Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Theory of linear and integer programming
Theory of linear and integer programming
Provably good routing in graphs: regular arrays
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Dual integer linear programs and the relationship between their optima
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
Exact and Approximate Algorithms for Scheduling Nonidentical Processors
Journal of the ACM (JACM)
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Algorithms for Scheduling Tasks on Unrelated Processors
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Probabilistic construction of deterministic algorithms: Approximating packing integer programs
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Fairness in Routing and Load Balancing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Group-strategyproof cost sharing mechanisms for makespan and other scheduling problems
Theoretical Computer Science
On Multi-dimensional Envy-Free Mechanisms
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fair cost-sharing methods for scheduling jobs on parallel machines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Partitioned EDF scheduling on a few types of unrelated multiprocessors
Real-Time Systems
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We consider the following scheduling problem. There are m parallel machines and n independent jobs. Each job is to be assigned to one of the machines. The processing of job j on machine i requires time pij. The objective is to find a schedule that minimizes the makespan. Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints. In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unless P = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.