Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
A New Insight into the Coffman-Graham Algorithm
SIAM Journal on Computing
Algorithms for Scheduling Independent Tasks
Journal of the ACM (JACM)
`` Strong '' NP-Completeness Results: Motivation, Examples, and Implications
Journal of the ACM (JACM)
Precedence constrained scheduling to minimize sum of weighted completion times on a single machine
Discrete Applied Mathematics
Two-Dimensional Gantt Charts and a Scheduling Algorithm of Lawler
SIAM Journal on Discrete Mathematics
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
Ruling Out PTAS for Graph Min-Bisection, Dense k-Subgraph, and Bipartite Clique
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Precedence constrained scheduling in (2-73p+1)·optimal
Journal of Computer and System Sciences
On the approximability of average completion time scheduling under precedence constraints
Discrete Applied Mathematics
Scheduling chain-structured tasks to minimize makespan and mean flow time
Information and Computation
Optimal Long Code Test with One Free Bit
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Operations Research Letters
On the Approximability of Single-Machine Scheduling with Precedence Constraints
Mathematics of Operations Research
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Already in 1966, Graham showed that a simple procedure called list scheduling yields a 2-approximation algorithm for the central problem of scheduling precedence constrained jobs on identical machines to minimize makespan. Till this date it has remained the best algorithm and whether it can or cannot be improved has become a major open problem in scheduling theory. We address this problem by establishing a quite surprising relation between the approximability of the considered problem and that of scheduling precedence constrained jobs on a single machine to minimize weighted completion time. More specifically, we prove that if the single machine problem is hard to approximate within a factor of 2-ε then the considered parallel machine problem, even in the case of unit processing times, is hard to approximate within a factor of 2-ζ, where ζ tends to 0 as ε tends to 0. Combining this with Bansal & Khot's recent hardness result for the single machine problem gives that it is NP-hard to improve upon the approximation ratio obtained by Graham, assuming a new variant of the unique games conjecture.