Multiprocessor scheduling with rejection
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Approximation techniques for average completion time scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Preemptive Scheduling with Rejection
ESA '00 Proceedings of the 8th Annual European Symposium on Algorithms
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On several scheduling problems with rejection or discretely compressible processing times
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
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We consider the general problem of scheduling a set of jobs where we may choose not to schedule certain jobs, and thereby incur a penalty for each rejected job. More specifically, we focus on choosing a set of jobs to reject and constructing a schedule for the remaining jobs so as to optimize the sum of the weighted completion times of the jobs scheduled plus the sum of the penalties of the jobs rejected. We give several techniques for designing scheduling algorithms under this criterion. Many of these techniques show how to reduce a problem with rejection to a (potentially more complex) scheduling problem without rejection. Some of the reductions are based on general properties of certain kinds of linear-programming relaxations of optimization problems, and therefore are applicable to problems outside of scheduling; we demonstrate this by giving an approximation algorithm for a variant of the facility-location problem. In the last section of the paper we consider a different notion of rejection in the context of scheduling: scheduling jobs with due dates so as to maximize the number of jobs that complete by their due dates, or equivalently to minimize the number of jobs that do not complete by their due date and that thus can be considered "rejected." We investigate the approximability of a simple version of this problem, giving approximation algorithms and characterizing integrality gaps of a class of linear-programming relaxations.