Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
A PTAS for minimizing the weighted sum of job completion times on parallel machines
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Approximation techniques for average completion time scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Non-approximability Results for Scheduling Problems with Minsum Criteria
Proceedings of the 6th International IPCO Conference on Integer Programming and Combinatorial Optimization
Improved Scheduling Algorithms for Minsum Criteria
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Scheduling-LPs Bear Probabilities: Randomized Approximations for Min-Sum Criteria
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
Approximation Schemes for Minimizing Average Weighted Completion Time with Release Dates
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Approximability of Average Completion Time Scheduling on Unrelated Machines
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
New constructions of mechanisms with verification
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Approximation algorithms for scheduling problems with a modified total weighted tardiness objective
Operations Research Letters
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We consider the well known problem of scheduling jobs with release dates to minimize their average weighted completion time. When multiple machines are available, the machine environment may range from identical machines (the processing time required by a job is invariant across the machines) at one end of the spectrum to unrelated machines (the processing time required by a job on each machine is specified by an arbitrary vector) at the other end. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms are known for even the most general machine environment of unrelated machines. Recently a PTAS was discovered for the case of identical parallel machines [1]. In contrast, the problem is MAX SNP-hard for unrelated machines [11]. An important open problem was to determine the approximability of the intermediate case of uniformly related machines where each machine has a speed and it takes p/s time to process a job of size p on a machine with speed s. We resolve the complexity of this problem by obtaining a PTAS. This improves the earlier known approximation ratio of (2 + Ɛ).