Inapproximability of H-Transversal/Packing

Given an undirected graph G = (VG, EG) and a fixed pattern graph H = (VH , EH ) with k vertices, we consider the H-Transversal and H-Packing problems. The former asks to find the smallest S ⊆ VG such that the subgraph induced by VG \ S does not have H as a subgraph, and the latter asks to find the maximum number of pairwise disjoint k-subsets S1, ..., Sm ⊆ VG such that the subgraph induced by each Si has H as a subgraph. We prove that if H is 2-connected, H-Transversal and H-Packing are almost as hard to approximate as general k-Hypergraph Vertex Cover and k-Set Packing, so it is NP-hard to approximate them within a factor of Ω(k) and Ω(k) respectively. We also show that there is a 1-connected H where H-Transversal admits an O(log k)-approximation algorithm, so that the

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Venkatesan Guruswami, Euiwoong Lee
• Keywords: Algorithms, APPROX 2015