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
Linear programming
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
The hardness of approximation: gap location
Computational Complexity
Approximation schemes for scheduling
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Improved bicriteria existence theorems for scheduling
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
Approximate majorization and fair online load balancing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Fairness in routing and load balancing
Journal of Computer and System Sciences - Special issue on Internet algorithms
Approximation Schemes for Scheduling on Uniformly Related and Identical Parallel Machines
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Load balancing in the L/sub p/ norm
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Operations Research Letters
Convex programming for scheduling unrelated parallel machines
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
An Optimal On-Line Algorithm for Preemptive Scheduling on Two Uniform Machines in the lpNorm
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
A Lower Bound for the On-Line Preemptive Machine Scheduling with lpNorm
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
A unified approach to scheduling on unrelated parallel machines
Journal of the ACM (JACM)
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A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different lp norms. We address this problem by introducing the concept of an All-norm 驴approximation algorithm, which supplies one solution that guarantees 驴approximation to all lp norms simultaneously. Specifically, we consider the problem of scheduling in the restricted assignment model, where there are m machines and n jobs, each is associated with a subset of the machines and shouldb e assignedto one of them. Previous work considered approximation algorithms for each norm separately. Lenstra et al. [12] showeda 2-approximation algorithm for the problem with respect to the l驴 norm. For any fixed lp norm the previously known approximation algorithm has a performance of 驴(p). We provide an all-norm 2-approximation polynomial algorithm for the restricted assignment problem. On the other hand, we show that for any given lp norm (p 1) there is no PTAS unless P=NP by showing an APX-hardness result. We also show for any given lp norm a FPTAS for any fixedn umber of machines.