Shared processor scheduling
We study the shared processor scheduling problem with a single shared processor to maximize total weighted overlap, where an overlap for a job is the amount of time it is processed on its private and shared processor in parallel. A polynomial-time optimization algorithm has been given for the problem with equal weights in the literature. This paper extends that result by showing an (log)-time optimization algorithm for a class of instances in which non-decreasing order of jobs with respect to processing times provides a non-increasing order with respect to weights—this instance generalizes the unweighted case of the problem. This algorithm also leads to a 1/2-approximation algorithm for the general weighted problem. The complexity of the weighted problem remains open.
Dariusz Dereniowski, Wiesław Kubiak. (2018). Shared processor scheduling, 21(6), 583-593. https://doi.org/10.1007/s10951-018-0566-0
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