Abstract

We consider a restricted version of the general Set Covering problem in which each set in the given set system intersects with any other set in at most 1 element. We show that the Set Covering problem with intersection 1 cannot be approximated within a o(log n) factor in random polynomial time unless NP ` ZT IME(n ). We also observe that the main challenge in derandomizing this reduction lies in find a hitting set for large volume combinatorial rectangles satisfying certain intersection properties. These properties are not satisfied by current methods of hitting set construction. An example

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