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- W3183992392 abstract "The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Benczur and Karger (1996) showed that given any $n$-vertex undirected weighted graph $G$ and a parameter $varepsilon in (0,1)$, there is a near-linear time algorithm that outputs a weighted subgraph $G'$ of $G$ of size $tilde{O}(n/varepsilon^2)$ such that the weight of every cut in $G$ is preserved to within a $(1 pm varepsilon)$-factor in $G'$. The graph $G'$ is referred to as a {em $(1 pm varepsilon)$-approximate cut sparsifier} of $G$. Subsequent recent work has obtained a similar result for the more general problem of hypergraph cut sparsifiers. However, all known sparsification algorithms require $Omega(n + m)$ time where $n$ denotes the number of vertices and $m$ denotes the number of hyperedges in the hypergraph. Since $m$ can be exponentially large in $n$, a natural question is if it is possible to create a hypergraph cut sparsifier in time polynomial in $n$, {em independent of the number of edges}. We resolve this question in the affirmative, giving the first sublinear time algorithm for this problem, given appropriate query access to the hypergraph." @default.
- W3183992392 created "2021-08-02" @default.
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- W3183992392 date "2021-01-01" @default.
- W3183992392 modified "2023-09-23" @default.
- W3183992392 title "Sublinear Time Hypergraph Sparsification via Cut and Edge Sampling Queries." @default.
- W3183992392 hasPublicationYear "2021" @default.
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