Two-Dimensional Gantt Charts and a Scheduling Algorithm of Lawler
SIAM Journal on Discrete Mathematics
Approximation Techniques for Average Completion Time Scheduling
SIAM Journal on Computing
A scheduling model for reduced CPU energy
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Algorithmic problems in power management
ACM SIGACT News
Energy-efficient algorithms for flow time minimization
ACM Transactions on Algorithms (TALG)
Getting the best response for your erg
ACM Transactions on Algorithms (TALG)
Communications of the ACM
Non-clairvoyant speed scaling for weighted flow time
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Speed Scaling for Weighted Flow Time
SIAM Journal on Computing
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the performance of smith's rule in single-machine scheduling with nonlinear cost
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Energy Aware Scheduling for Unrelated Parallel Machines
GREENCOM '12 Proceedings of the 2012 IEEE International Conference on Green Computing and Communications
| Hi-index | 0.00 |
We study scheduling problems on a machine of varying speed. Assuming a known speed function (given through an oracle) we ask for a cost-efficient scheduling solution. Our main result is a PTAS for minimizing the total weighted completion time on a machine of varying speed. This implies also a PTAS for the closely related problem of scheduling to minimize generalized global cost functions. The key to our results is a re-interpretation of the problem within the well-known two-dimensional Gantt chart: instead of the standard approach of scheduling in the time-dimension, we construct scheduling solutions in the weight-dimension. We also consider a dynamic problem variant in which deciding upon the speed is part of the scheduling problem and we are interested in the tradeoff between scheduling cost and speed-scaling cost, which is typically the energy consumption. We obtain two insightful results: (1) the optimal scheduling order is independent of the energy consumption and (2) the problem can be reduced to the setting where the speed of the machine is fixed, and thus admits a PTAS.