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
e-approximations with minimum packing constraint violation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Structure of a simple scheduling polyhedron
Mathematical Programming: Series A and B
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)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
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 Parallel Machines for the Customer Order Problem
Journal of Scheduling
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
Supply Chain Scheduling: Conflict and Cooperation in Assembly Systems
Operations Research
The Power of Preemption on Unrelated Machines and Applications to Scheduling Orders
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Inapproximability Results for Maximum Edge Biclique, Minimum Linear Arrangement, and Sparsest Cut
SIAM Journal on Computing
Minimizing the sum of weighted completion times in a concurrent open shop
Operations Research Letters
Operations Research Letters
Task assignment algorithms for two-type heterogeneous multiprocessors
Real-Time Systems
Algorithms with limited number of preemptions for scheduling on parallel machines
Journal of Combinatorial Optimization
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Scheduling jobs on unrelated parallel machines so as to minimize makespan is one of the basic problems in the area of machine scheduling. In the first part of the paper, we prove that the power of preemption, i.e., the worst-case ratio between the makespan of an optimal nonpreemptive and that of an optimal preemptive schedule, is at least 4. This matches the upper bound proposed in Lin and Vitter [Lin, J.-H., J. S. Vitter. 1992. ε-approximations with minimum packing constraint violation. Proc. 24th Annual ACM Sympos. Theory of Comput. (STOC), ACM, New York, 771--782] two decades ago. In the second part of the paper, we consider 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 cases, improving and extending a recent result by Leung et al. [Leung, J., H. Li, M. Pinedo, J. Zhang. 2007. Minimizing total weighted completion time when scheduling orders in a flexible environment with uniform machines. Inform. Processing Lett.103 119--129]. Finally, we study this problem in a parallel machine environment, obtaining a polynomial-time approximation scheme for several special cases.