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- W2000431286 abstract "The problem of scheduling a partially ordered set of unit length tasks on m identical processors is known to be NP-complete. There are efficient algorithms for only a few special cases of this problem. In this paper we analyze the effect of the structure of the precedence graph and the availability of the processors on the construction of optimal schedules. We prove that to find an optimal schedule it suffices to consider at each step only initial tasks which belong to the $m - 1$ highest components of the precedence graph. This result reduces the number of cases we have to check during the construction of an optimal schedule. Our method leads to polynomial algorithms if the number of processors is fixed and the precedence graph has a certain form. In particular, if the precedence graph contains only intrees and outtrees, this result leads to linear algorithms for finding an optimal schedule on two or three processors." @default.
- W2000431286 created "2016-06-24" @default.
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- W2000431286 date "1985-08-01" @default.
- W2000431286 modified "2023-09-26" @default.
- W2000431286 title "Scheduling Flat Graphs" @default.
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- W2000431286 doi "https://doi.org/10.1137/0214047" @default.
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