Related papers: Approximation Algorithms for Vertex-Connectivity A…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs…
We develop a polynomial time 3/2-approximation algorithm to solve the vertex cover problem on a class of graphs satisfying a property called ``active edge hypothesis''. The algorithm also guarantees an optimal solution on specially…
A searcher is tasked with exploring a graph with edge lengths and vertex weights, starting from a designated vertex. Initially, only the starting vertex is considered explored. At each step, the searcher adds an edge to the solution,…
This paper deals with the problem of finding a collection of vertex-disjoint paths in a given graph G=(V,E) such that each path has at least four vertices and the total number of vertices in these paths is maximized. The problem is NP-hard…
In the vertex connectivity augmentation problem, we are given an undirected $n$-vertex graph $G$, a set of links $L \subseteq \binom{V(G)}{2} \setminus E(G)$, and integers $\lambda$ and $k$. The task is to insert at most $k$ links from $L$…
For an edge-weighted connected undirected graph, the minimum $k$-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into $k$ connected components. The problem is NP-hard when $k$ is part…
We present a new approximation algorithm for the minimum 2-edge-connected spanning subgraph problem. Its approximation ratio is $\frac{4}{3}$, which matches the current best ratio. The approximation ratio of the algorithm is $\frac{6}{5}$…
Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex…
In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The…
Finding a smallest subgraph that is k-edge-connected, or augmenting a k-edge-connected graph with a smallest subset of given candidate edges to become (k+1)-edge-connected, are among the most fundamental Network Design problems. They are…
The Connected Vertex Cover problem, where the goal is to compute a minimum set of vertices in a given graph which forms a vertex cover and induces a connected subgraph, is a fundamental combinatorial problem and has received extensive…
We introduce and study two natural generalizations of the Connected VertexCover (VC) problem: the $p$-Edge-Connected and $p$-Vertex-Connected VC problem (where $p \geq 2$ is a fixed integer). Like Connected VC, both new VC problems are FPT,…
We study the k-route cut problem: given an undirected edge-weighted graph G=(V,E), a collection {(s_1,t_1),(s_2,t_2),...,(s_r,t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset…
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
In the Connected Dominating Set problem we are given a graph $G=(V,E)$ and seek a minimum size dominating set $S \subseteq V$ such that the subgraph $G[S]$ of $G$ induced by $S$ is connected. In the $2$-Edge-Connected Dominating Set problem…
Given an edge-weighted (metric/general) complete graph with $n$ vertices, the maximum weight (metric/general) $k$-cycle/path packing problem is to find a set of $\frac{n}{k}$ vertex-disjoint $k$-cycles/paths such that the total weight is…
In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a…
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…
Durand de Gevigney and Szigeti \cite{DgGSz} have recently given a min-max theorem for the $(2,k)$-connectivity augmentation problem. This article provides an $O(n^3(m+ n \textrm{ }log\textrm{ }n))$ algorithm to find an optimal solution for…