Approximation algorithms for scheduling unrelated parallel machines
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STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
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Mathematical Programming: Series A and B
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Improved approximation schemes for scheduling unrelated parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Multiprocessor Scheduling with Rejection
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ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Preemptive Scheduling with Rejection
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
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FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Small Approximate Pareto Sets for Bi-objective Shortest Paths and Other Problems
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
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FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Small Approximate Pareto Sets for Biobjective Shortest Paths and Other Problems
SIAM Journal on Computing
A survey on offline scheduling with rejection
Journal of Scheduling
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We consider the classical problem of scheduling a set of independent jobs on a set of unrelated machines with costs. We are given a set of n monoprocessor jobs and m machines where each job is to be processed without preemptions. Executing job j on machine i requires time pij ≥ 0 and incurs cost cij . Our objective is to find a schedule obtaining a tradeoff between the makespan and the total cost. We focus on the case where the number of machines is a fixed constant, and we propose a simple FPTAS that computes for any Ɛ 0 a schedule with makespan at most (1+Ɛ)T and cost at most Copt(T), in time O(n(n/Ɛ)m), given that there exists a schedule of makespan T, where Copt(T) is the cost of the minimum cost schedule which achieves a makespan of T. We show that the optimal makespan-cost trade-off (Pareto) curve can be approximated by an efficient polynomial time algorithm within any desired accuracy. Our results can also be applied to the scheduling problem where the rejection of jobs is allowed. Each job has a penalty associated to it, and one is allowed to schedule any subset of jobs. In this case the goal is the minimization of the makespan of the scheduled jobs and the total penalty of the rejected jobs.