Almost-Tight Bounds on Preserving Cuts in Classes of Submodular Hypergraphs
CoRR(2024)
摘要
Recently, a number of variants of the notion of cut-preserving hypergraph
sparsification have been studied in the literature. These variants include
directed hypergraph sparsification, submodular hypergraph sparsification,
general notions of approximation including spectral approximations, and more
general notions like sketching that can answer cut queries using more general
data structures than just sparsifiers. In this work, we provide reductions
between these different variants of hypergraph sparsification and establish new
upper and lower bounds on the space complexity of preserving their cuts. At a
high level, our results use the same general principle, namely, by showing that
cuts in one class of hypergraphs can be simulated by cuts in a simpler class of
hypergraphs, we can leverage sparsification results for the simpler class of
hypergraphs.
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