Related papers: On Temporal Graph Exploration
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…
We define the following parameter of connected graphs. For a given graph $G$ we place one agent in each vertex of $G$. Every pair of agents sharing a common edge is declared to be acquainted. In each round we choose some matching of $G$…
Historically studies of behaviour on networks have focused on the behaviour of individuals (node-based) or on the aggregate behaviour of the entire network. We propose a new method to decompose a temporal network into macroscale components…
Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static) graph-structured data. However, many real-world systems are dynamic in nature, since the graph and node/edge attributes change over time. In recent…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has…
A mobile agent, starting from a node $s$ of a simple undirected connected graph $G=(V,E)$, has to explore all nodes and edges of $G$ using the minimum number of edge traversals. To do so, the agent uses a deterministic algorithm that allows…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
This paper endeavors to learn time-varying graphs by using structured temporal priors that assume underlying relations between arbitrary two graphs in the graph sequence. Different from many existing chain structure based methods in which…
Modeling evolving interactions among entities is critical in many real-world tasks. For example, predicting driver maneuvers in traffic requires tracking how neighboring vehicles accelerate, brake, and change lanes relative to one another…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
Temporal graphs are graphs whose nodes and edges, together with their associated properties, continuously change over time. With the development of Internet of Things (IoT) systems, a subclass of the temporal graph, i.e., Property Evolution…
We revisit an old minor topic in algorithms, the deterministic walk on a finite graph which always moves toward the nearest unvisited vertex until every vertex is visited. There is an elementary connection between this cover time and…
Can we learn how to explore unknown spaces efficiently? To answer this question, we study the problem of Online Graph Exploration, the online version of the Traveling Salesperson Problem. We reformulate graph exploration as a reinforcement…
We study the problem of deterministically exploring an undirected and initially unknown graph with $n$ vertices either by a single agent equipped with a set of pebbles, or by a set of collaborating agents. The vertices of the graph are…
In this paper we study two natural models of \textit{random temporal} graphs. In the first, the \textit{continuous} model, each edge $e$ is assigned $l_e$ labels, each drawn uniformly at random from $(0,1]$, where the numbers $l_e$ are…
We consider a modified random walk which uses unvisited edges whenever possible, and makes a simple random walk otherwise. We call such a walk an edge-process. We assume there is a rule A, which tells the walk which unvisited edge to use…
The graph exploration problem is to visit all the nodes of a connected graph by a mobile entity, e.g., a robot. The robot has no a priori knowledge of the topology of the graph or of its size. Cohen et al. \cite{Ilcinkas08} introduced label…
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…