Related papers: On Kernelization and Approximation for the Vector …

Given a graph $G$, an integer $k\geq 0$, and a non-negative integral function $f:V(G) \rightarrow \mathcal{N}$, the Vector Domination problem asks whether a set $S$ of vertices, of cardinality $k$ or less, exists in $G$ so that every vertex…

We study a relaxation of the Vector Domination problem called Vector Connectivity (VecCon). Given a graph $G$ with a requirement $r(v)$ for each vertex $v$, VecCon asks for a minimum cardinality set $S$ of vertices such that every vertex…

We study the parameterized complexity of the connected version of the vertex cover problem, where the solution set has to induce a connected subgraph. Although this problem does not admit a polynomial kernel for general graphs (unless NP is…

In the $k$-connected directed Steiner tree problem ($k$-DST), we are given an $n$-vertex directed graph $G=(V,E)$ with edge costs, a connectivity requirement $k$, a root $r\in V$ and a set of terminals $T\subseteq V$. The goal is to find a…

In this paper we study the kernelization of the $d$-Path Vertex Cover ($d$-PVC) problem. Given a graph $G$, the problem requires finding whether there exists a set of at most $k$ vertices whose removal from $G$ results in a graph that does…

A matching cut is a partition of the vertex set of a graph into two sets $A$ and $B$ such that each vertex has at most one neighbor in the other side of the cut. The MATCHING CUT problem asks whether a graph has a matching cut, and has been…

Given a simple connected undirected graph G = (V, E), a set X \subseteq V(G), and integers k and p, STEINER SUBGRAPH EXTENSION problem asks if there exists a set S \supseteq X with at most k vertices such that G[S] is p-edge-connected. This…

Given a graph $G=(V,E)$ with non-negative real edge lengths and an integer parameter $k$, the Min-Max k-Tree Cover problem seeks to find a set of at most $k$ subtrees of $G$, such that the union of the trees is the vertex set $V$. The…

Finding a Steiner strongly $k$-arc-connected orientation is particularly relevant in network design and reliability, as it guarantees robust communication between a designated set of critical nodes. Kir\'aly and Lau (FOCS 2006) introduced a…

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$…

In the $\ell$-Component Order Connectivity problem ($\ell \in \mathbb{N}$), we are given a graph $G$ on $n$ vertices, $m$ edges and a non-negative integer $k$ and asks whether there exists a set of vertices $S\subseteq V(G)$ such that…

Dense subgraph discovery is an important graph-mining primitive with a variety of real-world applications. One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an…

A stable cutset in a graph $G$ is a set $S\subseteq V(G)$ such that vertices of $S$ are pairwise non-adjacent and such that $G-S$ is disconnected, i.e., it is both stable (or independent) set and a cutset (or separator). Unlike general…

We consider the parameterized complexity of the problem of tracking shortest s-t paths in graphs, motivated by applications in security and wireless networks. Given an undirected and unweighted graph with a source s and a destination t,…

Given a simple graph $G = (V, E)$ and a constant integer $k \ge 2$, the $k$-path vertex cover problem ({\sc P$k$VC}) asks for a minimum subset $F \subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path…

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 two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S has a prescribed number of neighbors in…

The Directed Steiner Network (DSN) problem takes as input a directed edge-weighted graph $G=(V,E)$ and a set $\mathcal{D}\subseteq V\times V$ of $k$ demand pairs. The aim is to compute the cheapest network $N\subseteq G$ for which there is…

In this paper we study the hardness of the $k$-Center problem on inputs that model transportation networks. For the problem, a graph $G=(V,E)$ with edge lengths and an integer $k$ are given and a center set $C\subseteq V$ needs to be chosen…

We revisit once more the problem of designing an oracle for answering connectivity queries in undirected graphs in the presence of vertex failures. Specifically, given an undirected graph $G$ with $n$ vertices and $m$ edges and an integer…