Parameterized and approximation complexity of Partial VC Dimension

Abstract : We introduce the problem Partial VC Dimension that asks, given a hypergraph H = (X, E)and integers k and ℓ, whether one can select a set C⊆X of k vertices of H such that the set {e∩C, e∈E} of distinct hyperedge-intersections with C has size at least ℓ. The sets e∩ C define equivalence classes over E. Partial VC Dimension is a generalization of VC Dimension, which corresponds to the case ℓ= 2k, and of Distinguishing Transversal, which corresponds to the case ℓ=|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 algorithmic complexity of Partial VC Dimension and Max Partial VC Dimension both on general hypergraphs and on more restricted instances, in particular, neighborhood hypergraphs of graphs.
Document type :
Journal articles
Complete list of metadatas

Cited literature [54 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02091342
Contributor : Christine Okret-Manville <>
Submitted on : Friday, April 5, 2019 - 3:59:19 PM
Last modification on : Wednesday, April 17, 2019 - 1:29:01 AM
Long-term archiving on: Saturday, July 6, 2019 - 2:36:11 PM

File

155324710011598.pdf
Files produced by the author(s)

Identifiers

Citation

Cristina Bazgan, Florent Foucaud, Florian Sikora. Parameterized and approximation complexity of Partial VC Dimension. Theoretical Computer Science, Elsevier, 2019, 766, ⟨10.1016/j.tcs.2018.09.013⟩. ⟨hal-02091342⟩

Share

Metrics

Record views

47

Files downloads

104