Approximation algorithms for NP-hard problems
When does a dynamic programming formulation guarantee the existence of an FPTAS?
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Dependent Randomized Rounding Algorithms
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Techniques for Scheduling with Rejection
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
A FPTAS for Approximating the Unrelated Parallel Machines Scheduling Problem with Costs
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
SOFA: Strategyproof Online Frequency Allocation for Multihop Wireless Networks
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
TOFU: semi-truthful online frequency allocation mechanism for wireless network
IEEE/ACM Transactions on Networking (TON)
Bin packing with rejection revisited
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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We consider the problem of preemptively scheduling a set of n jobs on m (identical, uniformly related, or unrelated) parallel machines. The scheduler may reject a subset of the jobs and thereby incur job-dependent penalties for each rejected job, and he must construct a schedule for the remaining jobs so as to optimize the preemptive makespan on the m machines plus the sum of the penalties of the jobs rejected. We provide a complete classification of these scheduling problems with respect to complexity and approximability. Our main results are on the variant with an arbitrary number of unrelated machines. This variant is APX-hard, and we design a 1.58-approximation algorithm for it. All other considered variants are weakly NP-hard, and we provide fully polynomial time approximation schemes for them.