Related papers: Approximation algorithms for hitting subgraphs
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…
Given a graph $G=(V,E)$ and an integer $k \ge 1$, a $k$-hop dominating set $D$ of $G$ is a subset of $V$, such that, for every vertex $v \in V$, there exists a node $u \in D$ whose hop-distance from $v$ is at most $k$. A $k$-hop dominating…
The k-Clique problem is a canonical hard problem in parameterized complexity. In this paper, we study the parameterized complexity of approximating the k-Clique problem where an integer k and a graph G on n vertices are given as input, and…
{\em Partial domination problem} is a generalization of the {\em minimum dominating set problem} on graphs. Here, instead of dominating all the nodes, one asks to dominate at least a fraction of the nodes of the given graph by choosing a…
Given a graph $G = (V, E)$ and an integer $k$, we study $k$-Vertex Seperator (resp. $k$-Edge Separator), where the goal is to remove the minimum number of vertices (resp. edges) such that each connected component in the resulting graph has…
Given a weighted hypergraph $\mathcal{H}(V, \mathcal{E} \subseteq 2^V, w)$, the approximate $k$-cover problem seeks for a size-$k$ subset of $V$ that has the maximum weighted coverage by \emph{sampling only a few hyperedges} in…
The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…
We study the fair k-set selection problem where we aim to select $k$ sets from a given set system such that the (weighted) occurrence times that each element appears in these $k$ selected sets are balanced, i.e., the maximum (weighted)…
We study the problem of counting the number of {\em isomorphic} copies of a given {\em template} graph, say $H$, in the input {\em base} graph, say $G$. In general, it is believed that polynomial time algorithms that solve this problem…
We consider the Sparse Hitting Set (Sparse-HS) problem, where we are given a set system $(V,\mathcal{F},\mathcal{B})$ with two families $\mathcal{F},\mathcal{B}$ of subsets of $V$. The task is to find a hitting set for $\mathcal{F}$ that…
Given a fixed small graph H and a larger graph G, an H-factor is a collection of vertex-disjoint subgraphs $H'\subset G$, each isomorphic to H, that cover the vertices of G. If G is the complete graph $K_n$ equipped with independent U(0,1)…
A graph homomorphism is a vertex map which carries edges from a source graph to edges in a target graph. The instances of the Weighted Maximum H-Colourable Subgraph problem (MAX H-COL) are edge-weighted graphs G and the objective is to find…
Graph modification problems are computational tasks where the goal is to change an input graph $G$ using operations from a fixed set, in order to make the resulting graph satisfy a target property, which usually entails membership to a…
In the Maximum Independent Set problem we are asked to find a set of pairwise nonadjacent vertices in a given graph with the maximum possible cardinality. In general graphs, this classical problem is known to be NP-hard and hard to…
$k$-defensive domination, a variant of the classical domination problem on graphs, seeks a minimum cardinality vertex set providing a surjective defense against any attack on vertices of cardinality bounded by a parameter $k$. The problem…
The minimum directed feedback vertex set problem consists in finding the minimum set of vertices that should be removed in order to make a directed graph acyclic. This is a well-known NP-hard optimization problem with applications in…
In the minimum Multicut problem, the input is an edge-weighted supply graph $G=(V,E)$ and a simple demand graph $H=(V,F)$. Either $G$ and $H$ are directed (DMulC) or both are undirected (UMulC). The goal is to remove a minimum weight set of…
A graph is $k$-connected if it has $k$ internally-disjoint paths between every pair of nodes. A subset $S$ of nodes in a graph $G$ is a $k$-connected set if the subgraph $G[S]$ induced by $S$ is $k$-connected; $S$ is an $m$-dominating set…
Let $G$ and $H$ be $k$-graphs ($k$-uniform hypergraphs); then a perfect $H$-packing in $G$ is a collection of vertex-disjoint copies of $H$ in $G$ which together cover every vertex of $G$. For any fixed $H$ let $\delta(H, n)$ be the minimum…
In this paper we study some variants of Dirac-type problems in hypergraphs. First, we show that for $k\ge 3$, if $H$ is a $k$-graph on $n\in k\mathbb N$ vertices with independence number at most $n/p$ and minimum codegree at least…