# 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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