Related papers: Assigning times to minimise reachability in tempor…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
In this paper we initiate the study of the temporal graph realization problem with respect to the fastest path durations among its vertices, while we focus on periodic temporal graphs. Given an $n \times n$ matrix $D$ and a $\Delta \in…
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…
In edge orientations, the goal is usually to orient (direct) the edges of an undirected $n$-vertex graph $G$ such that all out-degrees are bounded. When the graph $G$ is fully dynamic, i.e., admits edge insertions and deletions, we wish to…
We consider random temporal graphs, a version of the classical Erd\H{o}s--R\'enyi random graph G(n,p) where additionally, each edge has a distinct random time stamp, and connectivity is constrained to sequences of edges with increasing time…
Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of…
Many real-world phenomena exhibit strong hierarchical structure. Consequently, in many real-world directed social networks vertices do not play equal role. Instead, vertices form a hierarchy such that the edges appear mainly from upper…
Given an undirected graph, one can assign directions to each of the edges of the graph, thus orienting the graph. To be as egalitarian as possible, one may wish to find an orientation such that no vertex is unfairly hit with too many arcs…
Contagions (e.g. virus, gossip) spread over the nodes in propagation graphs. We can use the temporal and textual data of the nodes to compute the edge weights and then generate subgraphs with highly relevant nodes. This is beneficial to…
In this chapter, we focus on the problem of containing the spread of diseases taking place in both temporal and adaptive networks (i.e., networks whose structure `adapts' to the state of the disease). We specifically focus on the problem of…
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such…
We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a…
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
Graph Coloring consists in assigning colors to vertices ensuring that two adjacent vertices do not have the same color. In dynamic graphs, this notion is not well defined, as we need to decide if different colors for adjacent vertices must…
Many phenomena in real world social networks are interpreted as spread of influence between activated and non-activated network elements. These phenomena are formulated by combinatorial graphs, where vertices represent the elements and…
Finding dense subnetworks, with density based on edges or more complex structures, such as subgraphs or $k$-cliques, is a fundamental algorithmic problem with many applications. While the problem has been studied extensively in static…
We consider the problem of incremental cycle detection and topological ordering in a directed graph $G = (V, E)$ with $|V| = n$ nodes. In this setting, initially the edge-set $E$ of the graph is empty. Subsequently, at each time-step an…
In this paper we study the fixed-parameter tractability of the problem of deciding whether a given temporal graph admits a temporal walk that visits all vertices (temporal exploration) or, in some problem variants, a certain subset of the…