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- W2022671649 abstract "We give a deterministic polynomial-time method for finding a set cover in a set system (X, ℛ) of dual VC-dimensiond such that the size of our cover is at most a factor ofO(d log(dc)) from the optimal size,c. For constant VC-dimensional set systems, which are common in computational geometry, our method gives anO(logc) approximation factor. This improves the previous Θ(log⋎X⋎) bound of the greedy method and challenges recent complexity-theoretic lower bounds for set covers (which do not make any assumptions about the VC-dimension). We give several applications of our method to computational geometry, and we show that in some cases, such as those arising in three-dimensional polytope approximation and two-dimensional disk covering, we can quickly findO(c)-sized covers." @default.
- W2022671649 created "2016-06-24" @default.
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- W2022671649 date "1995-12-01" @default.
- W2022671649 modified "2023-09-26" @default.
- W2022671649 title "Almost optimal set covers in finite VC-dimension" @default.
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- W2022671649 doi "https://doi.org/10.1007/bf02570718" @default.
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