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- W2106984527 abstract "We study the relationship between the approximation factor for the Set-Cover problem and the parameters Δ : the maximum cardinality of any subset, and k : the maximum number of subsets containing any element of the ground set. We show an LP rounding based approximation of $(k-1)(1-e^{-frac{ln Delta}{k-1}}) +1$ , which is substantially better than the classical algorithms in the range k ≈ ln Δ, and also improves on related previous works [19,22]. For the interesting case when k = θ(logΔ) we also exhibit an integrality gap which essentially matches our approximation algorithm. We also prove a hardness of approximation factor of $Omegaleft(frac{log Delta}{(loglog Delta)^2}right)$ when k = θ(logΔ). This is the first study of the hardness factor specifically for this range of k and Δ, and improves on the only other such result implicitly proved in [18]." @default.
- W2106984527 created "2016-06-24" @default.
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- W2106984527 date "2012-01-01" @default.
- W2106984527 modified "2023-09-26" @default.
- W2106984527 title "New and Improved Bounds for the Minimum Set Cover Problem" @default.
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- W2106984527 doi "https://doi.org/10.1007/978-3-642-32512-0_25" @default.
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