{"paper":{"title":"Parameterized and Approximation Complexity of Partial VC Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Cristina Bazgan, Florent Foucaud, Florian Sikora","submitted_at":"2016-09-16T15:42:43Z","abstract_excerpt":"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 corresponds to the case $\\ell=|E|$ (the latter is also known as Test Cover in the dual hypergraph). We also in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05110","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}