On the Approximability of Partial VC Dimension - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2016

On the Approximability of Partial VC Dimension

Résumé

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 approximation complexity of Max Partial VC Dimension on general hypergraphs and on more restricted instances, in particular, neighborhood hypergraphs of graphs.

Dates et versions

hal-01431728 , version 1 (11-01-2017)

Identifiants

Citer

Cristina Bazgan, Florent Foucaud, Florian Sikora. On the Approximability of Partial VC Dimension. 10th International Conference, COCOA 2016, Dec 2016, Hong Kong, China. pp.92-106, ⟨10.1007/978-3-319-48749-6_7⟩. ⟨hal-01431728⟩
119 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More