Abstract:We study a natural generalization of the classical -net problem (Haussler-Welzl 1987), which we call the -t-net problem: Given a hypergraph on n vertices and parameters t and ≥ t n , find a minimum-sized family S of t-element subsets of vertices such that each hyperedge of size at least n contains a set in S. When t = 1, this corresponds to the -net problem.We prove that any sufficiently large hypergraph with VC-dimension d admits an -t-net of size O( (1+log t)d log 1 ). For some families of geometrically-defi… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.