Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximating total flow time on parallel machines
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Multiprocessor scheduling with rejection
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Algorithms for facility location problems with outliers
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
Scheduling Unrelated Machines by Randomized Rounding
SIAM Journal on Discrete Mathematics
Techniques for Scheduling with Rejection
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation
Mathematical Programming: Series A and B
Saving an epsilon: a 2-approximation for the k-MST problem in graphs
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A robust maximum completion time measure for scheduling
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Approximating the k-multicut problem
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Theoretical Computer Science
A unified approach to approximating partial covering problems
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Model-driven optimization using adaptive probes
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimizing Average Flow-time: Upper and Lower Bounds
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A constant factor approximation algorithm for k-median clustering with outliers
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
A primal-dual approximation algorithm for partial vertex cover: making educated guesses
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Better algorithms for minimizing average flow-time on related machines
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On-line scheduling of unit time jobs with rejection: minimizing the total completion time
Operations Research Letters
Energy efficient scheduling via partial shutdown
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A primal-dual approximation algorithm for min-sum single-machine scheduling problems
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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In classical scheduling problems, we are given jobs and machines, and have to schedule all the jobs to minimize some objective function. What if each job has a specified profit, and we are no longer required to process all jobs? Instead, we can schedule any subset of jobs whose total profit is at least a (hard) target profit requirement, while still trying to approximately minimize the objective function. We refer to this class of problems as scheduling with outliers . This model was initiated by Charikar and Khuller (SODA '06) for minimum max-response time in broadcast scheduling. In this paper, we consider three other well-studied scheduling objectives: the generalized assignment problem, average weighted completion time, and average flow time, for which LP-based approximation algorithms are provided. Our main results are: For the minimum average flow time problem on identical machines, we give an LP-based logarithmic approximation algorithm for the unit profits case, and complement this result by presenting a matching integrality gap. For the average weighted completion time problem on unrelated machines, we give a constant-factor approximation. The algorithm is based on randomized rounding of the time-indexed LP relaxation strengthened by knapsack-cover inequalities. For the generalized assignment problem with outliers, we outline a simple reduction to GAP without outliers to obtain an algorithm whose makespan is within 3 times the optimum makespan, and whose cost is at most (1 + *** ) times the optimal cost.