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Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…

Computational Complexity · Computer Science 2018-04-23 Hans-Joachim Böckenhauer , Janosch Fuchs , Walter Unger

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-07-19 Ioannis Lamprou , Russell Martin , Paul Spirakis

Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…

Data Structures and Algorithms · Computer Science 2026-05-06 Arnaud Casteigts , Michelle Döring , Nils Morawietz

A temporal (directed) graph is a graph whose edges are available only at specific times during its lifetime, $\tau$. Paths are sequences of adjacent edges whose appearing times are either strictly increasing or non-strictly increasingly…

Combinatorics · Mathematics 2023-03-01 Isnard Lopes Costa , Raul Lopes , Andrea Marino , Ana Silva

We consider the problem of inferring an edge-labeled graph from the sequence of edge labels seen in a walk of that graph. It has been known that this problem is solvable in $O(n \log n)$ time when the targets are path or cycle graphs. This…

Data Structures and Algorithms · Computer Science 2019-02-22 Shintaro Narisada , Diptarama Hendrian , Ryo Yoshinaka , Ayumi Shinohara

We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition…

Statistical Mechanics · Physics 2015-05-19 A. Asztalos , Z. Toroczkai

This paper considers a natural fault-tolerant shortest paths problem: for some constant integer $f$, given a directed weighted graph with no negative cycles and two fixed vertices $s$ and $t$, compute (either explicitly or implicitly) for…

Data Structures and Algorithms · Computer Science 2022-09-16 Virginia Vassilevska Williams , Eyob Woldeghebriel , Yinzhan Xu

Let $G=(V,E)$ be an undirected graph on $n$ vertices and $\lambda:E\to 2^{\mathbb{N}}$ a mapping that assigns to every edge a non-empty set of integer labels (times). Such a graph is {\em temporally connected} if a path exists with…

Discrete Mathematics · Computer Science 2021-04-29 Arnaud Casteigts , Joseph G. Peters , Jason Schoeters

Connectivity in temporal graphs relies on the notion of temporal paths, in which edges follow a chronological order (either strict or non-strict). In this work, we investigate the question of how to make a temporal graph connected. More…

Discrete Mathematics · Computer Science 2025-02-21 T. Bellitto , J. Bouton Popper , B. Escoffier

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…

Data Structures and Algorithms · Computer Science 2024-05-02 Nina Klobas , George B. Mertzios , Hendrik Molter , Paul G. Spirakis

A temporal graph is a graph whose edges only appear at certain points in time. Reachability in these graphs is defined in terms of paths that traverse the edges in chronological order (temporal paths). This form of reachability is neither…

Computational Complexity · Computer Science 2024-07-01 Arnaud Casteigts , Nils Morawietz , Petra Wolf

We consider the problem of assigning appearing times to the edges of a digraph in order to maximize the (average) temporal reachability between pairs of nodes. Motivated by the application to public transit networks, where edges cannot be…

Discrete Mathematics · Computer Science 2025-01-22 Filippo Brunelli , Pierluigi Crescenzi , Laurent Viennot

Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…

Data Structures and Algorithms · Computer Science 2011-02-02 Oksana Denysyuk , Luis Rodrigues

A temporal graph is a finite sequence of graphs, called snapshots, over the same vertex set. Many temporal graph problems turn out to be much more difficult than their static counterparts. One such problem is \textsc{Timeline Vertex Cover}…

Data Structures and Algorithms · Computer Science 2025-10-10 Anton Herrmann , Christian Komusiewicz , Nils Morawietz , Frank Sommer

We consider the task of graph exploration. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. A mobile agent has to visit all nodes and stop. The exploration time is the…

Data Structures and Algorithms · Computer Science 2016-11-17 Barun Gorain , Andrzej Pelc

Temporal graphs are a special class of graphs for which a temporal component is added to edges, that is, each edge possesses a set of times at which it is available and can be traversed. Many classical problems on graphs can be translated…

Data Structures and Algorithms · Computer Science 2025-04-10 Lapo Cioni , Riccardo Dondi , Andrea Marino , Jason Schoeters , Ana Silva

A \emph{temporal graph} is, informally speaking, a graph that changes with time. When time is discrete and only the relationships between the participating entities may change and not the entities themselves, a temporal graph may be viewed…

Discrete Mathematics · Computer Science 2015-03-03 Othon Michail

We consider temporal graphs with discrete time labels and investigate the size and the approximability of minimum temporally connected spanning subgraphs. We present a family of minimally connected temporal graphs with $n$ vertices and…

Data Structures and Algorithms · Computer Science 2016-02-23 Kyriakos Axiotis , Dimitris Fotakis

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…

Computational Complexity · Computer Science 2020-07-02 Till Fluschnik , Rolf Niedermeier , Valentin Rohm , Philipp Zschoche

Spreading processes on graphs are a natural model for a wide variety of real-world phenomena, including information spread over social networks and biological diseases spreading over contact networks. Often, the networks over which these…

Data Structures and Algorithms · Computer Science 2021-02-12 Jessica Enright , Kitty Meeks , George B. Mertzios , Viktor Zamaraev