Abstract
Assuming the Unique Games Conjecture (UGC), we show optimal inapproximability results for two classic scheduling problems. We obtain a hardness of 2 − ε for the problem of minimizing the total weighted completion time in concurrent open shops. We also obtain a hardness of 2 − ε for minimizing the makespan in the assembly line problem.
These results follow from a new inapproximability result for the Vertex Cover problem on k-uniform hypergraphs that is stronger and simpler than previous results. We show that assuming the UGC, for every k ≥ 2, the problem is inapproximable within k − ε even when the hypergraph is almost k -partite.
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Bansal, N., Khot, S. (2010). Inapproximability of Hypergraph Vertex Cover and Applications to Scheduling Problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6198. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14165-2_22
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