Related papers: On the edge capacitated Steiner tree problem

Given an edge-weighted directed graph $G=(V,E)$ on $n$ vertices and a set $T=\{t_1, t_2, \ldots, t_p\}$ of $p$ terminals, the objective of the \scss ($p$-SCSS) problem is to find an edge set $H\subseteq E$ of minimum weight such that $G[H]$…

The Steiner Tree problem is a classical problem in combinatorial optimization: the goal is to connect a set $T$ of terminals in a graph $G$ by a tree of minimum size. Karpinski and Zelikovsky (1996) studied the $\delta$-dense version of…

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a…

A rectilinear Steiner tree for a set $P$ of points in $\mathbb{R}^2$ is a tree that connects the points in $P$ using horizontal and vertical line segments. The goal of Minimal Rectilinear Steiner Tree is to find a rectilinear Steiner tree…

For a graph $G$, an edge-separating (resp. vertex-separating) path system of $G$ is a family of paths in $G$ such that for any pair of edges $e_1, e_2$ (resp. pair of vertices $v_1, v_2$) of $G$ there is at least one path in the family that…

Let $G=(V,E)$ be any undirected graph on $V$ vertices and $E$ edges. A path $\textbf{P}$ between any two vertices $u,v\in V$ is said to be $t$-approximate shortest path if its length is at most $t$ times the length of the shortest path…

The Euclidean Steiner tree problem, normally posed in two dimensions, seeks to connect a set of prescribed terminal nodes by placing additional nodes, known as Steiner points, with edges connecting such nodes either to another Steiner point…

Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…

We propose the reliability constrained k-rooted minimum spanning forest, a relevant optimization problem whose aim is to find a k-rooted minimum cost forest that connects given customers to a number of supply vertices, in such a way that a…

The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…

We show that the following variation of the single-source shortest path problem is NP-complete. Let a weighted, directed, acyclic graph $G=(V,E,w)$ with source and sink vertices $s$ and $t$ be given. Let in addition a mapping $f$ on $E$ be…

The problem of determining the smallest number of edges, $h(n;\bar{\kappa}\geq r)$, which guarantees that any graph with $n$ vertices and $h(n;\bar{\kappa}\geq r)$ edges will contain a pair of vertices joined by $r$ internally disjoint…

We study the Steiner Tree problem on unit disk graphs. Given a $n$ vertex unit disk graph $G$, a subset $R\subseteq V(G)$ of $t$ vertices and a positive integer $k$, the objective is to decide if there exists a tree $T$ in $G$ that spans…

We introduce the concept of Most, and Least, Compact Spanning Trees - denoted respectively by $T^*(G)$ and $T^\#(G)$ - of a simple, connected, undirected and unweighted graph $G(V, E, W)$. For a spanning tree $T(G) \in \mathcal{T}(G)$ to be…

Given a graph $G=(V,E)$, the minimum branch vertices problem consists in finding a spanning tree $T=(V,E')$ of $G$ minimizing the number of vertices with degree greater than two. We consider a simple combinatorial lower bound for the…

The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic…

In this paper we study the Spanning Tree Congestion problem, where we are given a graph $G=(V,E)$ and are asked to find a spanning tree $T$ of minimum maximum congestion. Here, the congestion of an edge $e\in T$ is the number of edges…

Consider a connected graph $G$ and let $T$ be a spanning tree of $G$. Every edge $e \in G-T$ induces a cycle in $T \cup \{e\}$. The intersection of two distinct such cycles is the set of edges of $T$ that belong to both cycles. We consider…

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…

We study the NP-hard Minimum Shared Edges (MSE) problem on graphs: decide whether it is possible to route $p$ paths from a start vertex to a target vertex in a given graph while using at most $k$ edges more than once. We show that MSE can…