Approximation algorithms for scheduling unrelated parallel machines

@article{Lenstra1987ApproximationAF,
  title={Approximation algorithms for scheduling unrelated parallel machines},
  author={Jan Karel Lenstra and David B. Shmoys and {\'E}va Tardos},
  journal={Mathematical Programming},
  year={1987},
  volume={46},
  pages={259-271}
}
We consider the following scheduling problem. There arem parallel machines andn independent jobs. Each job is to be assigned to one of the machines. The processing of jobj on machinei requires timepij. The objective is to find a schedule that minimizes the makespan.Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed… 

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References

SHOWING 1-10 OF 47 REFERENCES

A Polynomial Approximation Scheme for Scheduling on Uniform Processors: Using the Dual Approximation Approach

A family of polynomial-time algorithms are given such that the last job to finish is completed as quickly as possible and the algorithm delivers a solution that is within a relative error of the optimum.

Using dual approximation algorithms for scheduling problems: Theoretical and practical results

  • D. HochbaumD. Shmoys
  • Computer Science
    26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
  • 1985
A new approach to constructing approximation algorithms, which the aim is find superoptimal, but infeasible solutions, and the performance is measured by the degree of infeasibility allowed, which should find wide applicability for any optimization problem where traditional approximation algorithms have been particularly elusive.

A Polynomial Approximation Scheme for Machine Scheduling on Uniform Processors: Using the Dual Approximation Approach

A family of polynomial-time algorithms is given such that A∈ delivers a solution that is within a relative error of e of the optimum of the minimum makespan problem on uniform parallel processors.

APPROXIMATE AND EXACT ALGORITHMS FOR SCHEDULING INDEPENDENT TASKS ON UNRELATED PROCESSORS

The "unrelated" processors system which is treated is a generalization of the identical proc- essors sys tern where the processor's speed may vary according to the task being executed and it models the heterogeneous multiprocessor system where respectively specialized processors can execute the each type of tasks more efficiently than others.

Complexity Results for Multiprocessor Scheduling under Resource Constraints

The main results of this paper imply that almost all cases of this scheduling problem, even with only one resource, are NP-complete and hence are as difficult as the notorious traveling salesman problem.

Exact and Approximate Algorithms for Scheduling Nonidentical Processors

Exact and approximate algorithms are presented for scheduling independent tasks in a multiprocessor environment in which the processors have different speeds and are guaranteed to obtain solutions that are close to the optimal.

Algorithms for Scheduling Independent Tasks

Three general techniques are presented to obtain approximate solutions for optimization problems solvable in this way, and polynomial time algorithms are applied to obtain “good” approximate solutions.

Algorithms for Scheduling Tasks on Unrelated Processors

This is the best polynomial-time algorithm known for scheduling such sets of tasks and requires time O(nlogn) for every fixed value of m.

Cyclic Scheduling via Integer Programs with Circular Ones

This work identifies a large class of cyclic staffing problems for which special structure permits the ILP to be solved parametrically as a bounded series of network flow problems.