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- W2010996873 abstract "We prove semi-logarithmic inapproximability for a maximization problem called unique coverage: given a collection of sets, find a subcollection that maximizes the number of elements covered exactly once. Specifically, we prove O(1/ logσ(e)n) inapproximability assuming that NP n BPTIME(2ne) for some e > 0. We also prove O(1/log1/3-en) inapproximability, for any e > 0, assuming that refuting random instances of 3SAT is hard on average; and prove O(1/log n) inapproximability under a plausible hypothesis concerning the hardness of another problem, balanced bipartite independent set. We establish matching upper bounds up to exponents, even for a more general (budgeted) setting, giving an Ω(1/log n)-approximation algorithm as well as an Ω(1/log B)-approximation algorithm when every set has at most B elements. We also show that our inapproximability results extend to envy-free pricing, an important problem in computational economics. We describe how the (budgeted) unique coverage problem, motivated by real-world applications, has close connections to other theoretical problems including max cut, maximum coverage, and radio broad-casting." @default.
- W2010996873 created "2016-06-24" @default.
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- W2010996873 date "2006-01-22" @default.
- W2010996873 modified "2023-09-23" @default.
- W2010996873 title "Combination can be hard: approximability of the unique coverage problem" @default.
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- W2010996873 doi "https://doi.org/10.5555/1109557.1109577" @default.
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