Related papers: Parameterized Complexity of Secluded Connectivity …
Let $G=(V,E)$ be a graph. An ordering of $G$ is a bijection $\alpha: V\dom \{1,2,..., |V|\}.$ For a vertex $v$ in $G$, its closed neighborhood is $N[v]=\{u\in V: uv\in E\}\cup \{v\}.$ The profile of an ordering $\alpha$ of $G$ is…
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 $L$…
We study the Equitable Connected Partition (ECP for short) problem, where we are given a graph G=(V,E) together with an integer p, and our goal is to find a partition of V into p parts such that each part induces a connected sub-graph of G…
In the Directed Steiner Network problem, the input is a directed graph G, a subset T of k vertices of G called the terminals, and a demand graph D on T. The task is to find a subgraph H of G with the minimum number of edges such that for…
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…
Motivated by the role of triadic closures in social networks, and the importance of finding a maximum subgraph avoiding a fixed pattern, we introduce and initiate the parameterized study of the Strong F-closure problem, where F is a fixed…
We study the {\em verification} problem in distributed networks, stated as follows. Let $H$ be a subgraph of a network $G$ where each vertex of $G$ knows which edges incident on it are in $H$. We would like to verify whether $H$ has some…
We study the NP-complete Minimum Shared Edges (MSE) problem. Given an undirected graph, a source and a sink vertex, and two integers p and k, the question is whether there are p paths in the graph connecting the source with the sink and…
In the Multiple Allocation $k$-Hub Center (MA$k$HC), we are given a connected edge-weighted graph $G$, sets of clients $\mathcal{C}$ and hub locations $\mathcal{H}$, where ${V(G) = \mathcal{C} \cup \mathcal{H}}$, a set of demands…
We show that some natural problems that are XNLP-hard (which implies W[t]-hardness for all t) when parameterized by pathwidth or treewidth, become FPT when parameterized by stable gonality, a novel graph parameter based on optimal maps from…
Suppose N is a phylogenetic network indicating a complicated relationship among individuals and taxa. Often of interest is a much simpler network, for example, a species tree T, that summarizes the most fundamental relationships. The…
The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…
Given two sets of points in the plane, $P$ of $n$ terminals and $S$ of $m$ Steiner points, a Steiner tree of $P$ is a tree spanning all points of $P$ and some (or none or all) points of $S$. A Steiner tree with length of longest edge…
In this paper, we introduce the Fixed Topology Minimum-Length Tree with Neighborhood Problem, which aims to embed a rooted tree-shaped graph into a $d$-dimensional metric space while minimizing its total length provided that the nodes must…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…
We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…
For a phylogenetic tree, the phylogenetic diversity of a set A of taxa is the total weight of edges on paths to A. Finding small sets of maximal diversity is crucial for conservation planning, as it indicates where limited resources can be…
In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph…
Fixed parameter tractable algorithms for bounded treewidth are known to exist for a wide class of graph optimization problems. While most research in this area has been focused on exact algorithms, it is hard to find decompositions of…
Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…