arXiv subjects

Georg Tennigkeit

Publications and source records attributed to Georg Tennigkeit.

5 recordsLinked to original sources

arXiv2026

Reconfiguration of Temporal Networks under Reachability Constraints

Temporal networks model dynamic systems in which edges represent interactions and labels specify when these interactions occur. Examples include transportation networks, time-sensitive communication networks, and industrial control systems. In many such applications, an existing temporal network must be transformed into a desired one through a sequence of atomic modifications while maintaining essential functionality throughout the transformation. We formalize the time label reconfiguration problem and provide a theoretical framework for reasoning about such transformation processes. As temporal reachability is a central functionality in many temporal networks, we study a reconfiguration problem on directed temporal graphs subject to temporal reachability constraints. We are given a static graph with a designated set of sources, along with two labeling functions indicating an availability time for every edge. The goal is to transform one labeling into the other by changing the label of a single edge at a time while maintaining temporal reachability of the sources throughout. Our results reveal a sharp complexity transition: the problem is polynomial-time solvable for a single source but becomes PSPACE-hard with two sources. We also show that if the static graph is acyclic or an almost-tournament graph, then all valid labelings can be reconfigured into each other. Our proofs are constructive and yield polynomial-time algorithms.

cs.DS↗

arXiv2026

Maximizing Reachability via Shifting of Temporal Paths

We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote availability in time. This type of temporal graphs represent train networks. We consider shifting operations on the labels of the paths that maintain their temporal continuity. This means that we can move the availability of a temporal edge later or earlier in time, and propagate the shifts to all other affected edges of the path in order to preserve its temporal connectivity. We study the parameterized complexity of the problem with respect to the number of paths k, and the total budget b, where b is the maximum number of shifts we are allowed to perform. Our results reveal that fixed parameter tractability can be achieved (1) when parameterized both by k and b, and (2) when parameterized by k, and b is unconstrained. In almost every other case, e.g., parameterized by a single parameter or parameterized by k, while having a bound on b, we establish intractability lower bounds that are matched by XP algorithms.

cs.DS↗

arXiv2025

Temporal Graph Reconfiguration for Always-Connected Graphs

Network redesign problems ask for modifications to the edges of a given graph to satisfy certain properties. In temporal graphs, where edges are only active at certain times, we are sometimes only allowed to modify when the edges are going to be active. In practice, we might not even be able to perform all of the necessary modifications at once; changes must be applied step-by-step while the network is still in operation, meaning that the network must continue to satisfy some properties. To initiate a study in this area, we introduce the class of temporal graph reconfiguration problems. As a starting point, we consider the Layered Connectivity Reconfiguration (LCR) problem: Given two always-connected temporal graphs G1 and G2, determine if it is possible to transform G1 into G2 by changing the time at which a single temporal edge is active in each step, such that every intermediate temporal graph is always-connected. We provide a dynamic programming algorithm for the LCR problem. We also show that finding the shortest reconfiguration sequence between two temporal graphs is APX-hard. Additionally, we show that the LCR problem is equivalent to the Spanning Tree Sequence Reconfiguration (STSR) problem introduced by Hanaka et al. Therefore, our results also answer the two open questions presented by the authors: (i) find a simpler algorithm for the STSR problem, (ii) show that the STSR problem is inapproximable up to some factor.

cs.DS↗

arXiv2025

Parameterized Complexity of Temporal Connected Components: Treewidth and k-Path Graphs

We study the parameterized complexity of maximum temporal connected components (tccs) in temporal graphs, i.e., graphs that deterministically change over time. In a tcc, any pair of vertices must be able to reach each other via a time-respecting path. We consider both problems of maximum open tccs (openTCC), which allow temporal paths through vertices outside the component, and closed tccs (closedTCC) which require at least one temporal path entirely within the component for every pair. We focus on the structural parameter of treewidth, tw, and the recently introduced temporal parameter of temporal path number, tpn, which is the minimum number of paths needed to fully describe a temporal graph. We prove that these parameters on their own are not sufficient for fixed parameter tractability: both openTCC and closedTCC are NP-hard even when tw=9, and closedTCC is NP-hard when tpn=6. In contrast, we prove that openTCC is in XP when parameterized by tpn. On the positive side, we show that both problem become fixed parameter tractable under various combinations of structural and temporal parameters that include, tw plus tpn, tw plus the lifetime of the graph, and tw plus the maximum temporal degree.

cs.DS↗

arXiv2024

How Many Lines to Paint the City: Exact Edge-Cover in Temporal Graphs

Logistics and transportation networks require a large amount of resources to realize necessary connections between locations and minimizing these resources is a vital aspect of planning research. Since such networks have dynamic connections that are only available at specific times, intricate models are needed to portray them accurately. In this paper, we study the problem of minimizing the number of resources needed to realize a dynamic network, using the temporal graphs model. In a temporal graph, edges appear at specific points in time. Given a temporal graph and a natural number k, we ask whether we can cover every temporal edge exactly once using at most k temporal journeys; in a temporal journey consecutive edges have to adhere to the order of time. We conduct a thorough investigation of the complexity of the problem with respect to four dimensions: (a) whether the type of the temporal journey is a walk, a trail, or a path; (b) whether the chronological order of edges in the journey is strict or non-strict; (c) whether the temporal graph is directed or undirected; (d) whether the start and end points of each journey are given or not. We almost completely resolve the complexity of all these problems and provide dichotomies for each one of them with respect to k.

cs.SI↗