Abstract
We study the scheduling situation where n tasks, subjected to release dates and due dates, have to be scheduled on m parallel processors. We show that, when tasks have unit processing times and either require 1 or m processors simultaneously, the minimum maximal tardiness can be computed in polynomial time. Two algorithms are described. The first one is based on a linear programming formulation of the problem while the second one is a combinatorial algorithm. The complexity status of this “tall/small” task scheduling problem P|r i ,p i =1, size i ∈{1, m}|T max was unknown before, even for two processors.
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Baptiste, P., Schieber, B. A Note on Scheduling Tall/Small Multiprocessor Tasks with Unit Processing Time to Minimize Maximum Tardiness. Journal of Scheduling 6, 395–404 (2003). https://doi.org/10.1023/A:1024012811536
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DOI: https://doi.org/10.1023/A:1024012811536