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Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a…

Data Structures and Algorithms · Computer Science 2025-08-15 Rinku Kumar , Bodhisatwa Mazumdar , Subhrangsu Mandal

A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time "11 a.m." and duration "7…

Databases · Computer Science 2016-01-26 Huanhuan Wu , Yuzhen Huang , James Cheng , Jinfeng Li , Yiping Ke

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…

Data Structures and Algorithms · Computer Science 2023-02-28 Matthias Bentert , Leon Kellerhals , Rolf Niedermeier

In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…

Data Structures and Algorithms · Computer Science 2024-06-03 N. R. Aravind , Roopam Saxena

In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…

Data Structures and Algorithms · Computer Science 2025-04-22 George B. Mertzios , Hendrik Molter , Nils Morawietz , Paul G. Spirakis

Temporal graphs are graphs whose edges are only present at certain points in time. Reachability in these graphs relies on temporal paths, where edges are traversed chronologically. A temporal graph that offers all-pairs reachability is said…

Computational Complexity · Computer Science 2026-04-28 Arnaud Casteigts , Christian Komusiewicz , Nils Morawietz

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…

Computational Complexity · Computer Science 2020-07-10 Petra Mutzel , Lutz Oettershagen

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

Temporal graphs (in which edges are active at specified times) are of particular relevance for spreading processes on graphs, e.g.~the spread of disease or dissemination of information. Motivated by real-world applications, modification of…

Computational Complexity · Computer Science 2022-12-22 Jessica Enright , Kitty Meeks , Fiona Skerman

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…

Data Structures and Algorithms · Computer Science 2022-10-14 Danny Hermelin , Yuval Itzhaki , Hendrik Molter , Rolf Niedermeier

We introduce the TemporallyEdgeDisjointScheduleCompletion (TEDSC) problem in which we need to cover a set of temporal edge demands $D$ by routing $k$ temporal walks through a directed static graph while remaining temporally edge disjoint.…

Data Structures and Algorithms · Computer Science 2026-05-07 Michelle Döring , Niklas Mohrin , George Skretas

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…

Discrete Mathematics · Computer Science 2024-05-10 Tobia Marcucci , Jack Umenberger , Pablo A. Parrilo , Russ Tedrake

Temporal graphs are used to abstractly model real-life networks that are inherently dynamic in nature. Given a static underlying graph $G=(V,E)$, a temporal graph on $G$ is a sequence of snapshots $G_t$, one for each time step $t\geq 1$. In…

Computational Complexity · Computer Science 2019-03-12 Eleni C. Akrida , George B. Mertzios , Sotiris Nikoletseas , Christoforos Raptopoulos , Paul G. Spirakis , Viktor Zamaraev

This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…

Data Structures and Algorithms · Computer Science 2026-04-07 Tesshu Hanaka , Daisuke Tsuru

A graph whose edges only appear at certain points in time is called a temporal graph (among other names). Such a graph is temporally connected if each ordered pair of vertices is connected by a path which traverses edges in chronological…

Discrete Mathematics · Computer Science 2023-12-19 Arnaud Casteigts , Michael Raskin , Malte Renken , Viktor Zamaraev

A temporal graph is a graph for which the edge set can change from one time step to the next. This paper considers undirected temporal graphs defined over L time steps and connected at each time step. We study the Shortest Temporal…

Optimization and Control · Mathematics 2025-04-10 Stefan Balev , Éric Sanlaville , Antoine Toullalan

Computing a shortest path between two nodes in an undirected unweighted graph is among the most basic algorithmic tasks. Breadth first search solves this problem in linear time, which is clearly also a lower bound in the worst case.…

Data Structures and Algorithms · Computer Science 2023-08-01 Noga Alon , Allan Grønlund , Søren Fuglede Jørgensen , Kasper Green Larsen

Temporal graphs are a class of graphs defined by a constant set of vertices and a changing set of edges, each of which is known as a timestep. These graphs are well motivated in modelling real-world networks, where connections may change…

Data Structures and Algorithms · Computer Science 2025-05-21 Duncan Adamson

Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…

Data Structures and Algorithms · Computer Science 2020-02-19 Pratibha Choudhary

A temporal graph is a sequence of graphs (called layers) over the same vertex set -- describing a graph topology which is subject to discrete changes over time. A $\Delta$-temporal matching $M$ is a set of time edges $(e,t)$ (an edge $e$…

Data Structures and Algorithms · Computer Science 2021-04-26 Philipp Zschoche