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Classic Scheduling Theory

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Scheduling for Parallel Processing

Part of the book series: Computer Communications and Networks ((CCN))

Abstract

In this chapter, we outline the terminology of the classic deterministic scheduling theory. Examples of algorithms for basic problems of scheduling on parallel systems will be presented. Finally, we discuss advantages and disadvantages of this scheduling model. Classic deterministic scheduling theory collected a great body of knowledge which is comprehensively presented in many books, e.g. see [11, 13, 19, 42, 57]. It is neither intended nor possible to cover all this information here. The goal of this chapter is to present basic concepts of the classic deterministic scheduling theory which are shared in the later scheduling models.

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References

  1. T.L. Adam, K.M. Chandy, and J.R. Dickson. A comparison of list schedules for parallel processing systems. Communications of the ACM, 17(12):685–690, 1974.

    Article  MATH  Google Scholar 

  2. F. Afrati and I. Milis. Designing PTASs for MIN-SUM scheduling problems. Discrete Applied Mathematics, 154(4):622–639, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Agnetis, P.B. Mirchandani, D. Pacciarelli, and A. Pacifici. Scheduling problems with two competing agents. Operations Research, 52(2):229–242, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  4. K.R. Baker and G.D. Scudder. Sequencing with earliness and tardiness penalties: A review. Operations Research, 38(1):22–36, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  5. K.R. Baker and J.C. Smith. A multiple-criterion model for machine scheduling. Journal of Scheduling, 6:7–16, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  6. L. Becchetti, S. Leonardi, A. Marchetti-Spaccamela, and K. Pruhs. Semi-clairvoyant scheduling. Theoretical Computer Science, 324:325–335, 2004.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Bender, S. Muthukrishnan, and R. Rajaraman. Improved algorithms for stretch scheduling. In 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 762–771, 2002.

    Google Scholar 

  8. V. Berten, J. Goossens, and E. Jeannot. On the distribution of sequential jobs in random brokering for heterogeneous computational grids. IEEE Transactions on Parallel and Distributed Systems, 17(2):113–124, 2006.

    Article  Google Scholar 

  9. J. Błażewicz. Scheduling preemptible tasks on parallel processors with information loss. Technique et Science Informatiques, 3:415–420, 1984.

    MATH  Google Scholar 

  10. J. Błażewicz, M. Drozdowski, P. Formanowicz, W. Kubiak, and G. Schmidt. Scheduling preemptable tasks on parallel processors with limited availability. Parallel Computing, 26:1195–1211, 2000.

    Article  MathSciNet  Google Scholar 

  11. J. Błażewicz, K. Ecker, E. Pesch, G. Schmidt, and J. Węglarz. Scheduling Computer and Manufacturing Processes. Springer, Heidelberg, New York, 1996.

    MATH  Google Scholar 

  12. J. Błażewicz and M. Kovalyov. The complexity of two group scheduling problems. Journal of Scheduling, 5:477–485, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Brucker. Scheduling Algorithms. Springer, Berlin, 1995.

    MATH  Google Scholar 

  14. P. Brucker and S. Knust. Complexity results for scheduling problems. http://www.mathematik.uni-osnabrueck.de/research/OR/class/, 2006 [online accessed 9 November 2006].

  15. P.J. Brucker, M.R. Garey, and D.S. Johnson. Scheduling equal-length tasks under treelike precedence constraints to minimize maximum lateness. Mathematics of Operations Research, 2(3):275–284, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  16. J. Bruno, Jr. E.G. Coffman, and R. Sethi. Scheduling independent tasks to reduce mean finishing time. Communications of the ACM, 17(7):382–387, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  17. C. Chekuri and S. Khanna. Approximation algorithms for minimizing average weighted completion time. In J.Y. Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pages 11.1–11.30. CRC Press, Boca Raton, 2004.

    Google Scholar 

  18. C. Chekuri, R. Motwani, B. Natarajan, and C. Stein. Approximation techniques for average completion time scheduling. SIAM Journal on Computing, 31(1):146–166, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  19. P. Chrétienne, E.G. Coffman Jr., J.K. Lenstra, and Z. Liu, editors. Scheduling Theory and Its Applications Wiley, Chichester-England, 1995.

    MATH  Google Scholar 

  20. J. A. Cobb, M.G. Gouda, and A. El Nahas. Time-shift scheduling: Fair scheduling of flows in high speed networks. In Proceedings of the 1996 International Conference on Network Protocols (ICNP ’96), pages 6–13, 1996.

    Google Scholar 

  21. E.G. Coffman Jr., editor. Computer and Job-Shop Scheduling Theory. Wiley, New York, 1976.

    MATH  Google Scholar 

  22. E.G. Coffman Jr. and R.J. Graham. Optimal scheduling for two-processor systems. Acta Informatica, 1(3):200–213, 1972.

    Article  MathSciNet  Google Scholar 

  23. M.L. Dertouzos and A. Ka-Lau Mok. Multiprocessor on-line scheduling of hard-real-time tasks. IEEE Transactions on Software Engineering, 15(12):1497–1506, 1989.

    Article  Google Scholar 

  24. M. Drozdowski. New applications of the Munz and Coffman algorithm. Journal of Scheduling, 4(4):209–223, 2001.

    Article  MATH  MathSciNet  Google Scholar 

  25. J. Du, J.Y.-T. Leung, and G.H. Young. Minimizing mean flow time with release time constraint. Theoretical Computer Science, 75(3):347–355, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  26. Jr. E.G. Coffman, M.R. Garey, and D.S. Johnson. An application of bin-packing to multiprocessor scheduling. SIAM Journal on Computing, 7(1):1–17, 1978.

    Google Scholar 

  27. A. Federgruen and H. Groenevelt. Preemptive scheduling of uniform processors by ordinary network flows. Management Science, 32(3):341–349, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  28. D.G. Feitelson and L. Rudolph. Evaluation of design choices for gang scheduling using distributed hierarchical control. Journal of Parallel and Distributed Computing, 35(1):18–34, 1996.

    Article  MATH  Google Scholar 

  29. D.G. Feitelson and L. Rudolph. Metrics and benchmarking for parallel job scheduling. In D.G. Feitelson and L. Rudolph, editors, Job Scheduling Strategies for Parallel Processing. LNCS, volume 1459, pages 1–24. Springer Berlin, 1998.

    Chapter  Google Scholar 

  30. D.K. Friesen. Tighter bounds for the multifit processor scheduling algorithm. SIAM Journal on Computing, 13(1):170–181, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  31. M.R. Garey and D.S. Johnson. Two-processor scheduling with start-times and deadlines. SIAM Journal on Computing, 6:416–426, 1977.

    Article  MATH  MathSciNet  Google Scholar 

  32. 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 

  33. T. Gonzalez and S. Sahni. Preemptive scheduling of uniform processor systems. Journal of the ACM, 25(1):92–101, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  34. R.L. Graham. Bounds for certain multiprocessing timing anomalies. Bell System Technical Journal, 45(2):1563–1581, 1966.

    Google Scholar 

  35. R.L. Graham. Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics, 17(2):416–429, 1969.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  37. D.S. Hochbaum and D.B. Shmoys. Using dual approximation algorithms for scheduling problems: Theoretical and practical results. Journal of the ACM, 34(1):144–162, 1987.

    Article  MathSciNet  Google Scholar 

  38. H. Hoogeveen. Multicriteria scheduling. European Journal of Operational Research, 167:592–623, 2005.

    Article  MATH  MathSciNet  Google Scholar 

  39. H. Hoogeveen, P. Schuurman, and G.J. Woeginger. Non-approximability results for scheduling problems with minsum criteria. INFORMS Journal on Computing, 13(2):157–168, 2001.

    Article  MathSciNet  Google Scholar 

  40. W.A. Horn. Some simple scheduling algorithms. Naval Research Logistics, 21:177–185, 1974.

    Article  MATH  MathSciNet  Google Scholar 

  41. T.C. Hu. Parallel sequencing and assembly line problems. Operations Research, 9(6):841–848, 1961.

    Article  MathSciNet  Google Scholar 

  42. J.Y. Leung. Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press, Boca Raton, 2004.

    MATH  Google Scholar 

  43. B. Kalyanasundaram and K. Pruhs. Speed is as powerful as clairvoyance. In Proceedings of 36th Annual Symposium on Foundations of Computer Science (FOCS’95), pages 214–221, 1995.

    Google Scholar 

  44. R.M. Karp. Reducibility among combinatorial problems. In R.E. Miller and J.W. Thatcher, editors, Complexity of Computer Computations, pages 85–104. Plenum Press, New York, 1972.

    Google Scholar 

  45. H. Kasahara and S. Narita. Practical multiprocessor scheduling algorithms for efficient parallel processing. IEEE Transactions on Computers, 33(11):1023–1029, 1984.

    Article  Google Scholar 

  46. J. Labetoulle, E.L. Lawler, J.K. Lenstra, and A.H.G. Rinnoy Kan. Preemptive scheduling of uniform machines subject to release dates. In W. R. Pulleyblank, editor, Progress in Combinatorial Optimization, pages 245–261. Academic Press, New York, 1984.

    Google Scholar 

  47. J.K. Lenstra and A.H.G. Rinnoy Kan. Complexity of scheduling under precedence constraints. Operations Research, 26(1):22–35, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  48. S. Leonardi. A simpler proof of preemptive total flow time approximation on parallel machines. In E. Bampis, K. Jansen, and C. Kenyon, editors, Efficient Approximation and Online Algorithms. LNCS, volume 3484, pages 203–212. Springer Berlin, 2006.

    Chapter  Google Scholar 

  49. G. Malewicz, A.L. Rosenberg, and M. Yurkewych. Toward a theory for scheduling dags in internet-based computing. IEEE Transactions on Computers, 55(6):757–768, 2006.

    Article  Google Scholar 

  50. R. McNaughton. Scheduling with deadlines and loss functions. Management Science, 6(1):1–12, 1959.

    Article  MATH  MathSciNet  Google Scholar 

  51. R. Motwani, S. Phillips, and E. Torng. Non-clairvoyant scheduling. Theoretical Computer Science, 130(1):17–47, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  52. A.W. Mu’alem and D.G. Feitelson. Utilization, predictability, workloads, and user runtime estimates in scheduling the IBM SP2 with backfilling. IEEE Transactions on Parallel and Distributed Systems, 12(6):529–543, 2001.

    Article  Google Scholar 

  53. R.R. Muntz and E.G. Coffman Jr. Optimal preemptive scheduling on two-processor systems. IEEE Transactions on Computers, 18(11):1014–1020, 1969.

    Article  Google Scholar 

  54. R.R. Muntz and E.G. Coffman Jr. Preemptive scheduling of real-time tasks on multiprocessor systems. Journal of the ACM, 17(2):324–338, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  55. S. Muthukrishnan, R. Rajaramany, A. Shaheen, and J.E. Gehrke. Online scheduling to minimize average stretch. In Proceedings of 40th Annual Symposium on Foundations of Computer Science (FOCS’99), pages 433–443. IEEE, 1999.

    Google Scholar 

  56. N. Ni and L.N. Bhuyan. Fair scheduling in internet routers. IEEE Transactions on Computers, 51(6):686–701, 2002.

    Article  Google Scholar 

  57. M. Pinedo. Scheduling: Theory, Algorithms, and Systems. Prentice-Hall, Englewood Cliffs, 1995.

    MATH  Google Scholar 

  58. C.N. Potts and L.N. Wassenhove. Single machine scheduling to minimize total late work. Operations Research, 40:586–595, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  59. K. Pruhs, J. Sgall, and E. Torng. Online scheduling. In J.Y. Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pages 15.1–15.42. CRC Press, Boca Raton, 2004.

    Google Scholar 

  60. A. Rosenberg. On scheduling mesh-structured computations for internet-based computing. IEEE Transactions on Computers, 53(9):1176–1186, 2004.

    Article  Google Scholar 

  61. A. Rosenberg and M. Yurkewych. Guidelines for scheduling some common computation-dags for internet-based computing. IEEE Transactions on Computers, 54(4):428–438, 2005.

    Article  Google Scholar 

  62. M. Rothkopf. Scheduling independent tasks on parallel processors. Management Science, 12(5):437–447, 1966.

    Article  MathSciNet  Google Scholar 

  63. K. Rz?dca. Resource Management Models and Algorithms for Multi-Organizational Grids. Ph.D. thesis, Institut National Polytechnique de Grenoble and Polish-Japanese Institute of Information Technology, 2007.

    Google Scholar 

  64. G. Sabin and P. Sadayappan. Unfairness metrics for space-sharing parallel job schedulers. In D. Feitelson, E. Frachtenberg, L. Rudolph, and U. Schwiegelshohn, editors, Proceedings of 11th Workshop on Job Scheduling Strategies for Parallel Processing. LNCS, volume 3834, pages 238–256, Springer Berlin, 2005.

    Chapter  Google Scholar 

  65. S. Sahni. Algorithms for scheduling independent tasks. Journal of the ACM, 23(1):116–127, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  66. J. Sgall. On-line scheduling. In A. Fiat and G. Woeginger, editors, Online Algorithms: The State of the Art. LNCS, volume 1442, pages 196–231. Springer, Berlin, 1998.

    Google Scholar 

  67. Y. Shafransky. Notions of a problem and subproblem in operations research under the complexity analysis. In Proceedings of 10th International Workshop on Project Management and Scheduling (PMS’06), pages 319–324, Poznań, Poland, 2006.

    Google Scholar 

  68. R. Sitters. Two NP-hardness results for preemptive minsum scheduling of unrelated parallel machines. In K. Aardal and B. Gerards, editors, Proceedings of IPCO 2001. LNCS, volume 2081, pages 396–405, Springer Berlin, 2001.

    Google Scholar 

  69. M. Skutella and G. Woeginger. A PTAS for minimizing the weighted sum of job completion times on parallel machines. In Proceedings of the 31st Annual ACM Symposium on Theory of Computing (STOC’99), pages 400–407, 1999.

    Google Scholar 

  70. C. Stein and J. Wein. On the existence of schedules that are near-optimal for both makespan and total weighted completion time. Operations Research Letters, 21:115–122, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  71. V.G. Timkovsky. Reducibility among scheduling classes. In J.Y.Leung, editor, Handbook of Scheduling: Algorithms, Models, and Performance Analysis, pages 8.1–8.42. CRC Press, Boca Raton, 2004.

    Google Scholar 

  72. J.D. Ullman. NP-complete scheduling problems. J. Computer System Science, 10:384–393, 1975.

    Article  MATH  MathSciNet  Google Scholar 

  73. V.G. Vizing. Minimization of the maximum delay in servicing systems with interruption. U.S.S.R. Computatioanl Mathematics and Mathematical Physics, 22(3):227–233, 1982.

    Google Scholar 

  74. G. Woeginger. When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)? INFORMS Journal on Computing, 12(1):57–74, 2000. see also Electronic Colloquium on Computational Complexity, 2001, Report TR01-084, ISSN 1433-8092.

    Google Scholar 

  75. M. Yue. On the exact upper bound for the multifit processor scheduling algorithm. Annals of Operations Research, 24(1):233–259, 1990.

    Article  MATH  MathSciNet  Google Scholar 

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  1. Poznan University of Technology Inst. Computing Science, ul. Piotrowo 2, 60-695, Poznan, Poland

    Maciej Drozdowski

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Drozdowski, M. (2009). Classic Scheduling Theory. In: Scheduling for Parallel Processing. Computer Communications and Networks. Springer, London. https://doi.org/10.1007/978-1-84882-310-5_4

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  • DOI: https://doi.org/10.1007/978-1-84882-310-5_4

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