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List Scheduling

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 335 Accesses

Years and Authors of Summarized Original Work

  • 1966; Graham

Problem Definition

The paper of Graham [8] was published in the 1960s. Over the years, it served as a common example of online algorithms (though the original algorithm was designed as a simple approximation heuristic). The following basic setting is considered.

A sequence of n jobs is to be assigned to m identical machines. Each job should be assigned to one of the machines. Each job has a size associated with it, which can be seen as its processing time or its load. The load of a machine is the sum of sizes of jobs assigned to it. The goal is to minimize the maximum load of any machine, also called the makespan. We refer to this problem as Job Scheduling.

If jobs are presented one by one and each job needs to be assigned to a machine in tur, without any knowledge of future jobs, the problem is called online. Online algorithms are typically evaluated using the (absolute) competitive ratio, which is similar to the approximation...

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Recommended Reading

  1. Albers S (1999) Better bounds for online scheduling. SIAM J Comput 29(2):459–473

    Article  MathSciNet  MATH  Google Scholar 

  2. Azar Y, Epstein L (2004) On-line load balancing of temporary tasks on identical machines. SIAM J Discret Math 18(2):347–352

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen B, van Vliet A, Woeginger GJ (1994) New lower and upper bounds for on-line scheduling. Oper Res Lett 16:221–230

    Article  MathSciNet  MATH  Google Scholar 

  4. Epstein L (2000) A note on on-line scheduling with precedence constraints on identical machines. Inf Process Lett 76:149–153

    Article  MathSciNet  MATH  Google Scholar 

  5. Faigle U, Kern W, Turán G (1989) On the performane of online algorithms for partition problems. Acta Cybern 9:107–119

    MATH  Google Scholar 

  6. Fleischer R, Wahl M (2000) On-line scheduling revisited. J Sched 3:343–353

    Article  MathSciNet  MATH  Google Scholar 

  7. Gormley T, Reingold N, Torng E, Westbrook J (2000) Generating adversaries for request-answer games. In: Proceedings of the 11th symposium on discrete algorithms (SODA2000), San Francisco, pp 564–565

    Google Scholar 

  8. Graham RL (1966) Bounds for certain multiprocessing anomalies. Bell Syst Technol J 45:1563–1581

    Article  MATH  Google Scholar 

  9. Graham RL (1969) Bounds on multiprocessing timing anomalies. SIAM J Appl Math 17, 263–269

    MathSciNet  MATH  Google Scholar 

  10. Hochbaum DS, Shmoys DB (1987) Using dual approximation algorithms for scheduling problems: theoretical and practical results. J ACM 34(1):144–162

    Article  MathSciNet  Google Scholar 

  11. Noga J, Seiden SS (2001) An optimal online algorithm for scheduling two machines with release times. Theor Comput Sci 268(1):133–143

    Article  MathSciNet  MATH  Google Scholar 

  12. Rudin JF III, Chandrasekaran R (2003) Improved bounds for the online scheduling problem. SIAM J Comput 32:717–735

    Article  MathSciNet  MATH  Google Scholar 

  13. Rudin JF III (2001) Improved bounds for the online scheduling problem. Ph.D. thesis, The University of Texas at Dallas

    Google Scholar 

  14. Sgall J (1998) On-line scheduling. In: Fiat A, Woeginger GJ (eds) Online algorithms: the state of the art. Springer, Berlin/New York, pp 196–231

    Chapter  Google Scholar 

  15. Shmoys DB, Wein J, Williamson DP (1995) Scheduling parallel machines on-line. SIAM J Comput 24:1313–1331

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Haifa, Israel

    Leah Epstein

Authors
  1. Leah Epstein
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Correspondence to Leah Epstein .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Epstein, L. (2016). List Scheduling. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_205

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