Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Better Approximation Guarantees for Job-Shop Scheduling
SIAM Journal on Discrete Mathematics
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INFORMS Journal on Computing
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
(Acyclic) Job Shops are Hard to Approximate
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Tight bounds for permutation flow shop scheduling
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
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We resolve an open question raised by Feige & Scheideler by showing that the best known approximation algorithm for flow shops is essentially tight with respect to the used lower bound on the optimal makespan. We also obtain a nearly tight hardness result for the general version of flow shops, where jobs are not required to be processed on each machine. Similar results hold true when the objective is to minimize the sum of completion times.