32 Search Results for "Zamaraev, Viktor"

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.2025.35
Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage

Authors: Meng He and Kaiyu Wu

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

Abstract
We improve the recent succinct data structure result of Balakrishnan et al. for chordal graphs with bounded vertex leafage (SWAT 2024). A chordal graph is a widely studied graph class which can be characterized as the intersection graph of subtrees of a host tree, denoted as a tree representation of the chordal graph. The vertex leafage and leafage parameters of a chordal graph deal with the existence of a tree representation with a bounded number of leaves in either the subtrees representing the vertices or the host tree itself. We simplify the lower bound proof of Balakrishnan et al. which applied to only chordal graphs with bounded vertex leafage, and extend it to a lower bound proof for chordal graphs with bounded leafage as well. For both classes of graphs, the information-theoretic lower bound we (re-)obtain for k = o(n) is (k-1)nlog n - knlog k - o(knlog n) bits, where the leafage or vertex leafage of the graph is at most k = o(n). We further extend the range of the parameter k to Θ(n) as well. Then we give a succinct data structure using (k-1)nlog (n/k) + o(knlog n) bits to answer adjacent queries, which test the adjacency between pairs of vertices, in O((log k)/(log log n) + 1) time compared to the O(klog n) time of the data structure of Balakrishnan et al. For the neighborhood query which lists the neighbours of a given vertex, our query time is O((log n)/(log log n)) per neighbour compared to O(k²log n) per neighbour. We also extend the data structure ideas to obtain a succinct data structure for chordal graphs with bounded leafage k, answering an open question of Balakrishnan et al. Our succinct data structure, which uses (k-1)nlog (n/k) + o(knlog n) bits, has query time O(1) for the adjacent query and O(1) per neighbour for the neighborhood query. Using slightly more space (an additional (1+ε)nlog n bits for any ε > 0) allows distance queries, which compute the number of edges in the shortest path between two given vertices, to be answered in O(1) time as well.
Cite as

Meng He and Kaiyu Wu. Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 35:1-35:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{he_et_al:LIPIcs.WADS.2025.35,
  author =	{He, Meng and Wu, Kaiyu},
  title =	{{Succinct Data Structures for Chordal Graph with Bounded Leafage or Vertex Leafage}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{35:1--35:23},
  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.2025.35},
  URN =		{urn:nbn:de:0030-drops-242660},
  doi =		{10.4230/LIPIcs.WADS.2025.35},
  annote =	{Keywords: Chordal Graph, Leafage, Vertex Leafage, Succinct Data Structure}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.15
Symmetry Classes of Hamiltonian Cycles

Authors: Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk

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

Abstract
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a graph automorphism mapping one cycle to the other. This generalizes the extensively studied uniquely Hamiltonian graphs. In this paper, we show that Cayley graphs of abelian groups are not Hamiltonian-transitive (under some mild conditions and some non-surprising exceptions), i.e., they contain at least two structurally different Hamiltonian cycles. To show this, we reduce Hamiltonian-transitivity to properties of the prime factors of a Cartesian product decomposition, which we believe is interesting in its own right. We complement our results by constructing infinite families of regular Hamiltonian-transitive graphs and take a look at the opposite extremal case by constructing a family with many different Hamiltonian cycles up to symmetry.
Cite as

Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk. Symmetry Classes of Hamiltonian Cycles. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baligacs_et_al:LIPIcs.MFCS.2025.15,
  author =	{Balig\'{a}cs, J\'{u}lia and Brenner, Sofia and Lutz, Annette and Volk, Lena},
  title =	{{Symmetry Classes of Hamiltonian Cycles}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{15:1--15:18},
  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.2025.15},
  URN =		{urn:nbn:de:0030-drops-241221},
  doi =		{10.4230/LIPIcs.MFCS.2025.15},
  annote =	{Keywords: Hamiltonian cycles, graph automorphisms, Cayley graphs, abelian groups, Cartesian product of graphs}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.43
The Complexity of Computing Second Solutions

Authors: Fabian Egidy, Christian Glaßer, and Fynn Godau

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

Abstract
We study the complexity of computing second solutions for NP search problems, i. e., given a problem instance x and a valid solution y, we have to find another valid solution y'. Our main result shows that for typical NP decision problems, the complexity of computing second solutions is completely determined by the choice of the type of solution (i. e., the specific function problem), but independent of the underlying decision problem. More precisely, we show that for every X ∈ NP that is 1-paddable (a weak form of paddability), different choices of the type of solution lead to different second solution problems, which altogether have the same degree structure as the entire class of NP search problems (FNP). In fact, each degree of difficulty within FNP does occur as a second solution problem for X. This proves that typical NP decision problems have no intrinsic complexity w. r. t. the search for a second solution, but only the specification of the type of solution determines this complexity. This explains the empirical observation that the difficulty of computing second solutions strongly depends on the formulation of the problem. Moreover, we show that the complexities of a search problem and its second solution variant are independent in the following sense: For all search problems A and B representing two degrees of difficulty, there exists a search problem C such that 1) C is as difficult as A and 2) computing second solutions for C is as difficult as B.
Cite as

Fabian Egidy, Christian Glaßer, and Fynn Godau. The Complexity of Computing Second Solutions. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{egidy_et_al:LIPIcs.MFCS.2025.43,
  author =	{Egidy, Fabian and Gla{\ss}er, Christian and Godau, Fynn},
  title =	{{The Complexity of Computing Second Solutions}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{43:1--43:16},
  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.2025.43},
  URN =		{urn:nbn:de:0030-drops-241505},
  doi =		{10.4230/LIPIcs.MFCS.2025.43},
  annote =	{Keywords: function problems, another solution problem, turing machines}
}
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.MFCS.2025.70
Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width

Authors: Aliaume Lopez

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

Abstract
We construct an algorithm that inputs an MSO-interpretation from finite words to graphs, and decides if there exists a k ∈ ℕ such that the class of graphs induced by the interpretation is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using {1, …, k}. In case no such k exists, we also prove that the class of graphs is not well-quasi-ordered by the induced subgraph relation when vertices are freely labelled using any well-quasi-ordered set of labels. As a byproduct of our analysis, we prove that for classes of bounded linear clique-width, a weak version of a conjecture by Pouzet holds.
Cite as

Aliaume Lopez. Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 70:1-70:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lopez:LIPIcs.MFCS.2025.70,
  author =	{Lopez, Aliaume},
  title =	{{Labelled Well Quasi Ordered Classes of Bounded Linear Clique-Width}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{70:1--70:17},
  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.2025.70},
  URN =		{urn:nbn:de:0030-drops-241773},
  doi =		{10.4230/LIPIcs.MFCS.2025.70},
  annote =	{Keywords: well-quasi-ordering, linear clique-width, MSO transduction, automata theory}
}
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.2025.86
Optimal Distance Labeling for Permutation Graphs

Authors: Paweł Gawrychowski and Wojciech Janczewski

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

Abstract
A permutation graph is the intersection graph of a set of segments between two parallel lines. In other words, they are defined by a permutation π on n elements, such that u and v are adjacent if an only if u < v but π(u) > π(v). We consider the problem of computing the distances in such a graph in the setting of informative labeling schemes. The goal of such a scheme is to assign a short bitstring 𝓁(u) to every vertex u, such that the distance between u and v can be computed using only 𝓁(u) and 𝓁(v), and no further knowledge about the whole graph (other than that it is a permutation graph). This elegantly captures the intuition that we would like our data structure to be distributed, and often leads to interesting combinatorial challenges while trying to obtain lower and upper bounds that match up to the lower-order terms. For distance labeling of permutation graphs on n vertices, Katz, Katz, and Peleg [STACS 2000] showed how to construct labels consisting of 𝒪(log² n) bits. Later, Bazzaro and Gavoille [Discret. Math. 309(11)] obtained an asymptotically optimal bound by showing how to construct labels consisting of 9log{n}+𝒪(1) bits, and proving that 3log{n}-𝒪(log{log{n}}) bits are necessary. This however leaves a quite large gap between the known lower and upper bounds. We close this gap by showing how to construct labels consisting of 3log{n}+𝒪(1) bits.
Cite as

Paweł Gawrychowski and Wojciech Janczewski. Optimal Distance Labeling for Permutation Graphs. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 86:1-86:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.ICALP.2025.86,
  author =	{Gawrychowski, Pawe{\l} and Janczewski, Wojciech},
  title =	{{Optimal Distance Labeling for Permutation Graphs}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{86:1--86:18},
  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.2025.86},
  URN =		{urn:nbn:de:0030-drops-234632},
  doi =		{10.4230/LIPIcs.ICALP.2025.86},
  annote =	{Keywords: informative labeling, permutation graph, distance labeling}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.6
Dismountability in Temporal Cliques Revisited

Authors: Daniele Carnevale, Arnaud Casteigts, and Timothée Corsini

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

Abstract
A temporal graph is a graph whose edges are available only at certain points in time. It is temporally connected if the nodes can reach each other by paths that traverse the edges chronologically (temporal paths). Unlike static graphs, temporal graphs do not always admit small subsets of edges that preserve connectivity (temporal spanners) - there exist temporal graphs with Θ(n²) edges, all of which are critical. In the case of temporal cliques (the underlying graph is complete), spanners of size O(nlog n) are guaranteed. The original proof of this result by Casteigts et al. [ICALP 2019] combines a number of techniques, one of which is called dismountability. In a recent work, Angrick et al. [ESA 2024] simplified the proof and showed, among other things, that a one-sided version of dismountability can replace elegantly the second part of the proof. In this paper, we revisit methodically the dismountability principle. We start by characterizing the structure that a temporal clique must have if it is non 1-hop dismountable, then neither 1-hop nor 2-hop (i.e. non {1,2}-hop) dismountable, and finally non {1,2,3}-hop dismountable. It turns out that if a clique is k-hop dismountable for any other k, then it must also be {1,2,3}-hop dismountable, thus no additional structure can be obtained beyond this point. Interestingly, excluding 1-hop and 2-hop dismountability is already sufficient for reducing the spanner problem from cliques to extremally matched bicliques, where the O(nlog n) result is subsequently obtained. Put together with the strategy of Angrick et al., this entire result can now be recovered using only dismountability. An interesting by-product of our analysis is that any minimal counter-example to the existence of 4n spanners must satisfy the properties of non {1,2,3}-hop dismountable cliques. In the second part, we discuss further connections between dismountability and another technique called pivotability. In particular, we show that if a temporal clique is recursively k-hop dismountable, then it is also pivotable (and thus admits a 2n spanner, whatever k). We also study a family of labelings called full-range that forces both dismountability and pivotability. The latter gives some evidence that large lifetimes could be exploited more generally for the construction of spanners.
Cite as

Daniele Carnevale, Arnaud Casteigts, and Timothée Corsini. Dismountability in Temporal Cliques Revisited. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 6:1-6:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{carnevale_et_al:LIPIcs.SAND.2025.6,
  author =	{Carnevale, Daniele and Casteigts, Arnaud and Corsini, Timoth\'{e}e},
  title =	{{Dismountability in Temporal Cliques Revisited}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{6:1--6:18},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-230591},
  doi =		{10.4230/LIPIcs.SAND.2025.6},
  annote =	{Keywords: Dynamic networks, Temporal graphs, Reachability, Dismountability, Pivotability, Temporal spanners, Full-range graphs}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.3
Temporal Connectivity Augmentation

Authors: Thomas Bellitto, Jules Bouton Popper, and Bruno Escoffier

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

Abstract
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 precisely, we tackle the problem of finding, among a set of proposed temporal edges, the smallest subset such that its addition makes the graph temporally connected (TCA). We study the complexity of this problem and variants, under restricted lifespan of the graph, i.e. the maximum time step in the graph. Our main result on TCA is that for any fixed lifespan at least 2, it is NP-complete in both the strict and non-strict setting. We additionally provide a set of restrictions in the non-strict setting which makes the problem solvable in polynomial time and design an algorithm achieving this complexity. Interestingly, we prove that the source variant (making a given vertex a source in the augmented graph) is as difficult as TCA. On the opposite, we prove that the version where a list of connectivity demands has to be satisfied is solvable in polynomial time, when the size of the list is fixed. Finally, we highlight a variant of the previous case for which even with two pairs the problem is already NP-hard.
Cite as

Thomas Bellitto, Jules Bouton Popper, and Bruno Escoffier. Temporal Connectivity Augmentation. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bellitto_et_al:LIPIcs.SAND.2025.3,
  author =	{Bellitto, Thomas and Popper, Jules Bouton and Escoffier, Bruno},
  title =	{{Temporal Connectivity Augmentation}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{3:1--3:16},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-230565},
  doi =		{10.4230/LIPIcs.SAND.2025.3},
  annote =	{Keywords: Temporal graph, temporal connectivity}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.22
Brief Announcement: Exploring Word-Representable Temporal Graphs

Authors: Duncan Adamson

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

Abstract
Word-representable graphs are a subset of graphs that may be represented by a word w over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices alternate in the word w. We generalise this notion to temporal graphs, constructing timesteps by partitioning the word into factors (contiguous subwords) such that no factor contains more than one copy of any given symbol. With this definition, we study the problem of exploration, asking for the fastest schedule such that a given agent may explore all n vertices of the graph. We show that if the corresponding temporal graph is connected in every timestep, we may explore the graph in 2δ n timesteps, where δ is the lowest degree of any vertex in the graph. In general, we show that, for any temporal graph represented by a word of length at least n(2dn + d), with a connected underlying graph, the full graph can be explored in 2 d n timesteps, where d is the diameter of the graph.
Cite as

Duncan Adamson. Brief Announcement: Exploring Word-Representable Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 22:1-22:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adamson:LIPIcs.SAND.2025.22,
  author =	{Adamson, Duncan},
  title =	{{Brief Announcement: Exploring Word-Representable Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{22:1--22:6},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-230755},
  doi =		{10.4230/LIPIcs.SAND.2025.22},
  annote =	{Keywords: Temporal Graphs, Word-Representable Graphs}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.9
Spanner Enumeration for Temporal Graphs

Authors: Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno

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

Abstract
A spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP.
Cite as

Kazuhiro Kurita, Andrea Marino, Jason Schoeters, and Takeaki Uno. Spanner Enumeration for Temporal Graphs. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kurita_et_al:LIPIcs.SAND.2025.9,
  author =	{Kurita, Kazuhiro and Marino, Andrea and Schoeters, Jason and Uno, Takeaki},
  title =	{{Spanner Enumeration for Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{9:1--9:21},
  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.2025.9},
  URN =		{urn:nbn:de:0030-drops-230621},
  doi =		{10.4230/LIPIcs.SAND.2025.9},
  annote =	{Keywords: temporal graphs, temporal spanners, one-to-all connectivity, all-to-all connectivity enumeration, NP-completeness, Dual-hardness, binary partition tree, flashlight search, polynomial delay}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.16
Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions

Authors: Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer

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

Abstract
We study the Temporal Dominating Set problem, in which one asks whether a temporal graph 𝒢 = (G₁,… , G_T) given as a sequence of snapshot graphs, over the same vertex set V, has a set S of temporal vertices of size at most k such that each vertex v of V is dominated by some w ∈ S in the snapshot that contains w. Additionally, we consider Temporal Partial Dominating Set, where one asks whether at least t (and not necessarily all) vertices of V can be dominated by S and a further generalization in which the solution may only contain a bounded number of temporal vertices from each snapshot. We analyze how the complexity of Temporal (Partial) Dominating Set is influenced by the maximum snapshot degree and the structure of the underlying graph, the graph with vertex set V and whose edge set is the union of all snapshot edge sets. For example, we obtain a complexity dichotomy for the maximum snapshot degree and we show that Temporal Partial Dominating Set is fixed-parameter tractable for tw+Δ, where tw and Δ denote the treewidth and the maximum degree of the underlying graph of 𝒢, respectively. We also show which of our results transfer to the well-studied Temporal Vertex Cover problem. For example, we show that Temporal Vertex Cover is also fixed-parameter tractable for tw+Δ which substantially extends the previously known polynomial-time algorithms for the case that the underlying graph is a path or cycle.
Cite as

Anton Herrmann, Christian Komusiewicz, Nils Morawietz, and Frank Sommer. Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{herrmann_et_al:LIPIcs.SAND.2025.16,
  author =	{Herrmann, Anton and Komusiewicz, Christian and Morawietz, Nils and Sommer, Frank},
  title =	{{Temporal Dominating Set and Temporal Vertex Cover Under the Lense of Degree Restrictions}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{16:1--16:18},
  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.2025.16},
  URN =		{urn:nbn:de:0030-drops-230695},
  doi =		{10.4230/LIPIcs.SAND.2025.16},
  annote =	{Keywords: NP-hard problem, FPT-algorithm, Treewidth, Color coding}
}
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
DOI: 10.4230/LIPIcs.STACS.2025.36
MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal

Authors: Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma

Published in: LIPIcs, Volume 327, 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)

Abstract
In this paper, we study the parameterized complexity of the MaxMin versions of two fundamental separation problems: Maximum Minimal st-Separator and Maximum Minimal Odd Cycle Transversal (OCT), both parameterized by the solution size. In the Maximum Minimal st-Separator problem, given a graph G, two distinct vertices s and t and a positive integer k, the goal is to determine whether there exists a minimal st-separator in G of size at least k. Similarly, the Maximum Minimal OCT problem seeks to determine if there exists a minimal set of vertices whose deletion results in a bipartite graph, and whose size is at least k. We demonstrate that both problems are fixed-parameter tractable parameterized by k. Our FPT algorithm for Maximum Minimal st-Separator answers the open question by Hanaka, Bodlaender, van der Zanden & Ono [TCS 2019]. One unique insight from this work is the following. We use the meta-result of Lokshtanov, Ramanujan, Saurabh & Zehavi [ICALP 2018] that enables us to reduce our problems to highly unbreakable graphs. This is interesting, as an explicit use of the recursive understanding and randomized contractions framework of Chitnis, Cygan, Hajiaghayi, Pilipczuk & Pilipczuk [SICOMP 2016] to reduce to the highly unbreakable graphs setting (which is the result that Lokshtanov et al. tries to abstract out in their meta-theorem) does not seem obvious because certain "extension" variants of our problems are W[1]-hard.
Cite as

Ajinkya Gaikwad, Hitendra Kumar, Soumen Maity, Saket Saurabh, and Roohani Sharma. MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gaikwad_et_al:LIPIcs.STACS.2025.36,
  author =	{Gaikwad, Ajinkya and Kumar, Hitendra and Maity, Soumen and Saurabh, Saket and Sharma, Roohani},
  title =	{{MaxMin Separation Problems: FPT Algorithms for st-Separator and Odd Cycle Transversal}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine 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.2025.36},
  URN =		{urn:nbn:de:0030-drops-228622},
  doi =		{10.4230/LIPIcs.STACS.2025.36},
  annote =	{Keywords: Parameterized Complexity, FPT, MaxMin problems, Maximum Minimal st-separator, Maximum Minimal Odd Cycle Transversal, Unbreakable Graphs, CMSO, Long Induced Odd Cycles, Sunflower Lemma}
}
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