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Preprint 07-2010
Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)- Title
- Increasing speed scheduling and Flow scheduling
- Authors
- Classification
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not available
- Keywords
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Dynamic Flows, Earliest Arrival Flows, Scheduling with varying Speed, Weighted Sum of Completion Times, Approximation Algorithms
- Abstract
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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 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.
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