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We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
The computation of short paths in graphs with arc lengths is a pillar of graph algorithmics and network science. In a more diverse world, however, not every short path is equally valuable. For the setting where each vertex is assigned to a…
Let $G=(V,E,w)$ be a weighted directed graph without negative cycles. For two vertices $s,t\in V$, we let $d_{\le h}(s,t)$ be the minimum, according to the weight function $w$, of a path from $s$ to $t$ that uses at most $h$ edges, or hops.…
Vertex connectivity and its variants are among the most fundamental problems in graph theory, with decades of extensive study and numerous algorithmic advances. The directed variants of vertex connectivity are usually solved by manually…
In the Disjoint Shortest Paths problem one is given a graph $G$ and a set $\mathcal{T}=\{(s_1,t_1),\dots,(s_k,t_k)\}$ of $k$ vertex pairs. The question is whether there exist vertex-disjoint paths $P_1,\dots,P_k$ in $G$ so that each $P_i$…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
We discuss the complexity of path enumeration and counting in weighted temporal graphs. In a weighted temporal graph, each edge has an availability time, a traversal time and some real cost. We introduce two bicriteria temporal min-cost…
In real-world systems, the relationships and connections between components are highly complex. Real systems are often described as networks, where nodes represent objects in the system and edges represent relationships or connections…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Finding, counting and/or listing triangles (three vertices with three edges) in large graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
We present algorithms and experiments for the visualization of directed graphs that focus on displaying their reachability information. Our algorithms are based on the concepts of the path and channel decomposition as proposed in the…
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out degree of a vertex in the resulting directed graph. This…
We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do…