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- W2951976786 abstract "We introduce the problem Partial VC Dimension that asks, given a hypergraph $H=(X,E)$ and integers $k$ and $ell$, whether one can select a set $Csubseteq X$ of $k$ vertices of $H$ such that the set ${ecap C, ein E}$ of distinct hyperedge-intersections with $C$ has size at least $ell$. The sets $ecap C$ define equivalence classes over $E$. Partial VC Dimension is a generalization of VC Dimension, which corresponds to the case $ell=2^k$, and of Distinguishing Transversal, which corresponds to the case $ell=|E|$ (the latter is also known as Test Cover in the dual hypergraph). We also introduce the associated fixed-cardinality maximization problem Max Partial VC Dimension that aims at maximizing the number of equivalence classes induced by a solution set of $k$ vertices. We study the approximation complexity of Max Partial VC Dimension on general hypergraphs and on more restricted instances, in particular, neighborhood hypergraphs of graphs." @default.
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- W2951976786 date "2016-09-16" @default.
- W2951976786 modified "2023-09-25" @default.
- W2951976786 title "On the Approximability of Partial VC Dimension" @default.
- W2951976786 hasPublicationYear "2016" @default.
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