On the exact upper bound for the MULTIFIT processor scheduling algorithm
Annals of Operations Research
Parallel machines scheduling with nonsimultaneous machine available time
Discrete Applied Mathematics
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
The worst-case analysis of the MULTIFIT algorithm for scheduling nonsimultaneous parallel machines
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Information Processing Letters
The effect of machine availability on the worst-case performance of LPT
Discrete Applied Mathematics
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We consider the problem of scheduling a set of independent tasks on multiple same-speed processors with planned shutdown times with the aim of minimizing the makespan. We give an LPT-based algorithm, LPTX, which yields a maximum completion time that is less than or equal to 3/2 the optimal maximum completion time or 3/2 the time that passes from the start of the schedule until the latest end of a downtime. For problems where the optimal schedule ends after the last downtime, and when the downtimes represent fixed jobs, the LPTX maximum completion time is within 3/2 of the optimal maximum completion time. In addition, we show that this result is asymptotically tight for the class of polynomial algorithms assuming that PNP. We also show that the bound obtained previously for a similar problem, when no more than half of the machines are shut down at the same time, for the LPT algorithm is asymptotically tight in the class of polynomial algorithms if PNP.