Approximating Minimum-Size 2-Edge-Connected and 2-Vertex-Connected Spanning Subgraphs

Abstract

We study the unweighted 2-edge-connected and 2-vertex-connected spanning subgraph problems. A graph is 2-edge-connected if it is connected on removal of an edge, and it is 2-vertex-connected if it is connected on removal of a vertex. The problem of finding a minimum-size 2-edge-connected (or 2-vertex-connected) spanning subgraph of a given graph is NP-hard.

We present a 4/3-approximation algorithm for unweighted 2ECSS on 3-vertex-connected input graphs, which matches the best known approximation ratio due to Sebő and Vygen for the general unweighted 2ECSS problem, but our analysis is with respect to the D2 lower bound. We also give a 17/12-approximation algorithm for unweighted 2VCSS on graphs of minimum degree at least 3, which is lower than the best known ratios of 3/2 by Garg, Santosh and Singla and 10/7 by Heeger and Vygen for the general unweighted 2VCSS problem. These algorithms are accompanied by new theorems about the known lower bounds.