21 Search Results for "Viennot, Laurent"

Document
DOI: 10.4230/LIPIcs.SAND.2026.5
Complexity Gaps Between Point and Interval Temporal Graphs for Some Reachability Problems

Authors: Guillaume Aubian, Filippo Brunelli, Feodor F. Dragan, Guillaume Ducoffe, Michel Habib, Allen Ibiapina, and Laurent Viennot

Published in: LIPIcs, Volume 373, 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)

Abstract
Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration, delay of transmission. In the point model, edges appear at specific points in time, whereas in the more general interval model, edges can be present over specific time intervals. In both models, the delay for traversing an edge can change with each edge appearance. When time is discrete, the two models are equivalent in the sense that the presence of an edge during an interval is equivalent to a sequence of point-in-time occurrences of the edge. However, this transformation can drastically change the size of the input and has implications for complexity. Indeed, we show a gap between the two models with respect to the complexity of the classical problem of computing a fastest temporal path from a source vertex to a target vertex, i.e., a path where edges can be traversed one after another in time and such that the total duration from source to target is minimized. It can be solved in near-linear time in the point model, while we show that the interval model requires quadratic time under classical assumptions of fine-grained complexity. With respect to linear time, our lower bound implies a factor of the number of vertices, while the best known algorithm has a factor of the number of underlying edges. We also show a similar complexity gap for computing a shortest temporal path, i.e., a temporal path with a minimum number of edges. Here our lower bound matches known upper bounds up to a logarithmic factor. Interestingly, we show that near-linear time for fastest temporal path computation is possible in the interval model when it is restricted to uniform delay zero, i.e., when traversing an edge is instantaneous. However, this special case is not exempt from our lower bound for shortest temporal path computation. These two results should be contrasted with the computation of a foremost temporal path, i.e., a temporal path that arrives as early as possible. It is well known that this computation can be solved in near-linear time in both models. We also show that there is no gap in testing the all-to-all temporal connectivity of a temporal graph. We demonstrate a quadratic lower bound that applies to both the interval and point models and aligns with the existing upper bounds.
Cite as

Guillaume Aubian, Filippo Brunelli, Feodor F. Dragan, Guillaume Ducoffe, Michel Habib, Allen Ibiapina, and Laurent Viennot. Complexity Gaps Between Point and Interval Temporal Graphs for Some Reachability Problems. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{aubian_et_al:LIPIcs.SAND.2026.5,
  author =	{Aubian, Guillaume and Brunelli, Filippo and Dragan, Feodor F. and Ducoffe, Guillaume and Habib, Michel and Ibiapina, Allen and Viennot, Laurent},
  title =	{{Complexity Gaps Between Point and Interval Temporal Graphs for Some Reachability Problems}},
  booktitle =	{5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-427-7},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{373},
  editor =	{Mertzios, George B. and Richa, Andr\'{e}a W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2026.5},
  URN =		{urn:nbn:de:0030-drops-262395},
  doi =		{10.4230/LIPIcs.SAND.2026.5},
  annote =	{Keywords: Temporal graphs, Dynamic networks, Time-dependent networks, Temporal connectivity, Foremost, Fastest or Shortest temporal path, Fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.29
Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above

Authors: Timothy M. Chan, Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case [Duraj et al., 2024; Hsien-Chih Chang et al., 2024; Chan et al., 2025] where truly subquadratic-time algorithms were given for simple objects such as unit-disks and (axis-aligned) squares. However, in three or higher dimensions, there is no known truly subquadratic-time algorithm for any intersection graph of non-trivial objects, even basic ones such as unit balls or (axis-aligned) unit cubes. This was partially explained by the pioneering work of Bringmann et al. [Karl Bringmann et al., 2022] which gave several truly subquadratic lower bounds, notably for unit balls or unit cubes in 3D when the graph diameter Δ is at least Ω(log n), hinting at a pessimistic outlook for the complexity of the diameter problem in higher dimensions. In this paper, we substantially extend the landscape of diameter computation for objects in three and higher dimensions, giving a few positive results. Our highlighted findings include: 1) A truly subquadratic-time algorithm for deciding if the diameter of unit cubes in 3D is at most 3 (Diameter-3 hereafter), the first algorithm of its kind for objects in 3D or higher dimensions. Our algorithm is based on a novel connection to pseudolines, which is of independent interest. 2) A truly subquadratic time lower bound for Diameter-3 of unit balls in 3D under the Orthogonal Vector (OV) hypothesis, giving the first separation between unit balls and unit cubes in the small diameter regime. Previously, computing the diameter for both objects was known to be quadratic hard when the diameter is Ω(log n) [Karl Bringmann et al., 2022]. 3) A near-linear-time algorithm for Diameter-2 of unit cubes in 3D, generalizing the previous result for unit squares in 2D [Karl Bringmann et al., 2022]. 4) A truly subquadratic-time algorithm and lower bound for Diameter-2 and Diameter-3 of rectangular boxes (of arbitrary dimension and sizes), respectively.
Cite as

Timothy M. Chan, Hsien-Chih Chang, Jie Gao, Sándor Kisfaludi-Bak, Hung Le, and Da Wei Zheng. Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 29:1-29:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chan_et_al:LIPIcs.SoCG.2026.29,
  author =	{Chan, Timothy M. and Chang, Hsien-Chih and Gao, Jie and Kisfaludi-Bak, S\'{a}ndor and Le, Hung and Zheng, Da Wei},
  title =	{{Charting the Diameter Computation Landscape of Intersection Graphs in 3D and Above}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{29:1--29:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.29},
  URN =		{urn:nbn:de:0030-drops-258357},
  doi =		{10.4230/LIPIcs.SoCG.2026.29},
  annote =	{Keywords: Graph Diameter, Geometric Intersection Graphs, Unit Ball Graphs}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.30
Computing the Girth of a Segment Intersection Graph

Authors: Timothy M. Chan and Yuancheng Yu

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
We present an algorithm that computes the girth of the intersection graph of n given line segments in the plane in O(n^1.483) expected time. This is the first such algorithm with O(n^{3/2-ε}) running time for a positive constant ε, and makes progress towards an open question posed by Chan (SODA 2023). The main techniques include (i) the usage of recent subcubic algorithms for bounded-difference min-plus matrix multiplication, and (ii) an interesting variant of the planar graph separator theorem. The result extends to intersection graphs of connected algebraic curves or semialgebraic sets of constant description complexity.
Cite as

Timothy M. Chan and Yuancheng Yu. Computing the Girth of a Segment Intersection Graph. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chan_et_al:LIPIcs.SoCG.2026.30,
  author =	{Chan, Timothy M. and Yu, Yuancheng},
  title =	{{Computing the Girth of a Segment Intersection Graph}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.30},
  URN =		{urn:nbn:de:0030-drops-258364},
  doi =		{10.4230/LIPIcs.SoCG.2026.30},
  annote =	{Keywords: Geometric intersection graphs, girth, shortest paths, graph separators, matrix multiplication}
}
Document
DOI: 10.4230/LIPIcs.FUN.2026.29
Finding Shortest Walks in Kuru Kuru Kururin

Authors: Mickaël Laurent and Maher Mallem

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
This paper serves as a celebration of the twenty-fifth anniversary of Kuru Kuru Kururin. Although this video game is presented as a collection of two-dimensional puzzles based on rotation, it naturally invites players to complete its levels as quickly as possible. This has led to a surprisingly rich and challenging playing field to finding foremost temporal walks. In this work, we tackle this problem both in theory and in practice. First, we introduce a model for the game and provide an in-depth complexity analysis. Most notably, we show how each gameplay mechanic independently brings a layer of NP-hardness and/or co-NP-hardness. We also provide a pseudo-polynomial time algorithm for the general problem and identify several cases which can be solved in polynomial time. Along the way, we discuss connections to the more established framework of temporal graphs, both in the point model and the interval model. Then, we propose simple and flexible algorithmic techniques to reduce state space and guide the search, offering trade-offs between precision and computation speed in practice. These techniques were implemented and tested using a full recreation of the game physics and the levels from the original game. We demonstrate the efficiency of our framework in several settings - with or without taking damage, with or without unintended game mechanics - and relate empirical struggles which we encountered in practice to our complexity analysis. Our implementation is open source and fully available online, offering a novel and amusing setting to benchmark shortest path algorithms.
Cite as

Mickaël Laurent and Maher Mallem. Finding Shortest Walks in Kuru Kuru Kururin. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{laurent_et_al:LIPIcs.FUN.2026.29,
  author =	{Laurent, Micka\"{e}l and Mallem, Maher},
  title =	{{Finding Shortest Walks in Kuru Kuru Kururin}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.29},
  URN =		{urn:nbn:de:0030-drops-257480},
  doi =		{10.4230/LIPIcs.FUN.2026.29},
  annote =	{Keywords: Shortest path, Complexity}
}
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.STACS.2026.18
Optimal Deterministic Rendezvous in Labeled Lines

Authors: Yann Bourreau, Ananth Narayanan, and Alexandre Nolin

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

Abstract
In a rendezvous task, a set of mobile agents initially dispersed in a network have to gather at an arbitrary common site. We consider the rendezvous problem on the infinite labeled line, with 2 initially asleep agents, without communication, and a synchronous notion of time. Each node on the line is labeled with a unique positive integer. The initial distance between the two agents is denoted by D. Time is divided into rounds and measured from the moment an agent first wakes up. We denote by τ the delay between the two agents' wake up times. If awake in a given round T, an agent at a node v has three options: stay at the node v, take port 0, or take port 1. If it decides to stay, the agent will still be at node v in round T+1. Otherwise, it will be at one of the two neighbors of v on the infinite line, depending on the port it chose. The agents achieve rendezvous in T rounds if they are at the same node in round T. We aim for a deterministic algorithm for this problem. The problem was recently considered by Miller and Pelc [Distributed Computing, 2025]. With 𝓁_{max} the largest label of the two starting nodes, they showed that no algorithm can guarantee rendezvous in o(D log^* 𝓁_{max}) rounds. The lower bound follows from a connection with the LOCAL model of distributed computing, and holds even if the agents are guaranteed simultaneous wake-up (τ = 0) and are told their initial distance D. Miller and Pelc also gave an algorithm of optimal matching complexity O(D log^* 𝓁_{max}) when the agents know D, but only obtained the higher bound of O(D² (log^* 𝓁_{max})³) when D is unknown to the agents. In this paper, we improve this second complexity to a tight O(D log^* 𝓁_{max}), closing the gap between the best known lower and upper bounds. In fact, our algorithm achieves rendezvous in O(D log^* 𝓁_{min}) rounds, where 𝓁_{min} is the smallest label within distance O(D) of the two starting positions. We obtain this result by having the agents compute sparse subsets of the nodes to gather at (formally, ruling sets over the line), as well as some general observations about the setting of rendezvous on labeled graphs.
Cite as

Yann Bourreau, Ananth Narayanan, and Alexandre Nolin. Optimal Deterministic Rendezvous in Labeled Lines. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bourreau_et_al:LIPIcs.STACS.2026.18,
  author =	{Bourreau, Yann and Narayanan, Ananth and Nolin, Alexandre},
  title =	{{Optimal Deterministic Rendezvous in Labeled Lines}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{18:1--18:20},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-255071},
  doi =		{10.4230/LIPIcs.STACS.2026.18},
  annote =	{Keywords: mobile agents, rendezvous, ruling set, deterministic algorithms, labeled line}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2025.25
On the Complexity of Distributed Edge Coloring and Orientation Problems

Authors: Sebastian Brandt, Fabian Kuhn, and Zahra Parsaeian

Published in: LIPIcs, Volume 361, 29th International Conference on Principles of Distributed Systems (OPODIS 2025)

Abstract
Understanding the role of randomness when solving locally checkable labeling (LCL) problems in the LOCAL model has been one of the top priorities in the research on distributed graph algorithms in recent years. For LCL problems in bounded-degree graphs, it is known that randomness cannot help more than polynomially, except in one case: if the deterministic complexity of an LCL problem is in Ω(log n) and its randomized complexity is in o(log n), then the randomized complexity is guaranteed to be O(poly(log log n)) and it is even known to be O(log log n) in bounded-degree trees. However, the fundamental question of which problems with a deterministic complexity of Ω(log n) can be solved exponentially faster using randomization still remains wide open. We make a step towards answering this question by studying a simple, but natural class of LCL problems: so-called degree splitting problems. These problems come in two varieties: coloring problems where the edges of a graph have to be colored with 2 colors and orientation problems where each edge needs to be oriented. For an exact classification, it is most natural to consider the Δ-regular case (for Δ = O(1)), where we obtain the following results. - We exactly characterize the complexity of problems where the edges need to be colored with two colors, say red and blue. We show that for every y ∈ {0,… ,Δ-1}, the problem of red-blue coloring the edges such that every node of degree Δ has either y or y+1 red edges has randomized complexity O(log log n) in general graphs of maximum degree Δ. Any other problem, i.e., any problem that does not allow two consecutive red degrees, is already known to have randomized complexity Ω(log n) even in Δ-regular trees. We note that a set of edges F such that every node has either y or y+1 incident edges in F is also known as a {y,y+1}-factor of a graph. - For edge orientations, we show that for any two r₁ and r₂ such that r₁,r₂ ≤ Δ/2 and r₁+r₂ ≥ Δ/2, there are randomized algorithms with round complexities O(log log n) in trees and Õ(log⁴log n) in general graphs to compute an edge orientation such that all nodes have outdegree r₁ ± O(√{ΔlogΔ}) or Δ-r₂ ± O(√{ΔlogΔ}). Further, there exists a constant c > 0 such that for any 0 ≤ r₁+r₂ ≤ Δ/2, the problem of computing an edge orientation in which all outdegrees are either at most r₁-c⋅ √{Δ} or at least Δ-r₂+c⋅√{Δ} has randomized complexity Ω(log n) even in Δ-regular trees. While our results are cleanest to state for the Δ-regular case, all our algorithms naturally generalize to nodes of any degree d < Δ in general graphs of maximum degree Δ. All our algorithms also naturally generalize to the unbounded degree case and they then have a randomized complexity of Õ(Δ) ⋅ log log n (resp. Õ(Δ ⋅log⁴log n) for orienting general graphs).
Cite as

Sebastian Brandt, Fabian Kuhn, and Zahra Parsaeian. On the Complexity of Distributed Edge Coloring and Orientation Problems. In 29th International Conference on Principles of Distributed Systems (OPODIS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 361, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{brandt_et_al:LIPIcs.OPODIS.2025.25,
  author =	{Brandt, Sebastian and Kuhn, Fabian and Parsaeian, Zahra},
  title =	{{On the Complexity of Distributed Edge Coloring and Orientation Problems}},
  booktitle =	{29th International Conference on Principles of Distributed Systems (OPODIS 2025)},
  pages =	{25:1--25:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-409-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{361},
  editor =	{Arusoaie, Andrei and Onica, Emanuel and Spear, Michael and Tucci-Piergiovanni, Sara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2025.25},
  URN =		{urn:nbn:de:0030-drops-251982},
  doi =		{10.4230/LIPIcs.OPODIS.2025.25},
  annote =	{Keywords: LCL problems, binary labeling problems, degree splitting}
}
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.ESA.2025.39
Going Beyond Surfaces in Diameter Approximation

Authors: Michał Włodarczyk

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

Abstract
Calculating the diameter of an undirected graph requires quadratic running time under the Strong Exponential Time Hypothesis and this barrier works even against any approximation better than 3/2. For planar graphs with positive edge weights, there are known (1+ε)-approximation algorithms with running time poly(1/ε, log n)⋅ n. However, these algorithms rely on shortest path separators and this technique falls short to yield efficient algorithms beyond graphs of bounded genus. In this work we depart from embedding-based arguments and obtain diameter approximations relying on VC set systems and the local treewidth property. We present two orthogonal extensions of the planar case by giving (1+ε)-approximation algorithms with the following running times: - 𝒪_h((1/ε)^𝒪(h) ⋅ nlog² n)-time algorithm for graphs excluding an apex graph of size h as a minor, - 𝒪_d((1/ε)^𝒪(d) ⋅ nlog² n)-time algorithm for the class of d-apex graphs. As a stepping stone, we obtain efficient (1+ε)-approximate distance oracles for graphs excluding an apex graph of size h as a minor. Our oracle has preprocessing time 𝒪_h((1/ε)⁸⋅ nlog nlog W) and query time 𝒪_h((1/ε)²⋅log n log W), where W is the metric stretch. Such oracles have been so far only known for bounded genus graphs. All our algorithms are deterministic.
Cite as

Michał Włodarczyk. Going Beyond Surfaces in Diameter Approximation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{wlodarczyk:LIPIcs.ESA.2025.39,
  author =	{W{\l}odarczyk, Micha{\l}},
  title =	{{Going Beyond Surfaces in Diameter Approximation}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{39:1--39:19},
  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.2025.39},
  URN =		{urn:nbn:de:0030-drops-245076},
  doi =		{10.4230/LIPIcs.ESA.2025.39},
  annote =	{Keywords: diameter, approximation, distance oracles, graph minors, treewidth}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.12
Testing Whether a Subgraph Is Convex or Isometric

Authors: Sergio Cabello

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

Abstract
We consider the following two algorithmic problems: given a graph G and a subgraph H ⊆ G, decide whether H is an isometric or a geodesically convex subgraph of G. It is relatively easy to see that the problems can be solved by computing the distances between all pairs of vertices. We provide a conditional lower bound showing that, for sparse graphs with n vertices and Θ(n) edges, we cannot expect to solve the problem in O(n^{2-ε}) time for any constant ε > 0. We also show that the problem can be solved in subquadratic time for planar graphs and in near-linear time for graphs of bounded treewidth. Finally, we provide a near-linear time algorithm for the setting where G is a plane graph and H is defined by a few cycles in G.
Cite as

Sergio Cabello. Testing Whether a Subgraph Is Convex or Isometric. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cabello:LIPIcs.WADS.2025.12,
  author =	{Cabello, Sergio},
  title =	{{Testing Whether a Subgraph Is Convex or Isometric}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{12:1--12:16},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-242439},
  doi =		{10.4230/LIPIcs.WADS.2025.12},
  annote =	{Keywords: convex subgraph, isometric subgraph, plane graph}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.109
Faster Diameter Computation in Graphs of Bounded Euler Genus

Authors: Kacper Kluk, Marcin Pilipczuk, Michał Pilipczuk, and Giannos Stamoulis

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

Abstract
We show that for any fixed integer k ⩾ 0, there exists an algorithm that computes the diameter and the eccentricies of all vertices of an input unweighted, undirected n-vertex graph of Euler genus at most k in time 𝒪_k(n^{2-1/25}). Furthermore, for the more general class of graphs that can be constructed by clique-sums from graphs that are of Euler genus at most k after deletion of at most k vertices, we show an algorithm for the same task that achieves the running time bound 𝒪_k(n^{2-1/356} log^{6k} n). Up to today, the only known subquadratic algorithms for computing the diameter in those graph classes are that of [Ducoffe, Habib, Viennot; SICOMP 2022], [Le, Wulff-Nilsen; SODA 2024], and [Duraj, Konieczny, Potępa; ESA 2024]. These algorithms work in the more general setting of K_h-minor-free graphs, but the running time bound is 𝒪_h(n^{2-c_h}) for some constant c_h > 0 depending on h. That is, our savings in the exponent of the polynomial function of n, as compared to the naive quadratic algorithm, are independent of the parameter k. The main technical ingredient of our work is an improved bound on the number of distance profiles, as defined in [Le, Wulff-Nilsen; SODA 2024], in graphs of bounded Euler genus.
Cite as

Kacper Kluk, Marcin Pilipczuk, Michał Pilipczuk, and Giannos Stamoulis. Faster Diameter Computation in Graphs of Bounded Euler Genus. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 109:1-109:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kluk_et_al:LIPIcs.ICALP.2025.109,
  author =	{Kluk, Kacper and Pilipczuk, Marcin and Pilipczuk, Micha{\l} and Stamoulis, Giannos},
  title =	{{Faster Diameter Computation in Graphs of Bounded Euler Genus}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{109:1--109:19},
  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.2025.109},
  URN =		{urn:nbn:de:0030-drops-234869},
  doi =		{10.4230/LIPIcs.ICALP.2025.109},
  annote =	{Keywords: Diameter, eccentricity, subquadratic algorithms, surface-embeddable graphs}
}
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.SEA.2024.8
Practical Computation of Graph VC-Dimension

Authors: David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
For any set system ℋ = (V,ℛ), ℛ ⊆ 2^V, a subset S ⊆ V is called shattered if every S' ⊆ S results from the intersection of S with some set in ℛ. The VC-dimension of ℋ is the size of a largest shattered set in V. In this paper, we focus on the problem of computing the VC-dimension of graphs. In particular, given a graph G = (V,E), the VC-dimension of G is defined as the VC-dimension of (V, N), where N contains each subset of V that can be obtained as the closed neighborhood of some vertex v ∈ V in G. Our main contribution is an algorithm for computing the VC-dimension of any graph, whose effectiveness is shown through experiments on various types of practical graphs, including graphs with millions of vertices. A key aspect of its efficiency resides in the fact that practical graphs have small VC-dimension, up to 8 in our experiments. As a side-product, we present several new bounds relating the graph VC-dimension to other classical graph theoretical notions. We also establish the W[1]-hardness of the graph VC-dimension problem by extending a previous result for arbitrary set systems.
Cite as

David Coudert, Mónika Csikós, Guillaume Ducoffe, and Laurent Viennot. Practical Computation of Graph VC-Dimension. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{coudert_et_al:LIPIcs.SEA.2024.8,
  author =	{Coudert, David and Csik\'{o}s, M\'{o}nika and Ducoffe, Guillaume and Viennot, Laurent},
  title =	{{Practical Computation of Graph VC-Dimension}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.8},
  URN =		{urn:nbn:de:0030-drops-203731},
  doi =		{10.4230/LIPIcs.SEA.2024.8},
  annote =	{Keywords: VC-dimension, graph, algorithm}
}
Document
DOI: 10.4230/LIPIcs.STACS.2024.13
Temporalizing Digraphs via Linear-Size Balanced Bi-Trees

Authors: Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)

Abstract
In a directed graph D on vertex set v₁,… ,v_n, a forward arc is an arc v_iv_j where i < j. A pair v_i,v_j is forward connected if there is a directed path from v_i to v_j consisting of forward arcs. In the Forward Connected Pairs Problem (FCPP), the input is a strongly connected digraph D, and the output is the maximum number of forward connected pairs in some vertex enumeration of D. We show that FCPP is in APX, as one can efficiently enumerate the vertices of D in order to achieve a quadratic number of forward connected pairs. For this, we construct a linear size balanced bi-tree T (an out-branching and an in-branching with same size and same root which are vertex disjoint in the sense that they share no vertex apart from their common root). The existence of such a T was left as an open problem (Brunelli, Crescenzi, Viennot, Networks 2023) motivated by the study of temporal paths in temporal networks. More precisely, T can be constructed in quadratic time (in the number of vertices) and has size at least n/3. The algorithm involves a particular depth-first search tree (Left-DFS) of independent interest, and shows that every strongly connected directed graph has a balanced separator which is a circuit. Remarkably, in the request version RFCPP of FCPP, where the input is a strong digraph D and a set of requests R consisting of pairs {x_i,y_i}, there is no constant c > 0 such that one can always find an enumeration realizing c.|R| forward connected pairs {x_i,y_i} (in either direction).
Cite as

Stéphane Bessy, Stéphan Thomassé, and Laurent Viennot. Temporalizing Digraphs via Linear-Size Balanced Bi-Trees. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 13:1-13:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bessy_et_al:LIPIcs.STACS.2024.13,
  author =	{Bessy, St\'{e}phane and Thomass\'{e}, St\'{e}phan and Viennot, Laurent},
  title =	{{Temporalizing Digraphs via Linear-Size Balanced Bi-Trees}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{13:1--13:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.13},
  URN =		{urn:nbn:de:0030-drops-197235},
  doi =		{10.4230/LIPIcs.STACS.2024.13},
  annote =	{Keywords: digraph, temporal graph, temporalization, bi-tree, #1\{in-branching, out-branching, in-tree, out-tree\}, forward connected pairs, left-maximal DFS}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.35
Collective Tree Exploration via Potential Function Method

Authors: Romain Cosson and Laurent Massoulié

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
We study the problem of collective tree exploration (CTE) in which a team of k agents is tasked to traverse all the edges of an unknown tree as fast as possible, assuming complete communication between the agents [FGKP06]. In this paper, we present an algorithm performing collective tree exploration in 2n/k+𝒪(kD) rounds, where n is the number of nodes in the tree, and D is the tree depth. This leads to a competitive ratio of 𝒪(√k), the first polynomial improvement over the 𝒪(k) ratio of depth-first search. Our analysis holds for an asynchronous generalization of collective tree exploration. It relies on a game with robots at the leaves of a continuously growing tree extending the "tree-mining game" of [C23] and resembling the "evolving tree game" of [BCR22]. Another surprising consequence of our results is the existence of algorithms {𝒜_k}_{k ∈ ℕ} for layered tree traversal (LTT) with cost at most 2L/k+𝒪(kD), where L is the sum of all edge lengths. For the case of layered trees of width w and unit edge lengths, our guarantee is thus in 𝒪(√wD).
Cite as

Romain Cosson and Laurent Massoulié. Collective Tree Exploration via Potential Function Method. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 35:1-35:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cosson_et_al:LIPIcs.ITCS.2024.35,
  author =	{Cosson, Romain and Massouli\'{e}, Laurent},
  title =	{{Collective Tree Exploration via Potential Function Method}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{35:1--35:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.35},
  URN =		{urn:nbn:de:0030-drops-195638},
  doi =		{10.4230/LIPIcs.ITCS.2024.35},
  annote =	{Keywords: collective exploration, online algorithms, evolving tree, competitive analysis}
}
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