Related papers: A Polynomial Time Algorithm for Steiner Tree when …
The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP-…
Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…
Given a graph, the sparsest cut problem asks for a subset of vertices whose edge expansion (the normalized cut given by the subset) is minimized. In this paper, we study a generalization of this problem seeking for $ k $ disjoint subsets of…
The Steiner Multicycle problem consists of, given a complete graph, a weight function on its vertices, and a collection of pairwise disjoint non-unitary sets called terminal sets, finding a minimum weight collection of vertex-disjoint…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…
In this paper, we consider the problem of determining in polynomial time whether a given planar point set $P$ of $n$ points admits 4-connected triangulation. We propose a necessary and sufficient condition for recognizing $P$, and present…
The transversal hypergraph problem is the task of enumerating the minimal hitting sets of a hypergraph. It is a long-standing open question whether this can be done in output-polynomial time. For hypergraphs whose solutions have bounded…
Let $\mathcal{C}$ and $\mathcal{D}$ be hereditary graph classes. Consider the following problem: given a graph $G\in\mathcal{D}$, find a largest, in terms of the number of vertices, induced subgraph of $G$ that belongs to $\mathcal{C}$. We…
In this paper, we investigate the $k$-path coloring problem, a variant of vertex coloring arising in the context of integrated circuit manufacturing. In this setting, typical industrial instances exhibit a `tree-like' structure. We exploit…
We study the Directed Feedback Vertex Set problem parameterized by the treewidth of the input graph. We prove that unless the Exponential Time Hypothesis fails, the problem cannot be solved in time $2^{o(t\log t)}\cdot n^{\mathcal{O}(1)}$…
We study the {\sc multicut on trees} and the {\sc generalized multiway Cut on trees} problems. For the {\sc multicut on trees} problem, we present a parameterized algorithm that runs in time $O^{*}(\rho^k)$, where $\rho = \sqrt{\sqrt{2} +…
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 length-constrained minimum spanning tree (MST) we are given an $n$-node graph $G = (V,E)$ with edge weights $w : E \to \mathbb{Z}_{\geq 0}$ and edge lengths $l: E \to \mathbb{Z}_{\geq 0}$ along with a root node $r \in V$ and a…
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…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
In the minimum planarization problem, given some $n$-vertex graph, the goal is to find a set of vertices of minimum cardinality whose removal leaves a planar graph. This is a fundamental problem in topological graph theory. We present a…
In the \emph{budgeted rooted node-weighted Steiner tree} problem, we are given a graph $G$ with $n$ nodes, a predefined node $r$, two weights associated to each node modelling costs and prizes. The aim is to find a tree in $G$ rooted at $r$…
In the Euclidean Steiner Tree problem, we are given as input a set of points (called terminals) in the $\ell_2$-metric space and the goal is to find the minimum-cost tree connecting them. Additional points (called Steiner points) from the…