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On lazy bureaucrat scheduling with common deadlines

Author

Listed:
  • Ling Gai

    (Zhejiang University)

  • Guochuan Zhang

    (Zhejiang University)

Abstract

Lazy bureaucrat scheduling is a new class of scheduling problems introduced by Arkin et al. (Inf. Comput. 184:129–146, 2003). In this paper we focus on the case where all the jobs share a common deadline. Such a problem is denoted as CD-LBSP, which has been considered by Esfahbod et al. (Algorithms and data structures. Lecture notes in computer science, vol. 2748, pp. 59–66, 2003). We first show that the worst-case ratio of the algorithm SJF (Shortest Job First) is two under the objective function [min-time-spent], and thus answer an open question posed in (Esfahbod, et al. in Algorithms and data structures. Lecture notes in computer science, vol. 2748, pp. 59–66, 2003). We further present two approximation schemes A k and B k both having worst-case ratio of $\frac{k+1}{k}$ , for any given integer k>0, under the objective functions [min-makespan] and [min-time-spent], respectively. Finally, we prove that the problem CD-LBSP remains NP-hard under several objective functions, even if all jobs share the same release time.

Suggested Citation

  • Ling Gai & Guochuan Zhang, 2008. "On lazy bureaucrat scheduling with common deadlines," Journal of Combinatorial Optimization, Springer, vol. 15(2), pages 191-199, February.
    • Handle: RePEc:spr:jcomop:v:15:y:2008:i:2:d:10.1007_s10878-007-9076-2
    DOI: 10.1007/s10878-007-9076-2
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    Citations

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    Cited by:

    1. Ling Gai & Guochuan Zhang, 2018. "Online lazy bureaucrat scheduling with a machine deadline," Journal of Combinatorial Optimization, Springer, vol. 35(2), pages 530-537, February.
    2. Furini, Fabio & Ljubić, Ivana & Sinnl, Markus, 2017. "An effective dynamic programming algorithm for the minimum-cost maximal knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 262(2), pages 438-448.
    3. Laurent Gourvès & Jérôme Monnot & Lydia Tlilane, 2018. "Subset sum problems with digraph constraints," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 937-964, October.

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