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- W2563150266 abstract "Abstract For the hierarchical scheduling problem on identical machines to minimize the maximum T-time of all machines under the condition that the total completion time of all jobs is minimum, where the T-time of a machine is defined as the total completion time of jobs scheduled on the machine, it is NP-hard if the number of the machines is fixed, and strongly NP-hard otherwise. When the number of the machines is fixed, a forward dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS) have been presented in a literature. In the literature, it is showed that the worst-case ratio of the classical algorithm SPT is at most 11 6 and at least 5 3 . In this paper, we give an improved worst-case ratio, which is at most 9 5 and at least 7 4 , of the algorithm. Another algorithm, whose worst-case ratio is at most 7 6 and at least 35 33 , is provided for the two-machine case. On the other hand, we present a backward dynamic programming algorithm and an FPTAS with the better time complexities." @default.
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- W2563150266 date "2017-04-01" @default.
- W2563150266 modified "2023-09-27" @default.
- W2563150266 title "Notes on a hierarchical scheduling problem on identical machines" @default.
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- W2563150266 doi "https://doi.org/10.1016/j.ipl.2016.12.001" @default.
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