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
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Efficient approximation algorithms for scheduling malleable tasks
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Dependent Rounding in Bipartite Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximation schemes for parallel machine scheduling problems with controllable processing times
Computers and Operations Research
Approximation Algorithms for Scheduling on Multiple Machines
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Scheduling parallel jobs with linear speedup
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Unrelated parallel machine scheduling with resource dependent processing times
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Parallel machine scheduling with flexible resources
Computers and Industrial Engineering
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We consider a scheduling problem on unrelated parallel machines with the objective to minimize the makespan. In addition to its machine dependence, the processing time of any job is dependent on the usage of a scarce renewable resource, e.g. workers. A given amount of that resource can be distributed over the jobs in process at any time. The more of the resource is allocated to a job, the smaller is its processing time. This model generalizes the classical unrelated parallel machine scheduling problem by adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied by Shmoys and Tardos. On the basis of an integer linear programming formulation for (a relaxation of) the problem, we adopt a randomized LP rounding technique from Kumar et al. (FOCS 2005) in order to obtain a deterministic, integral LP solution that is close to optimum. We show how this rounding procedure can be used to derive a deterministic 3.75-approximation algorithm for the scheduling problem. This improves upon previous results, namely a deterministic 6.83-approximation, and a randomized 4-approximation. The improvement is due to the better LP rounding and a new scheduling algorithm that can be viewed as a restricted version of the harmonic algorithm for bin packing.