deutsch, D.: Quantum theory, the church-turing principle and the universal quantum computer. Proc. R. Soc. Lond. A400, 97–117 (1985)

    Google Scholar 

  17. Durr, C., Hoyer, P.: A quantum algortithm for finding the minimum (1996). arXiv:quant-ph/9607014v2

  18. Ebenlendr, T., Křćal, M., Sgall, J.: Graph balancing: a special case of scheduling unrelated parallel machines. In: Proceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’08, pp. 483–490. Society for Industrial and Applied Mathematics, Philadelphia (2008)

    Google Scholar 

  19. Efraimidis, P., Spirakis, P.: Randomized approximation schemes for scheduling unrelated parallel machines. Electronic Colloquium on Computational Complexity (ECCC) (2000). TR 00-007

  20. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7), 467–488 (1982)

    Article  Google Scholar 

  21. Friesen, D.K.: Tighter bounds for the multifit processor scheduling algorithm. SIAM J. Comput. 13(1), 170–181 (1984)

    Article  Google Scholar 

  22. Gairing, M., Monien, B., Woclaw, A.: A faster combinatorial approximation algorithm for scheduling unrelated parallel machines. Theor. Comp. Sci. 380(1–2), 87–99 (2007). Automata, Languages and Programming

    Article  Google Scholar 

  23. Garey, M., Johnson, D.: Computers and Intractability: A Theory of NP Completeness. W.H. Freeman and Co., San Fransisco (1979)

    Google Scholar 

  24. Garg, N., Jain, S., Swamy, C.: A randomized algorithm for flow shop scheduling. In: FSTTCS, pp. 213–218 (1999)

  25. Ge, Y., Watson, L.T.: Quantum Computing Applied to Optimization. Tech. rep., Virginia Polytechnic Institute and State University (1999). Working Paper TR-99-03 Computer Science

  26. Ghirardi, M., Potts, C.N.: Makespan minimization for scheduling unrelated parallel machines: a recovering beam search approach. Eur. J. Oper. Res. 165(2), 457–467 (2005). Project Management and Scheduling

    Article  Google Scholar 

  27. Glass, C.A., Potts, C.N., Shade, P.: Unrelated parallel machine scheduling using local search. Math. Comput. Model. 20(2), 41–52 (1994)

    Article  Google Scholar 

  28. Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986). doi:10.1016/0305-0548(86)90048-1

    Article  Google Scholar 

  29. Graham, R.: Bounds for certain multiprocessor anomalies. Bell Syst. Tech. J. 45, 1563–1581 (1986)

    Google Scholar 

  30. Graham, R., Lawler, E., Lenstra, J., Kan, A.R.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discrete Math. 4, 287–326 (1979)

    Article  Google Scholar 

  31. Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM J. Appl. Math. 17(2), 416–429 (1969)

    Article  Google Scholar 

  32. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28’th Annual ACM Symposium on the Theory of Computing, pp. 212–219 (1996)

  33. Hariri, A.M.A., Potts, C.N.: Heuristics for scheduling unrelated parallel machines. Comput. Oper. Res 18(3), 323–331 (1991)

    Article  Google Scholar 

  34. Hauchbaum, D.S. (ed.): Approximation Algorithms for NP-hard Problems. Boston, MA (1997)

  35. Ho, Y., Pepyne, D.: Simple explanation of the no-free-lunch theorem and its implications. J. Optim. Theory Appl. 115, 549–570 (2002)

    Article  Google Scholar 

  36. Hochbaum, D.S., Shmoys, D.B.: Using dual approximation algorithms for scheduling problems theoretical and practical results. J. ACM 34, 144–162 (1987)

    Article  Google Scholar 

  37. Hogg, T., Mochon, C., Rieffel, E., Polak, W.: Tools for quantum algorithms (1998). arXiv:quant-ph/9811073v2

  38. Hogg, T., Portnov, D.: Quantum optimization (2000). arXiv:quant-ph/0006090v1

  39. Hopfield, J.J., Tank, D.: “neural” computation of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985)

    Google Scholar 

  40. Horowitz, E., Sahni, S.: Exact and approximate algorithms for scheduling nonidentical processors. J. ACM 23, 317–327 (1976)

    Article  Google Scholar 

  41. Hromkovic, J.: Algorithmics for Hard Problems: Introduction to Combinatorial Optimization, Randomization, Approximation and Heuristics. Springer-Verlag, Berlin (2010)

    Google Scholar 

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

    Article  Google Scholar 

  43. Kan, A.R.: Machine Scheduling Problems: Classification, Complexity and Computations. Nijhoff (1976)

  44. Karp, R.M.: On the computational complexity of combinatorial problems. Networks 5, 45–68 (1975)

    Google Scholar 

  45. Kirkpatrick, S., Jr., C.D.G., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983). doi:10.1126/science.220.4598.671

    Article  Google Scholar 

  46. Langston, M.A.: Processor Scheduling with Improved Heuristic Algorithms. Ph.D. thesis, Texas A&M University (1981). AAI8118275

  47. Lenstra, J.K., Shmoys, D.B., Tardos, É.: Approximation algorithms for scheduling unrelated parallel machines. Math. Program. 46, 259–271 (1990)

    Article  Google Scholar 

  48. Linn, R., Zhang, W.: Hybrid flow shop scheduling: a survey. Comput. Ind. Eng. 37(1–2), 57–61 (1999). Proceedings of the 24th international conference on computers and industrial engineering

    Article  Google Scholar 

  49. Lu, F., Marinescu, D.C.: An R∥ Cmax quantum scheduling algorithm (2005). arXiv:quant-ph/0511028v6

  50. Lu, F., Marinescu, D.C.: An R||C max quantaum scheduling algorithm. Quantum Info. Process. 6(3), 159–178 (2007)

    Article  Google Scholar 

  51. Lu, P., Yu, C.: An improved randomized truthful mechanism for scheduling unrelated machines. In: Susanne Albers, P.W. (ed.) Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science STACS 2008, pp. 527–538. IBFI Schloss Dagstuhl, Bordeaux France (2008). URL: http://hal.archives-ouvertes.fr/hal-00232972/en/

  52. Macready, W.G., Wolpert, D.H.: What makes an optimization problem hard? (1995). Santa Fe Institute Working Paper: 95-05-046

  53. Martello, S., Soumis, F., Toth, P.: Exact and approximation algorithms for makespan minimization on unrelated parallel machines. Discrete Appl. Math. 75(2), 169–188 (1997)

    Article  Google Scholar 

  54. Michiels, W., Aarts, E., Korst, J.: Theoretical Aspects of Local Search. Springer, Berlin (2007)

    Google Scholar 

  55. Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  56. Mu’alem, A., Schapira, M.: Setting lower bounds on truthfulness: extended abstract. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’07, pp. 1143–1152. Society for Industrial and Applied Mathematics, Philadelphia (2007)

    Google Scholar 

  57. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  58. Nisan, N., Ronen, A.: Algorithmic mechanism design (extended abstract). In: Proceedings of the 31st Annual ACM Symposium on Theory of Computing, STOC ’99, pp. 129–140. ACM, New York (1999)

    Chapter  Google Scholar 

  59. Papadimitriou, C., Yannakakis, M.: Towards an architecture-independent analysis of parallel algorithms. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, STOC ’88, pp. 510–513. ACM, New York (1988)

    Chapter  Google Scholar 

  60. Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization Algorithms and Complexity. Englewood Cliffs, NJ (1982)

    Google Scholar 

  61. Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43(3), 425–440 (1991)

    Article  Google Scholar 

  62. Park, B.J., Choi, H.R., Kim, H.S.: A hybrid genetic algorithm for the job shop scheduling problems. Comput. Ind. Eng. 45, 597–613 (2003)

    Article  Google Scholar 

  63. Piersma, N., van Dijk, W.: A local search heuristic for unrelated parallel machine scheduling with efficient neighborhood search. Math. Comput. Model 24(9), 11–19 (1996)

    Article  Google Scholar 

  64. Plotkin, S., Shmoys, D., Tardos, E.: Fast approximation algorithms for fractional packing and covering problems. Annual IEEE Symposium on Foundations of Computer Science, pp. 495–504 (1991)

  65. Potts, C.N.: Analysis of a linear programming heuristic for scheduling unrelated parallel machines. Discrete Appl. Math 10(2), 155–164 (1985)

    Article  Google Scholar 

  66. Reeves, C.R.: Modern Heuristic Techniques for Combinatorial Problems, chap. 1, pp. 1–14. Orient Longman, Himayat Nagar (1993)

  67. Reeves, C.R.: Genetic algorithms for the operations researcher. INFORMS J. Comput. 9(3), 231–250 (1997)

    Article  Google Scholar 

  68. Scheduling unrelated machines by randomized bounding. SIAM J. Discrete Math. 15(4), 450–469 (2002)

    Google Scholar 

  69. Schulz, A.S., Skutella, M.: Scheduling unrelated machines by randomized rounding. SIAM J. Discrete Math 15, 450–469 (1999)

    Article  Google Scholar 

  70. Schuurman, P., Woegiunger, G.: Polynimial time approximation algorithms for machine scheduling: ten open problems. J. Sched. 2(5) (1999)

  71. Shchepin, E.V., Vakhania, N.: An optimal rounding gives a better approximation for scheduling unrelated machines. Oper. Res. Lett. 33(2), 127–133 (2005)

    Article  Google Scholar 

  72. Shor, P.: Algorithms for quantum computation: discrete log and factoring. In: Goldwasser, S. (ed.) Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)

    Chapter  Google Scholar 

  73. Simon, D.: On the power of quantum computation. Annual IEEE Symposium on Foundations of Computer Science, pp. 116–123 (1994)

  74. Steffen, M., van Dam, W., Hogg, T., Breyta, G., Chuang, I.: Experimental implementation of an adiabatic quantum optimization algorithm. Phys. Rev. Lett. 90(6), 067,903 (2003). doi:10.1103/PhysRevLett.90.067903

    Article  Google Scholar 

  75. Stern, H.E.: Minimizing makespan for independent jobs on nonidentical machines—an optimal procedure. Tech. rep., Ben-Gurion Uinversity of the Negev, Ber-Seva (1976). Working Paper 2/75 Dept. Of Industrial Engineering and Management

  76. Suresh, V.: Efficient Algorithms for Scheduling Jobs in Unrelated Parallel Machines. Ph.D. thesis, Indian Institute of Technology, Madras (1994)

  77. Svensson, O.: Santa claus schedules jobs on unrelated machines (2010). arXiv:1011.1168v1 [cs.DS]

  78. van de Velde, S.L.: Duality-based algorithms for scheduling unrelated parallel machines. INFORMS J. Comput. 5(2), 192–205 (1993)

    Article  Google Scholar 

  79. Vredeveld, T.: Combinatorial Approximation Algorithms Guranteed Versus Experimental Performance. Ph.D. thesis, Technical University of Eindhoven, Eindhoev (2002)

  80. Watrous, J.: Quantum computational complexity (2008). arXiv:quant-ph/0804.3401v1

  81. Weise, T., Zapf, M., Chiong, R., Urbaneja, A.J.N.: Why is optimization difficult? In: Chiong, R. (ed.) Nature-Inspired Algorithms for Optimisation, Studies in Computational Intelligence, vol. 193, chap. 1, pp. 1–50. Springer (2009)

  82. Wolpert, D.H., Macready, W.G.: No Free Lunch Theorems for Search (1995). Santa Fe Institute Working Paper: 95-02-010

  83. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions On Evolutionary Computation, pp. 67–82 (1997)

Download references

Author information

Authors and Affiliations

  1. MetLife Inc, 300 Davidson Avenue, Somerset, NJ, USA

    Suresh Kamath

Authors
  1. Suresh Kamath
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Suresh Kamath.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamath, S. Unrelated parallel machine scheduling—perspectives and progress. OPSEARCH 48, 318–334 (2011). https://doi.org/10.1007/s12597-011-0059-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12597-011-0059-9

Keywords

Search

Navigation