On 2-coverings and 2-packings of laminar families

Abstract

Let H be a laminar family of subsets of a groundset V.A k-cover of H is a multiset C of edges on V such that for every subset S in H, C has at least k edges that have exactly one end in S.A k-packing of H is a multiset P of edges on V such that for every subset S in H, P has at most k • u(S) edges that have exactly one end in S. Here, u assigns an integer capacity to each subset in H. Our main results are: (a) Given a k-cover C of H, there is an efficient algorithm to find a 1-cover contained in C of size