Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Approximate algorithms scheduling parallelizable tasks
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Scheduling problems for parallel dedicated machines under multiple resource constraints
Discrete Applied Mathematics - International symposium on combinatorial optimisation
Approximation Algorithms for Scheduling on Multiple Machines
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An R || Cmax Quantum Scheduling Algorithm
Quantum Information Processing
Scheduling identical parallel machines and operators within a period based changing mode
Computers and Operations Research
A unified approach to scheduling on unrelated parallel machines
Journal of the ACM (JACM)
Scheduling parallel jobs with linear speedup
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
LP rounding and an almost harmonic algorithm for scheduling with resource dependent processing times
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Parallel machine scheduling with flexible resources
Computers and Industrial Engineering
Operations Research Letters
| Hi-index | 0.00 |
We consider unrelated parallel machine scheduling problems with the objective to minimize the schedule makespan. In addition to its machine-dependence, the processing time of any job is also dependent on the usage of a scarce renewable resource. An amount of k units of that resource, e.g. workers, can be distributed over the jobs in process, and the more of that resource is allocated to a job, the smaller its processing time. The model generalizes the classical unrelated machine scheduling problem, adding a resource-time tradeoff. It is also a natural variant of a generalized assignment problem studied previously by Shmoys and Tardos, the difference lying in the fact the resource is renewable and not a total budget constraint. We use a two-phased LP rounding technique to assign resources to jobs and jobs to machines. Combined with Graham's list scheduling, we thus prove the existence of a $(4+2\sqrt{2})$-approximation algorithm. We show how our approach can be adapted to scheduling problems with dedicated machines as well, with an improvement of the performance bound to $(3+2\sqrt{2})$. Moreover, we derive a lower bound of 2 for the employed LP-based analysis, and we prove a (3/2)-inapproximability result.