On the Approximability of Partial VC Dimension

@article{Bazgan2016OnTA,
  title={On the Approximability of Partial VC Dimension},
  author={Cristina Bazgan and Florent Foucaud and Florian Sikora},
  journal={ArXiv},
  year={2016},
  volume={abs/1609.05110}
}
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 \(C\subseteq X\) of k vertices of H such that the set \(\{e\cap C, e\in E\}\) of distinct hyperedge-intersections with C has size at least \(\ell \). The sets \(e\cap C\) 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… 

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