Related papers: Tight algorithms for connectivity problems paramet…
In the vertex connectivity problem, given an undirected $n$-vertex $m$-edge graph $G$, we need to compute the minimum number of vertices that can disconnect $G$ after removing them. This problem is one of the most well-studied graph…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…
The graph parameter of pathwidth can be seen as a measure of the topological resemblance of a graph to a path. A popular definition of pathwidth is given in terms of node search where we are given a system of tunnels that is contaminated by…
We introduce merge-width, a family of graph parameters that unifies several structural graph measures, including treewidth, degeneracy, twin-width, clique-width, and generalized coloring numbers. Our parameters are based on new…
Consensus problems for strings and sequences appear in numerous application contexts, ranging from bioinformatics over data mining to machine learning. Closing some gaps in the literature, we show that several fundamental problems in this…
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on…
Treewidth and hypertree width have proven to be highly successful structural parameters in the context of the Constraint Satisfaction Problem (CSP). When either of these parameters is bounded by a constant, then CSP becomes solvable in…
This paper settles the computational complexity of model checking of several extensions of the monadic second order (MSO) logic on two classes of graphs: graphs of bounded treewidth and graphs of bounded neighborhood diversity. A classical…
Bayesian network structure learning is the notoriously difficult problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact…
In the Vertex Planarization problem one asks to delete the minimum possible number of vertices from an input graph to obtain a planar graph. The parameterized complexity of this problem, parameterized by the solution size (the number of…
Mining cohesive subgraphs in attributed graphs is an essential problem in the domain of graph data analysis. The integration of fairness considerations significantly fuels interest in models and algorithms for mining fairness-aware cohesive…
We revisit the (structurally) parameterized complexity of Induced Matching and Acyclic Matching, two problems where we seek to find a maximum independent set of edges whose endpoints induce, respectively, a matching and a forest. Chaudhary…
This paper provides an in-depth study of the fundamental problems of finding small subgraphs in distributed dynamic networks. While some problems are trivially easy to handle, such as detecting a triangle that emerges after an edge…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
Consider an Erd\"os-Renyi random graph in which each edge is present independently with probability 1/2, except for a subset $\sC_N$ of the vertices that form a clique (a completely connected subgraph). We consider the problem of…
In this paper we compare and illustrate the algorithmic use of graphs of bounded tree-width and graphs of bounded clique-width. For this purpose we give polynomial time algorithms for computing the four basic graph parameters independence…
In this paper we study the Spanning Tree Congestion problem, where we are given a graph $G=(V,E)$ and are asked to find a spanning tree $T$ of minimum maximum congestion. Here, the congestion of an edge $e\in T$ is the number of edges…
One of the most important algorithmic meta-theorems is a famous result by Courcelle, which states that any graph problem definable in monadic second-order logic with edge-set quantifications (i.e., MSO2 model-checking) is decidable in…
Finding cohesive subgraphs in a large graph has many important applications, such as community detection and biological network analysis. Clique is often a too strict cohesive structure since communities or biological modules rarely form as…