Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Approximation algorithms for scheduling unrelated parallel machines
Mathematical Programming: Series A and B
Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Bounding the Power of Preemption in Randomized Scheduling
SIAM Journal on Computing
On Preemptive Scheduling of Unrelated Parallel Processors by Linear Programming
Journal of the ACM (JACM)
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines
Mathematics of Operations Research
Convex quadratic and semidefinite programming relaxations in scheduling
Journal of the ACM (JACM)
Scheduling Unrelated Machines by Randomized Rounding
SIAM Journal on Discrete Mathematics
Non-Approximability Results for Scheduling Problems with Minsum Criteria
INFORMS Journal on Computing
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Scheduling orders for multiple product types to minimize total weighted completion time
Discrete Applied Mathematics
Information Processing Letters
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Single machine precedence constrained scheduling is a vertex cover problem
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Operations Research Letters
On the configuration-LP for scheduling on unrelated machines
ESA'11 Proceedings of the 19th European conference on Algorithms
Robust algorithms for preemptive scheduling
ESA'11 Proceedings of the 19th European conference on Algorithms
Black-box reductions for cost-sharing mechanism design
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
Mathematics of Operations Research
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Scheduling jobs on unrelated parallel machines so as to minimize the makespan is one of the basic, well-studied problems in the area of machine scheduling. In the first part of the paper we prove that the power of preemption, i.e., the ratio between the makespan of an optimal nonpreemptive and an optimal preemptive schedule, is exactly 4. This result is a definite answer to an important basic open problem in scheduling. The proof of the lower bound is based on a clever iterative construction while the rounding technique we use to prove the upper bound is an adaptation of Shmoys and Tardos' rounding for the generalized assignment problem. In the second part of the paper we apply this adaptation to the more general setting in which orders, consisting of several jobs, have to be processed on unrelated parallel machines so as to minimize the sum of weighted completion times of the orders. We obtain the first constant factor approximation algorithms for the preemptive and nonpreemptive case, improving and extending a recent result by Leung et. al.