33 Search Results for "Molter, Hendrik"

Document
DOI: 10.4230/LIPIcs.STACS.2026.24
Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics

Authors: Justine Cauvi, Nils Morawietz, and Laurent Viennot

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
In this work, we follow the current trend on temporal graph realization, where one is given a property P and the goal is to determine whether there is a temporal graph, that is, a graph where the edge set changes over time, with property P. We consider the problems where the given property P is a prescribed matrix for the duration, length, or earliest arrival time of pairwise temporal paths. This means that we are given a matrix D and ask whether there is a temporal graph such that for any ordered pair of vertices (s,t), D_{s,t} equals the duration (length, or earliest arrival time, respectively) of any temporal path from s to t minimizing that specific temporal path metric. For shortest and earliest arrival temporal paths, we are the first to consider these problems as far as we know. We analyze these problems for many settings such as: strict and non-strict paths, periodic and non-periodic temporal graphs, and limited number of labels per edge (limited number of occurrences per edge over time). In contrast to all other path metrics, we show that for the earliest arrival times, we can achieve polynomial-time algorithms in periodic and non-periodic temporal graphs and for strict and and non-strict paths. However, the problem becomes NP-hard when the matrix does not contain a single integer but a set or range of possible allowed values. As we show, the problem can still be solved efficiently in this scenario, when the number of entries with more than one value is small, that is, we develop an FPT-algorithm for the number of such entries. For the setting of fastest paths, we achieve new hardness results that answers an open question by Klobas, Mertzios, Molter, and Spirakis [Theor. Comput. Sci. '25] about the parameterized complexity of the problem with respect to the vertex cover number and significantly improves over a previous hardness result for the feedback vertex set number. When considering shortest paths, we show that the periodic versions are polynomial-time solvable whereas the non-periodic versions become NP-hard.
Cite as

Justine Cauvi, Nils Morawietz, and Laurent Viennot. Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 24:1-24:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cauvi_et_al:LIPIcs.STACS.2026.24,
  author =	{Cauvi, Justine and Morawietz, Nils and Viennot, Laurent},
  title =	{{Foremost, Fastest, Shortest: Temporal Graph Realization Under Various Path Metrics}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{24:1--24:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.24},
  URN =		{urn:nbn:de:0030-drops-255139},
  doi =		{10.4230/LIPIcs.STACS.2026.24},
  annote =	{Keywords: network design, temporal paths, foremost paths, fastest paths, shortest paths, non-strict paths, periodic temporal graphs}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.4
On the Complexity of Secluded Path Problems

Authors: Tesshu Hanaka and Daisuke Tsuru

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
This paper investigates the complexity of finding secluded paths in graphs. We focus on the Short Secluded Path problem and a natural new variant we introduce, Shortest Secluded Path. Formally, given an undirected graph G = (V, E), two vertices s,t ∈ V, and two integers k,l, the Short Secluded Path problem asks whether there exists an s-t path of length at most k with at most l neighbors. This problem is known to be computationally hard: it is W[1]-hard when parameterized by the path length k or by cliquewidth, and para-NP-complete when parameterized by the number l of neighbors. The fixed-parameter tractability is known for k+l or treewidth. In this paper, we expand the parameterized complexity landscape by designing (1) an XP algorithm parameterized by cliquewidth and (2) fixed-parameter algorithms parameterized by neighborhood diversity and twin cover number, respectively. As a byproduct, our results also provide parameterized algorithms for the classic s-t k-Path problem. Furthermore, we introduce the Shortest Secluded Path problem, which seeks a shortest s-t path with the minimum number of neighbors. In contrast to the hardness of the original problem, we reveal that this variant is solvable in polynomial time on unweighted graphs. We complete this by showing that for edge-weighted graphs, the problem becomes W[1]-hard yet remains in XP when parameterized by the shortest path distance between s and t.
Cite as

Tesshu Hanaka and Daisuke Tsuru. On the Complexity of Secluded Path Problems. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hanaka_et_al:LIPIcs.IPEC.2025.4,
  author =	{Hanaka, Tesshu and Tsuru, Daisuke},
  title =	{{On the Complexity of Secluded Path Problems}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.4},
  URN =		{urn:nbn:de:0030-drops-251361},
  doi =		{10.4230/LIPIcs.IPEC.2025.4},
  annote =	{Keywords: Secluded path, Parameterized complexity, Polynomial-time algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.53
A Parameterized Study of Secluded Structures in Directed Graphs

Authors: Jonas Schmidt, Shaily Verma, and Nadym Mallek

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Given an undirected graph G and an integer k, the Secluded Π-Subgraph problem asks you to find a maximum size induced subgraph that satisfies a property Π and has at most k neighbors in the rest of the graph. This problem has been extensively studied; however, there is no prior study of the problem in directed graphs. This question has been mentioned by Jansen et al. [ISAAC'23]. In this paper, we initiate the study of Secluded Subgraph problems in directed graphs by incorporating different notions of neighborhoods: in-neighborhood, out-neighborhood, and their union. Formally, we call these problems {In, Out, Total}-Secluded Π-Subgraph, where given a directed graph G and an integer k, we want to find an induced subgraph satisfying Π of maximum size that has at most k in/out/total-neighbors in the rest of the graph, respectively. We investigate the parameterized complexity of these problems for different properties Π. In particular, we prove the following parameterized results: - We design an FPT algorithm for the Total-Secluded Strongly Connected Subgraph problem when parameterized by k. - We show that the Out-Secluded ℱ-Free Subgraph problem with parameter k is W[1]-hard, where ℱ is a family of directed graphs except any subgraph of a star graph whose edges are directed towards the center. This result also implies that In/Out-Secluded DAG is W[1]-hard, unlike the undirected variants of the two problems, which are FPT. - We design an FPT-algorithm for In/Out/Total-Secluded α-Bounded Subgraph when parameterized by k, where α-bounded graphs are a superclass of tournaments. - For undirected graphs, we improve the best-known FPT algorithm for Secluded Clique by providing a faster FPT algorithm that runs in time 1.6181^k n^𝒪(1).
Cite as

Jonas Schmidt, Shaily Verma, and Nadym Mallek. A Parameterized Study of Secluded Structures in Directed Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 53:1-53:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schmidt_et_al:LIPIcs.ISAAC.2025.53,
  author =	{Schmidt, Jonas and Verma, Shaily and Mallek, Nadym},
  title =	{{A Parameterized Study of Secluded Structures in Directed Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{53:1--53:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.53},
  URN =		{urn:nbn:de:0030-drops-249616},
  doi =		{10.4230/LIPIcs.ISAAC.2025.53},
  annote =	{Keywords: Secluded Subgraph, Parametrized Complexity, Directed Graphs, Strong Connectivity}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.17
Realization of Temporally Connected Graphs Based on Degree Sequences

Authors: Arnaud Casteigts, Michelle Döring, and Nils Morawietz

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
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 (Göbel et al., 1991). In this article, we relax this problem and ask whether a given degree sequence can be realized as a temporally connected graph. Our main results are a complete characterization of the feasible cases, and a recognition algorithm that runs in 𝒪(n) time for graphical degree sequences (realized as simple temporal graphs) and in 𝒪(n+m) time for multigraphical degree sequences (realized as non-simple temporal graphs, where the number of time labels on an edge corresponds to the multiplicity of the edge in the multigraph). In fact, these algorithms can be made constructive at essentially no cost. Namely, we give a constructive 𝒪(n+m) time algorithm that outputs, for a given (multi)graphical degree sequence 𝐝, a temporally connected graph whose underlying (multi)graph is a realization of 𝐝, if one exists.
Cite as

Arnaud Casteigts, Michelle Döring, and Nils Morawietz. Realization of Temporally Connected Graphs Based on Degree Sequences. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casteigts_et_al:LIPIcs.ISAAC.2025.17,
  author =	{Casteigts, Arnaud and D\"{o}ring, Michelle and Morawietz, Nils},
  title =	{{Realization of Temporally Connected Graphs Based on Degree Sequences}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{17:1--17:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.17},
  URN =		{urn:nbn:de:0030-drops-249256},
  doi =		{10.4230/LIPIcs.ISAAC.2025.17},
  annote =	{Keywords: temporal paths, gossiping, (multi)graphical degree sequences, edge-disjoint spanning trees, linear time algorithms}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.27
Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs

Authors: Michelle Döring

Published in: LIPIcs, Volume 359, 36th International Symposium on Algorithms and Computation (ISAAC 2025)

Abstract
Temporal graphs model networks whose connections are available only at specific points in time. Several definitional subtleties - whether paths must follow strictly increasing time labels (strict vs. non-strict), whether adjacent edges cannot appear simultaneously (proper), and whether edges are forbidden to appear multiple times (simple) - give rise to different temporal graph settings. These distinctions directly impact the definition of temporal reachability, a core concept in temporal graph theory. Casteigts, Corsini, and Sarkar [TCS24] introduced a framework of equivalence notions to compare the expressive power of these settings focusing solely on undirected temporal graphs. In this work, we extend their framework to include the fundamental dimension of directed vs. undirected. Our contribution is three-fold. We (1) complete the undirected hierarchy by resolving the two open questions from [TCS24], (2) fully characterize the hierarchy of the directed settings, and (3) compare the directed and undirected settings, showing that directed temporal graphs are strictly more expressive than undirected temporal graphs in terms of reachability. Our structural results highlight both the limitations and strengths of various temporal graph settings - for example, directed + strict + simple graphs can realize every possible reachability graph, while directed + proper graphs necessarily induce at least one transitive reachability on each directed cycle. We also provide transformation procedures between temporal settings offering practical tools for transferring algorithms and hardness results across models.
Cite as

Michelle Döring. Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doring:LIPIcs.ISAAC.2025.27,
  author =	{D\"{o}ring, Michelle},
  title =	{{Simple, Strict, Proper, and Directed: Comparing Reachability in Directed and Undirected Temporal Graphs}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-408-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{359},
  editor =	{Chen, Ho-Lin and Hon, Wing-Kai and Tsai, Meng-Tsung},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2025.27},
  URN =		{urn:nbn:de:0030-drops-249353},
  doi =		{10.4230/LIPIcs.ISAAC.2025.27},
  annote =	{Keywords: temporal graphs, directed graphs, temporal reachability, dynamic networks}
}
Document
DOI: 10.4230/OASIcs.ATMOS.2025.3
Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases

Authors: Julia Meusel, Matthias Müller-Hannemann, and Klaus Reinhardt

Published in: OASIcs, Volume 137, 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)

Abstract
We study the complexity of the directed periodic temporal graph realization problem. This work is motivated by the design of periodic schedules in public transport with constraints on the quality of service. Namely, we require that the fastest path between (important) pairs of vertices is upper bounded by a specified maximum duration, encoded in an upper distance matrix D. While previous work has considered the undirected version of the problem, the application in public transport schedule design requires the flexibility to assign different departure times to the two directions of an edge. A problem instance can only be feasible if all values of the distance matrix are at least shortest path distances. However, the task of realizing exact fastest path distances in a periodic temporal graph is often too restrictive. Therefore, we introduce a minimum slack parameter k that describes a lower bound on the maximum allowed waiting time on each path. We concentrate on tree topologies and provide a full characterization of the complexity landscape with respect to the period Δ and the minimum slack parameter k, showing a sharp threshold between NP-complete cases and cases which are always realizable. We also provide hardness results for the special case of period Δ = 2 for general directed and undirected graphs.
Cite as

Julia Meusel, Matthias Müller-Hannemann, and Klaus Reinhardt. Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025). Open Access Series in Informatics (OASIcs), Volume 137, pp. 3:1-3:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{meusel_et_al:OASIcs.ATMOS.2025.3,
  author =	{Meusel, Julia and M\"{u}ller-Hannemann, Matthias and Reinhardt, Klaus},
  title =	{{Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases}},
  booktitle =	{25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2025)},
  pages =	{3:1--3:22},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-404-8},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{137},
  editor =	{Sauer, Jonas and Schmidt, Marie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2025.3},
  URN =		{urn:nbn:de:0030-drops-247594},
  doi =		{10.4230/OASIcs.ATMOS.2025.3},
  annote =	{Keywords: Periodic timetabling, service quality, temporal graph, graph realization, complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.93
Recognizing and Realizing Temporal Reachability Graphs

Authors: Thomas Erlebach, Othon Michail, and Nils Morawietz

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A temporal graph 𝒢 = (G,λ) can be represented by an underlying graph G = (V,E) together with a function λ that assigns to each edge e ∈ E the set of time steps during which e is present. The reachability graph of 𝒢 is the directed graph D = (V,A) with (u,v) ∈ A if and only if there is a temporal path from u to v. We study the Reachability Graph Realizability (RGR) problem that asks whether a given directed graph D = (V,A) is the reachability graph of some temporal graph. The question can be asked for undirected or directed temporal graphs, for reachability defined via strict or non-strict temporal paths, and with or without restrictions on λ (simple, proper, or both). Answering an open question posed by Casteigts et al. (TCS 2024), we show that all variants of the problem are NP-complete, except for two variants that become trivial in the directed case. For undirected temporal graphs, we consider the complexity of the problem with respect to the solid graph, that is, the graph containing all edges that could potentially receive a label in any realization. We show that the RGR problem is fixed-parameter tractable for the feedback edge set number of the solid graph. As we show, the latter parameter can presumably not be replaced by smaller parameters like feedback vertex set number or treedepth, since the problem is W[2]-hard for them.
Cite as

Thomas Erlebach, Othon Michail, and Nils Morawietz. Recognizing and Realizing Temporal Reachability Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 93:1-93:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{erlebach_et_al:LIPIcs.ESA.2025.93,
  author =	{Erlebach, Thomas and Michail, Othon and Morawietz, Nils},
  title =	{{Recognizing and Realizing Temporal Reachability Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{93:1--93:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.93},
  URN =		{urn:nbn:de:0030-drops-245627},
  doi =		{10.4230/LIPIcs.ESA.2025.93},
  annote =	{Keywords: parameterized complexity, temporal graphs, FPT algorithm, feedback edge set, directed graph recognition}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.23
Novel Complexity Results for Temporal Separators with Deadlines

Authors: Riccardo Dondi and Manuel Lafond

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider two variants, (s,z,𝓁)-Temporal Separator and (s,z,𝓁)-Temporal Cut, respectively, of the vertex separator and the edge cut problem in temporal graphs. The goal is to remove the minimum number of vertices (temporal edges, respectively) in order to delete all the temporal paths that have time travel at most 𝓁 between a source vertex s and target vertex z. First, we solve an open problem in the literature showing that (s,z,𝓁)-Temporal Separator is NP-hard even when the underlying graph has pathwidth bounded by four. We complement this result showing that (s,z,𝓁)-Temporal Separator can be solved in polynomial time for graphs of pathwidth bounded by three. Then we consider the approximability of (s,z,𝓁)-Temporal Separator and we show that it cannot be approximated within factor 2^Ω(log^{1-ε}|V|) for any constant ε > 0, unless NP ⊆ ZPP (V is the vertex set of the input temporal graph) and that the strict version is approximable within factor 𝓁-1 (we show also that it is unliklely that this factor can be improved). Then we consider the (s,z,𝓁)-Temporal Cut problem, we show that it is APX-hard and we present a 2 log₂(2𝓁) approximation algorithm.
Cite as

Riccardo Dondi and Manuel Lafond. Novel Complexity Results for Temporal Separators with Deadlines. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dondi_et_al:LIPIcs.WADS.2025.23,
  author =	{Dondi, Riccardo and Lafond, Manuel},
  title =	{{Novel Complexity Results for Temporal Separators with Deadlines}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{23:1--23:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.23},
  URN =		{urn:nbn:de:0030-drops-242545},
  doi =		{10.4230/LIPIcs.WADS.2025.23},
  annote =	{Keywords: Temporal Graphs, Graph Algorithms, Graph Separators, Parameterized Complexity, Approximation Complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.75
Temporal Graph Realization with Bounded Stretch

Authors: George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
A periodic temporal graph, in its simplest form, is a graph in which every edge appears exactly once in the first Δ time steps, and then it reappears recurrently every Δ time steps, where Δ is a given period length. This model offers a natural abstraction of transportation networks where each transportation link connects two destinations periodically. From a network design perspective, a crucial task is to assign the time-labels on the edges in a way that optimizes some criterion. In this paper we introduce a very natural optimality criterion that captures how the temporal distances of all vertex pairs are "stretched", compared to their physical distances, i.e. their distances in the underlying static (non-temporal) graph. Given a static graph G, the task is to assign to each edge one time-label between 1 and Δ such that, in the resulting periodic temporal graph with period Δ, the duration of the fastest temporal path from any vertex u to any other vertex v is at most α times the distance between u and v in G. Here, the value of α measures how much the shortest paths are allowed to be stretched once we assign the periodic time-labels. Our results span three different directions: First, we provide a series of approximation and NP-hardness results. Second, we provide approximation and fixed-parameter algorithms. Among them, we provide a simple polynomial-time algorithm (the radius-algorithm) which always guarantees an approximation strictly smaller than Δ, and which also computes the optimum stretch in some cases. Third, we consider a parameterized local search extension of the problem where we are given the temporal labeling of the graph, but we are allowed to change the time-labels of at most k edges; for this problem we prove that it is W[2]-hard but admits an XP algorithm with respect to k.
Cite as

George B. Mertzios, Hendrik Molter, Nils Morawietz, and Paul G. Spirakis. Temporal Graph Realization with Bounded Stretch. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 75:1-75:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{mertzios_et_al:LIPIcs.MFCS.2025.75,
  author =	{Mertzios, George B. and Molter, Hendrik and Morawietz, Nils and Spirakis, Paul G.},
  title =	{{Temporal Graph Realization with Bounded Stretch}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{75:1--75:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.75},
  URN =		{urn:nbn:de:0030-drops-241829},
  doi =		{10.4230/LIPIcs.MFCS.2025.75},
  annote =	{Keywords: Temporal graph, periodic temporal labeling, fastest temporal path, graph realization, temporal connectivity, stretch}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.7
Temporal Explorability Games

Authors: Pete Austin, Sougata Bose, Nicolas Mazzocchi, and Patrick Totzke

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Temporal graphs extend ordinary graphs with discrete time that affects the availability of edges. We consider solving games played on temporal graphs where one player aims to explore the graph, i.e., visit all vertices. The complexity depends majorly on two factors: the presence of an adversary and how edge availability is specified. We demonstrate that on static graphs, where edges are always available, solving explorability games is just as hard as solving reachability games. In contrast, on temporal graphs, the complexity of explorability coincides with generalized reachability (NP-complete for one-player and PSPACE-complete for two player games). We show that if temporal graphs are given symbolically, even one-player reachability (and thus explorability and generalized reachability) games are PSPACE-hard. For one player, all these are also solvable in PSPACE and for two players, they are in PSPACE, EXP and EXP, respectively.
Cite as

Pete Austin, Sougata Bose, Nicolas Mazzocchi, and Patrick Totzke. Temporal Explorability Games. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{austin_et_al:LIPIcs.CONCUR.2025.7,
  author =	{Austin, Pete and Bose, Sougata and Mazzocchi, Nicolas and Totzke, Patrick},
  title =	{{Temporal Explorability Games}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{7:1--7:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.7},
  URN =		{urn:nbn:de:0030-drops-239575},
  doi =		{10.4230/LIPIcs.CONCUR.2025.7},
  annote =	{Keywords: Temporal Graphs, Explorability, Reachability, Games}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.120
Treewidth Parameterized by Feedback Vertex Number

Authors: Hendrik Molter, Meirav Zehavi, and Amit Zivan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We provide the first algorithm for computing an optimal tree decomposition for a given graph G that runs in single exponential time in the feedback vertex number of G, that is, in time 2^{𝒪(fvn(G))}⋅ n^{𝒪(1)}, where fvn(G) is the feedback vertex number of G and n is the number of vertices of G. On a classification level, this improves the previously known results by Chapelle et al. [Discrete Applied Mathematics '17] and Fomin et al. [Algorithmica '18], who independently showed that an optimal tree decomposition can be computed in single exponential time in the vertex cover number of G. One of the biggest open problems in the area of parameterized complexity is whether we can compute an optimal tree decomposition in single exponential time in the treewidth of the input graph. The currently best known algorithm by Korhonen and Lokshtanov [STOC '23] runs in 2^{𝒪(tw(G)²)}⋅ n⁴ time, where tw(G) is the treewidth of G. Our algorithm improves upon this result on graphs G where fvn(G) ∈ o(tw(G)²). On a different note, since fvn(G) is an upper bound on tw(G), our algorithm can also be seen either as an important step towards a positive resolution of the above-mentioned open problem, or, if its answer is negative, then a mark of the tractability border of single exponential time algorithms for the computation of treewidth.
Cite as

Hendrik Molter, Meirav Zehavi, and Amit Zivan. Treewidth Parameterized by Feedback Vertex Number. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{molter_et_al:LIPIcs.ICALP.2025.120,
  author =	{Molter, Hendrik and Zehavi, Meirav and Zivan, Amit},
  title =	{{Treewidth Parameterized by Feedback Vertex Number}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{120:1--120:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.120},
  URN =		{urn:nbn:de:0030-drops-234979},
  doi =		{10.4230/LIPIcs.ICALP.2025.120},
  annote =	{Keywords: Treewidth, Tree Decomposition, Exact Algorithms, Single Exponential Time, Feedback Vertex Number, Dynamic Programming}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.12
Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs

Authors: Kamran Ayoubi and Lata Narayanan

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
In the temporal graph exploration problem, an agent wishes to visit all the vertices of a temporal graph, moving at most one edge in every time step. In restless exploration, the agent is required to move in every step, and cannot wait at a vertex. We study the problem of restless exploration in vertex-permuted graphs, which are a class of temporal graphs in which the topology of the graph stays the same in every time step. In other words, in a vertex permuted temporal graph, in every step i, the graph G_i is isomorphic to the same base graph G. We give a precise characterization of graphs G such that restless exploration is possible in every vertex-permuted graph with base graph G. Our technique is based on an a characterization of networks in which there is an online distributed algorithm for restless token dissemination. Finally we describe some families of graphs in which restless exploration is always possible, and some in which it is not.
Cite as

Kamran Ayoubi and Lata Narayanan. Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ayoubi_et_al:LIPIcs.SAND.2025.12,
  author =	{Ayoubi, Kamran and Narayanan, Lata},
  title =	{{Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.12},
  URN =		{urn:nbn:de:0030-drops-230658},
  doi =		{10.4230/LIPIcs.SAND.2025.12},
  annote =	{Keywords: Temporal graphs, Vertex permuted graphs, Restless exploration, Periodic graphs, Token dissemination}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.8
Matching and Edge Cover in Temporal Graphs

Authors: Lapo Cioni, Riccardo Dondi, Andrea Marino, Jason Schoeters, and Ana Silva

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
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 to temporal graphs, and the results may differ. In this paper, we define the {Temporal Edge Cover} and {Temporal Matching} problems and show that they are NP-complete even when fixing the lifetime or when the underlying graph is a tree. We then describe two FPT algorithms, with parameters lifetime and treewidth, that solve the two problems. We also find lower bounds for the approximation of the two problems and give two approximation algorithms which match these bounds. Finally, we discuss the differences between the problems in the temporal and the static framework.
Cite as

Lapo Cioni, Riccardo Dondi, Andrea Marino, Jason Schoeters, and Ana Silva. Matching and Edge Cover in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 8:1-8:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cioni_et_al:LIPIcs.SAND.2025.8,
  author =	{Cioni, Lapo and Dondi, Riccardo and Marino, Andrea and Schoeters, Jason and Silva, Ana},
  title =	{{Matching and Edge Cover in Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{8:1--8:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.8},
  URN =		{urn:nbn:de:0030-drops-230614},
  doi =		{10.4230/LIPIcs.SAND.2025.8},
  annote =	{Keywords: graphs, temporal graphs, edge cover, matching, parameterized algorithm, approximation algorithm}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.21
Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases

Authors: Julia Meusel, Matthias Müller-Hannemann, and Klaus Reinhardt

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
We study the complexity of the directed periodic temporal graph realization problem. This work is motivated by the design of periodic schedules in public transport with constraints on the quality of service. Namely, we require that the fastest path between (important) pairs of vertices is upper bounded by a specified maximum duration, encoded in an upper distance matrix D. While previous work has considered the undirected version of the problem, the application in public transport schedule design requires the flexibility to assign different departure times to the two directions of an edge. A problem instance can only be feasible if all values of the distance matrix are at least shortest path distances. However, the task of realizing exact fastest path distances in a periodic temporal graph is often too restrictive. Therefore, we introduce a minimum slack parameter k that describes a lower bound on the maximum allowed waiting time on each path. We concentrate on tree topologies and provide a full characterization of the complexity landscape with respect to the period Δ and the minimum slack parameter k, showing a sharp threshold between NP-complete cases and cases which are always realizable. We also provide hardness results for the special case of period Δ = 2 for general directed and undirected graphs.
Cite as

Julia Meusel, Matthias Müller-Hannemann, and Klaus Reinhardt. Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 21:1-21:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{meusel_et_al:LIPIcs.SAND.2025.21,
  author =	{Meusel, Julia and M\"{u}ller-Hannemann, Matthias and Reinhardt, Klaus},
  title =	{{Brief Announcement: Directed Temporal Tree Realization for Periodic Public Transport: Easy and Hard Cases}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{21:1--21:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.21},
  URN =		{urn:nbn:de:0030-drops-230747},
  doi =		{10.4230/LIPIcs.SAND.2025.21},
  annote =	{Keywords: Temporal graph, fastest temporal path, graph realization, periodic scheduling}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.7
Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs

Authors: David C. Kutner and Anouk Sommer

Published in: LIPIcs, Volume 330, 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)

Abstract
In train networks, carefully-chosen delays may be beneficial for certain passengers, who would otherwise miss some connection. Given a simple (directed or undirected) temporal graph and a set of passengers (each specifying a starting vertex, an ending vertex, and a desired arrival time), we ask whether it is possible to delay some of the edges of the temporal graph to realize all the passengers' demands. We call this problem DelayBetter (DB), and study it along with two variants: in δ-DelayBetter, each delay must be of at most δ; in (δ-)Path DB, passengers also fully specify the vertices they should visit on their journey. On the positive side, we give a polynomial-time algorithm for Path DB and δ-Path DB, and obtain as a corollary a polynomial-time algorithm for DB and δ-DB on trees. We also provide an fpt algorithm for both problems parameterized by the size of the graph’s Feedback Edge Set together with the number of passengers. On the negative side, we show NP-completeness of (1-)DB on bounded-degree temporal graphs even when the lifetime is 2, and of (10-)DB on bounded-degree planar temporal graphs of lifetime 19. Our results complement previous work studying reachability problems in temporal graphs with delaying operations. This is to our knowledge the first such problem in which the aim is to facilitate travel between specific points (as opposed to facilitating or impeding a broadcast from one or many sources).
Cite as

David C. Kutner and Anouk Sommer. Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kutner_et_al:LIPIcs.SAND.2025.7,
  author =	{Kutner, David C. and Sommer, Anouk},
  title =	{{Better Late, Then? The Hardness of Choosing Delays to Meet Passenger Demands in Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.7},
  URN =		{urn:nbn:de:0030-drops-230604},
  doi =		{10.4230/LIPIcs.SAND.2025.7},
  annote =	{Keywords: Temporal Graphs, Computational Complexity, Delay Management, Train Networks}
}
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