Inapproximability of Hypergraph Vertex Cover and Applications to Scheduling Problems

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.

• Type: Conference
• Year: 2010
• Where: ICALP
• Authors: Nikhil Bansal, Subhash Khot
• Keywords: Assembly Line Problem, ICALP 2010, Programming Languages, Total Weighted Completion, Vertex Cover Problem