Increasing speed scheduling and Flow scheduling [article]

Sebastian Stiller, Andreas Wiese, Technische Universität Berlin
2021
Network 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
more » ... EPTAS. Without release dates we can proof a tight approximation factor of (sqrt{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 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.
doi:10.14279/depositonce-14471 fatcat:cawsgke5ezdgdpucy4i5bz3fjq