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Encyclopedia of Algorithms pp 1216–1218Cite as

Maximizing the Minimum Machine Load

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  • First Online:

  • 42 Accesses

Years and Authors of Summarized Original Work

  • 1982; Deuermeyer, Friesen, Langston

  • 1997; Woeginger

  • 1998; Azar, Epstein

Problem Definition

In a scheduling problem we have to find an optimal schedule of jobs. Here we consider the parallel machines case, where m machines are given, and we can use them to schedule the jobs. In the most fundamental model, each job has a known processing time, and to schedule the job we have to assign it to a machine, and we have to give its starting time and a completion time, where the difference between the completion time and the starting time is the processing time. No machine may simultaneously run two jobs. If no further assumptions are given then the machines can schedule the jobs assigned to them without an idle time and the total time required to schedule the jobs on a machine is the sum of the processing times of the jobs assigned to it. We call this value the load of the machine.

Concerning the machine environment three different models are...

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Recommended Reading

  1. Azar Y, Epstein L (1998) On-line machine covering. J Sched 1(2):67–77

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  2. Bezáková I, Dani V (2005) Nobody left behind: fair allocation of indivisible goods. ACM SIGecom Exch 5.3

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  3. Csirik J, Kellerer H, Woeginger GJ (1992) The exact LPT-bound for maximizing the minimum completion time. Oper Res Lett 11:281–287

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  4. Deuermeyer BL, Friesen DK, Langston MA (1982) Scheduling to maximize the minimum processor finish time in a multiprocessor system. SIAM J Discret Methods 3:190–196

    Article  MathSciNet  MATH  Google Scholar 

  5. He Y, Zhang GC (1999) Semi on-line scheduling on two identical machines. Computing 62:179–187

    Article  MathSciNet  MATH  Google Scholar 

  6. Tan Z, Wu Y (2007) Optimal semi-online algorithms for machine covering. Theor Comput Sci 372: 69–80

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  7. Woeginger GJ (1997) A polynomial time approximation scheme for maximizing the minimum machine completion time. Oper Res Lett 20(4):149–154

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Informatics, University of Szeged, Szeged, Hungary

    Csanad Imreh

Authors
  1. Csanad Imreh
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Correspondence to Csanad Imreh .

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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Imreh, C. (2016). Maximizing the Minimum Machine Load. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_503

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