Network flows and scheduling have been studied intensely, but mostly separately. In many applications a joint optimization model for routing and scheduling is desireable. Therefore, we study flows over time with a demand split into jobs. Our objective is to minimize the weighted sum of completion times of these jobs. This is closely related to preemptive scheduling on a single machine with a processing speed increasing over time. For both, flow scheduling and increasing speed scheduling, we provide an EPTAS. Without release dates we can prove a tight approximation factor of (√3+1)/2 for Smith's rule, by fully characterizing the worst case instances. We give exact algorithms for some special cases and a dynamic program for speed functions with a constant number of speeds. We can prove a competitive ratio of 2 for the online version. We also study the class of blind algorithms, i.e., those which schedule without knowledge of the speed function. © 2010 Springer-Verlag.
CITATION STYLE
Stiller, S., & Wiese, A. (2010). Increasing speed scheduling and flow scheduling. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6507 LNCS, pp. 279–290). https://doi.org/10.1007/978-3-642-17514-5_24
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