@incollection{StillerWiese2010,
Title = {Increasing speed scheduling and Flow scheduling},
Author = {Stiller, Sebastian and Wiese, Andreas},
Booktitle = {Algorithms and Computation (ISAAC 2010)},
Pages = {279–290},
Year = {2010},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Institution = {Technische Universit\"at Berlin},
Abstract = {Flows and scheduling have been studied intensely, but 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. The 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 proof a tight approximation factor of $(\sqrt3+1)/2$ 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 proof 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. For both online, and blind algorithm we provide a lower bound.},
Keywords = {Dynamic Flows, Earliest Arrival Flows, Scheduling with varying Speed, Weighted Sum of Completion Times, Approximation Algorithms}
}