Minimum $2$-vertex-twinless connected spanning subgraph problem

Abstract

Given a $2$-vertex-twinless connected directed graph $G=(V,E)$, the minimum $2$-vertex-twinless connected spanning subgraph problem is to find a minimum cardinality edge subset $E^t\subseteq E$ such that the subgraph $(V,E^t)$ is $2$-vertex-twinless connected. Let $G^1$ be a minimal $2$-vertex-connected subgraph of $G$. In this paper we present a $(2+a_t/2)$-approximation algorithm for the minimum $2$-vertex-twinless connected spanning subgraph problem, where $a_t$ is the number of twinless articulation points in $G^1$.