Related papers: On the Threshold of Intractability
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
We study the parameterized complexity of transforming graphs into Uniform Cluster graphs, where each component is an equal-sized clique. We consider Uniform Cluster Vertex Deletion (UCVD), Uniform Cluster Edge Deletion (UCED), Uniform…
We study the parameterized complexity of separating a small set of vertices from a graph by a small vertex-separator. That is, given a graph $G$ and integers $k$, $t$, the task is to find a vertex set $X$ with $|X| \le k$ and $|N(X)| \le…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social…
We consider the Global Minimum Vertex-Cut problem: given an undirected vertex-weighted graph $G$, compute a minimum-weight subset of its vertices whose removal disconnects $G$. The problem is closely related to Global Minimum Edge-Cut,…
In the Min $k$-Cut problem, input is an edge weighted graph $G$ and an integer $k$, and the task is to partition the vertex set into $k$ non-empty sets, such that the total weight of the edges with endpoints in different parts is minimized.…
A graph operation that {\em contracts edges} is one of the fundamental operations in the theory of graph minors. Parameterized Complexity of editing to a family of graphs by contracting $k$ edges has recently gained substantial scientific…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
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…
Simplifying graphs is a very applicable problem in numerous domains, especially in computational geometry. Given a geometric graph and a threshold, the minimum-complexity graph simplification asks for computing an alternative graph of…
Motivated by the recent rapid growth of research for algorithms to cluster multi-layer and temporal graphs, we study extensions of the classical Cluster Editing problem. In Multi-Layer Cluster Editing we receive a set of graphs on the same…
Given a graph G = (V,E) and an integer k, an edge modification problem for a graph property P consists in deciding whether there exists a set of edges F of size at most k such that the graph H = (V,E \vartriangle F) satisfies the property…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
Removing all connections between two vertices s and z in a graph by removing a minimum number of vertices is a fundamental problem in algorithmic graph theory. This (s,z)-separation problem is well-known to be polynomial solvable and serves…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
A book embedding of a graph is a drawing that maps vertices onto a line and edges to simple pairwise non-crossing curves drawn into pages, which are half-planes bounded by that line. Two-page book embeddings, i.e., book embeddings into 2…
We study the Telephone Broadcasting problem in graphs with restricted structure. Given a designated source in an undirected graph, the goal is to disseminate a message to all vertices in the minimum number of rounds, where in each round…
We introduce a temporal Steiner network problem in which a graph, as well as changes to its edges and/or vertices over a set of discrete times, are given as input; the goal is to find a minimal subgraph satisfying a set of $k$…
In well-studied graph modification problems, adding and deleting vertices and edges are used as graph editing operations. We propose a model for graph modification on geometric intersection graphs called Geometric Graph Edit Distance that…