Journal of Computer Science and Technology

, Volume 21, Issue 6, pp 984–988 | Cite as

Semi-Online Algorithms for Scheduling with Machine Cost

  • Yi-Wei JiangEmail author
  • Yong He
Short Paper


In this paper, we consider the following semi-online List Model problem with known total size. We are given a sequence of independent jobs with positive sizes, which must be assigned to be processed on machines. No machines are initially provided, and when a job is revealed the algorithm has the option to purchase new machines. By normalizing all job sizes and machine cost, we assume that the cost of purchasing one machine is 1. We further know the total size of all jobs in advance. The objective is to minimize the sum of the makespan and the number of machines to be purchased. Both non-preemptive and preemptive versions are considered. For the non-preemptive version, we present a new lower bound 6/5 which improves the known lower bound 1.161. For the preemptive version, we present an optimal semi-online algorithm with a competitive ratio of 1 in the case that the total size is not greater than 4, and an algorithm with a competitive ratio of 5/4 otherwise, while a lower bound 1.0957 is also presented for general case.


semi-online preemptive scheduling machine cost competitive ratio 


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  1. [1]
    Imreh C, Noga J. Scheduling with machine cost. In Proc. RANDOM-APPROX’99, Berkley, USA, Lecture Notes in Computer Science, 1999, 1671: 168–176.Google Scholar
  2. [2]
    Dósa G, He Y. Better on-line algorithms for scheduling with machine cost. SIAM J. Computing, 2004, 33: 1035–1051.CrossRefzbMATHGoogle Scholar
  3. [3]
    Jiang Y, He Y. Preemptive online algorithms for scheduling with machine cost. Acta Informatica, 2005, 41: 315–340.CrossRefMathSciNetzbMATHGoogle Scholar
  4. [4]
    He Y, Cai S. Semi-online scheduling with machine cost. Journal of Computer Science and Technology, 2002, 17: 781–787.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Cai S, He Y. Quasi-online algorithms for scheduling non-increasing processing jobs with processor cost. Acta Automatica Sinica, 2003, 29: 917–921. (in Chinese)MathSciNetGoogle Scholar
  6. [6]
    Graham R L. Bounds on multiprocessing finishing anomalies. SIAM Journal on Applied Mathematics, 1969, 17(4): 416–429.CrossRefMathSciNetzbMATHGoogle Scholar
  7. [7]
    He Y, Zhang G. Semi-online scheduling on two identical machines. Computing, 1999, 62: 179–187.CrossRefMathSciNetzbMATHGoogle Scholar
  8. [8]
    Kellerer H, Kotov V, Speranza M R, Tuza Z. Semi on-line algorithms for the partition problem. Operations Research Letters, 1997, 21: 235–242.CrossRefMathSciNetzbMATHGoogle Scholar
  9. [9]
    Dósa G, He Y. Semi-online algorithms for parallel machine scheduling problems. Computing, 2004, 72: 355–363.CrossRefMathSciNetzbMATHGoogle Scholar
  10. [10]
    Epstein L. Bin stretching revisited. Acta Informatica, 2003, 39: 97–117.CrossRefMathSciNetzbMATHGoogle Scholar
  11. [11]
    He Y, Jiang Y. Optimal algorithms for semi-online preemptive scheduling problems on two uniform machines. Acta Informatica, 2004, 40: 367–383.CrossRefMathSciNetzbMATHGoogle Scholar
  12. [12]
    Seiden S. A guessing game and randomized online algorithms. In Proc. the 32nd Annual ACM Symposium on the Theory of Computing, ACM, New York, 2000, pp.592–601.Google Scholar
  13. [13]
    McNaughton R. Scheduling with deadlines and loss functions. Management Sciences, 1959, 6: 1–12.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Faculty of ScienceZhejiang Sci-Tech UniversityHangzhouP.R. China
  2. 2.Department of MathematicsZhejiang UniversityHangzhouP.R. China

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