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• W2949081789 abstract "This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F subseteq E$ with the objective of minimizing the cardinality (or cost in the weighted case) of $F$. We consider a parameterized relaxation of this problem, where given some $0 leq epsilon < 1$, the goal is to construct an edge $(1 - epsilon)$-cover, namely, a subset of edges incident to all but an $epsilon$-fraction of the vertices (or their benefit in the weighted case). The key limitation imposed on the algorithm is that its space is limited to (poly)logarithmically many bits per vertex. Our main result is an asymptotically tight trade-off between $epsilon$ and the approximation ratio: We design a semi-streaming algorithm that on input graph $G$, constructs a succinct data structure $mathcal{D}$ such that for every $0 leq epsilon 1 / sqrt{n} O (sqrt{n}), & text{otherwise} end{array} right. , . ] In particular for the traditional set cover problem we obtain an $O(sqrt{n})$-approximation. This algorithm is proved to be best possible by establishing a family (parameterized by $epsilon$) of matching lower bounds." @default.
• W2949081789 created "2019-06-27" @default.
• W2949081789 creator A5000264005 @default.
• W2949081789 creator A5051186002 @default.
• W2949081789 date "2014-04-27" @default.
• W2949081789 modified "2023-09-25" @default.
• W2949081789 title "Semi-Streaming Set Cover" @default.
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• W2949081789 hasPublicationYear "2014" @default.
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