Related papers: Structural Parameters for Steiner Orientation
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
In the Euclidean Bottleneck Steiner Tree problem, the input consists of a set of $n$ points in $\mathbb{R}^2$ called terminals and a parameter $k$, and the goal is to compute a Steiner tree that spans all the terminals and contains at most…
A graph is geometric 1-planar if it admits a straight-line drawing where each edge is crossed at most once. We provide the first systematic study of the parameterized complexity of recognizing geometric 1-planar graphs. By substantially…
We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of…
Over the past decade, we witness an increasing amount of interest in the design of exact exponential-time and parameterized algorithms for problems in Graph Drawing. Unfortunately, we still lack knowledge of general methods to develop such…
In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…
In this paper, we study the \textsf{Planar Disjoint Paths} problem: Given an undirected planar graph $G$ with $n$ vertices and a set $T$ of $k$ pairs $(s_i,t_i)_{i=1}^k$ of vertices, the goal is to find a set $\mathcal P$ of $k$ pairwise…
Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to…
Given a graph $G=(V,E)$, two vertices $s,t\in V$, and two integers $k,\ell$, the Short Secluded Path problem is to find a simple $s$-$t$-path with at most $k$ vertices and $\ell$ neighbors. We study the parameterized complexity of the…
We consider Directed Steiner Forest (DSF), a fundamental problem in network design. The input to DSF is a directed edge-weighted graph $G = (V, E)$ and a collection of vertex pairs $\{(s_i, t_i)\}_{i \in [k]}$. The goal is to find a minimum…
We give a dynamic programming solution to find the minimum cost of a diameter constrained Steiner tree in case of directed graphs. Then we show a simple reduction from undirected version to the directed version to realize an algorithm of…
The Path Contraction and Cycle Contraction problems take as input an undirected graph $G$ with $n$ vertices, $m$ edges and an integer $k$ and determine whether one can obtain a path or a cycle, respectively, by performing at most $k$ edge…
We consider the problem of computing a Steiner tree of minimum cost under a hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs with bounded treewidth…
In this paper, we study a survivable network design problem on directed graphs, 2-Connected Directed Steiner Tree (2-DST): given an $n$-vertex weighted directed graph, a root $r$, and a set of $h$ terminals $S$, find a min-cost subgraph $H$…
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…
In the Telephone Broadcast problem we are given a graph $G=(V,E)$ with a designated source vertex $s\in V$. Our goal is to transmit a message, which is initially known only to $s$, to all vertices of the graph by using a process where in…
We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),\cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$…
Some of the most fundamental and well-studied graph parameters are the Diameter (the largest shortest paths distance) and Radius (the smallest distance for which a "center" node can reach all other nodes). The natural and important…
We consider an important generalization of the Steiner tree problem, the \emph{Steiner forest problem}, in the Euclidean plane: the input is a multiset $X \subseteq \mathbb{R}^2$, partitioned into $k$ color classes $C_1, C_2, \ldots, C_k…
Given a connected graph $G$ and a terminal set $R \subseteq V(G)$, the minimum Steiner tree problem (ST) asks for a tree that spans all of $R$ with at most $r$ vertices from $V(G)\backslash R$, for some integer $r\geq 0$. A \emph{split…