Related papers: Minimum $2$-vertex-twinless connected spanning sub…
Let $G=(V,E)$ be a strongly connected graph with $|V|\geq 3$. For $T\subseteq V$, the strongly connected graph $G$ is $2$-T-connected if $G$ is $2$-edge-connected and for each vertex $w$ in $T$, $w$ is not a strong articulation point. This…
Let $G=(V,E)$ be a twinless strongly connected graph. a vertex $v\in V$ is a twinless articulation point if the subrgraph obtained from $G$ by removing the vertex $v$ is not twinless strongly connected. An edge $e\in E$ is a twinless bridge…
A directed graph $G=(V,E)$ is strongly biconnected if $G$ is strongly connected and its underlying graph is biconnected. A strongly biconnected directed graph $G=(V,E)$ is called $2$-vertex-strongly biconnected if $|V|\geq 3$ and the…
We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio both $\frac{4}{3}$. Using a common theme, the algorithms and their…
We present a $\frac{10}{7}$-approximation algorithm for the minimum two-vertex-connected spanning subgraph problem.
Wu and Grumbach introduced the concept of strongly biconnected directed graphs. A directed graph $G=(V,E)$ is called strongly biconnected if the directed graph $G$ is strongly connected and the underlying undirected graph of $G$ is…
Let $G=(V,E)$ be a strongly biconnected directed graph. In this paper we consider the problem of computing an edge subset $H \subseteq E$ of minimum size such that the directed subgraph $(V,H)$ is strongly biconnected.
Let $G$ be a strongly connected directed graph. We consider the following three problems, where we wish to compute the smallest strongly connected spanning subgraph of $G$ that maintains respectively: the $2$-edge-connected blocks of $G$…
We provide algorithms for the minimum 2-edge-connected spanning subgraph problem and the minimum 2-vertex-connected spanning subgraph problem with approximation ratio $\frac{9}{7}$. This improves upon a recent algorithm with ratio slightly…
The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a spanning subgraph $S$ of $G$ with the…
We obtain a polynomial-time 17/12-approximation algorithm for the minimum-cost 2-vertex-connected spanning subgraph problem, restricted to graphs of minimum degree at least 3. Our algorithm uses the framework of ear-decompositions for…
The $2$-Edge-Connected Spanning Subgraph problem (2-ECSS) is one of the most fundamental and well-studied problems in the context of network design. In the problem, we are given an undirected graph $G$, and the objective is to find a…
Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that…
In the 2-Vertex-Connected Spanning Subgraph problem (2-VCSS), we are given an undirected graph $G$, and the objective is to find a 2-vertex-connected spanning subgraph $S$ of $G$ with the minimum number of edges. In the context of…
The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the…
In the k-2VC problem, we are given an undirected graph G with edge costs and an integer k; the goal is to find a minimum-cost 2-vertex-connected subgraph of G containing at least k vertices. A slightly more general version is obtained if…
Let $G=(V,E))$ be a directed graph. A $2$-twinless block in $G$ is a maximal vertex set $B\subseteq V$ of size at least $2$ such that for each pair of distinct vertices $x,y \in B$, and for each vertex $w\in V\setminus\left\lbrace x,y…
Let $G=(V,E)$ be a directed graph. A $2$-edge-twinless block in $G$ is a maximal vertex set $C^{t}\subseteq V$ with $|C^{t}|>1$ such that for any distinct vertices $v,w \in C^{t}$, and for every edge $e\in E$, the vertices $v,w$ are in the…
A labelled, undirected graph is a graph whose edges have assigned labels, from a specific set. Given a labelled, undirected graph, the well-known minimum labelling spanning tree problem is aimed at finding the spanning tree of the graph…
We present a simple linear-time algorithm that finds a spanning tree $T$ of a given $2$-edge-connected graph $G$ such that each vertex $v$ of $T$ has degree at most $\lceil \frac{\deg_G(v)}{2}\rceil + 1$.