25 Search Results for "Kammer, Frank"

Document
DOI: 10.4230/LIPIcs.STACS.2026.32
Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid

Authors: Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter

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

Abstract
Research in explorable uncertainty addresses combinatorial optimization problems where there is partial information about the values of numeric input parameters, and exact values of these parameters can be determined by performing costly queries. The goal is to design an adaptive query strategy that minimizes the query cost incurred in computing an optimal solution. Solving such problems generally requires that we be able to solve the associated verification problem: given the answers to all queries in advance, find a minimum-cost set of queries that certifies an optimal solution to the combinatorial optimization problem. We present a polynomial-time algorithm for verifying a minimum-weight basis of a matroid, where each weight lies in a given uncertainty area. These areas may be finite sets, real intervals, or unions of open and closed intervals, strictly generalizing previous work by Erlebach and Hoffman which only handled the special case of open intervals. Our algorithm introduces new techniques to address the resulting challenges. Verification problems are of particular importance in the area of explorable uncertainty, as the structural insights and techniques used to solve the verification problem often heavily influence work on the corresponding online problem and its stochastic variant. In our case, we use structural results from the verification problem to give a best-possible algorithm for a promise variant of the corresponding adaptive online problem. Finally, we show that our algorithms can be applied to two learning-augmented variants of the minimum-weight basis problem under explorable uncertainty.
Cite as

Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter. Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{diwan_et_al:LIPIcs.STACS.2026.32,
  author =	{Diwan, Haya and Hellerstein, Lisa and Megow, Nicole and Schl\"{o}ter, Jens},
  title =	{{Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{32:1--32:20},
  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.2026.32},
  URN =		{urn:nbn:de:0030-drops-255216},
  doi =		{10.4230/LIPIcs.STACS.2026.32},
  annote =	{Keywords: Matroid verification, minimum-weight basis, query strategy, uncertainty matroid, explorable uncertainty}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.21
A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs

Authors: Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden

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

Abstract
We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithm due to Bouchitté and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vertices.
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Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden. A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grigoriev_et_al:LIPIcs.IPEC.2025.21,
  author =	{Grigoriev, Alexander and Kobayashi, Yasuaki and Tamaki, Hisao and van der Zanden, Tom C.},
  title =	{{A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.21},
  URN =		{urn:nbn:de:0030-drops-251530},
  doi =		{10.4230/LIPIcs.IPEC.2025.21},
  annote =	{Keywords: potential maximal cliques, treewidth, planar graphs, triconnected planar graphs, polynomial delay generation}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2025.29
Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings

Authors: Michael Elberfeld, Frank Kammer, and Johannes Meintrup

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

Abstract
We call a graph G separable if a balanced separator can be computed for G of size O(n^ε) with ε < 1. Many real-world graphs are separable such as graphs of bounded genus, graphs of constant treewidth, and graphs excluding a fixed minor. In particular, the well-known planar graphs are separable. We present a succinct encoding of separable graphs G such that, after the encoding is computed, any number of depth-first searches (DFS) can be performed from any given start vertex, each in o(n) time and o(n) bits in the word RAM model. After the execution of a DFS, the succinct encoding of G is augmented such that the DFS tree is encoded inside the encoding while maintaining succinctness. Afterward, the encoding provides common DFS-related queries in constant time. These queries include queries such as lowest-common ancestor of two given vertices in the DFS tree or queries that output the lowpoint of a given vertex in the DFS tree. Furthermore, for planar graphs, we show that the succinct encoding can be computed in O(n) bits and expected linear time, and a compact variant can be constructed in O(n) time and bits. For other separable graph classes 𝒢 the runtime and space usage depends on the specific algorithms used to find balanced separators in graphs of 𝒢.
Cite as

Michael Elberfeld, Frank Kammer, and Johannes Meintrup. Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 29:1-29:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{elberfeld_et_al:LIPIcs.ISAAC.2025.29,
  author =	{Elberfeld, Michael and Kammer, Frank and Meintrup, Johannes},
  title =	{{Space-Efficient Depth-First Search via Augmented Succinct Graph Encodings}},
  booktitle =	{36th International Symposium on Algorithms and Computation (ISAAC 2025)},
  pages =	{29:1--29:16},
  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.2025.29},
  URN =		{urn:nbn:de:0030-drops-249379},
  doi =		{10.4230/LIPIcs.ISAAC.2025.29},
  annote =	{Keywords: Depth-First Search, Succinct, Space Efficient, Separable Graphs, Planar Graphs, Table Lookup, r-Division}
}
Document
DOI: 10.4230/LIPIcs.GD.2025.28
Treewidth of Outer k-Planar Graphs

Authors: Rafał Pyzik

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
Treewidth is an important structural graph parameter that quantifies how closely a graph resembles a tree-like structure. It has applications in many algorithmic and combinatorial problems. In this paper, we study the treewidth of outer k-planar graphs, that is, graphs admitting a convex drawing (a straight-line drawing where all vertices lie on a circle) in which every edge crosses at most k other edges. We also consider the more general class of outer min-k-planar graphs, which are graphs admitting a convex drawing where for every crossing of two edges at least one of these edges is crossed at most k times. Firman, Gutowski, Kryven, Okada and Wolff [GD 2024] proved that every outer k-planar graph has treewidth at most 1.5k+2 and provided a lower bound of k+2 for even k. We establish a lower bound of 1.5k+0.5 for every odd k. Additionally, they showed that every outer min-k-planar graph has treewidth at most 3k+1. We improve this upper bound to 3⋅⌊k/2⌋+4. Our approach also allows us to upper bound the separation number, a parameter closely related to treewidth, of outer min-k-planar graphs by 2⋅⌊k/2⌋+4. This improves upon the previous bound of 2k+1 and achieves a bound with an optimal multiplicative constant.
Cite as

Rafał Pyzik. Treewidth of Outer k-Planar Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pyzik:LIPIcs.GD.2025.28,
  author =	{Pyzik, Rafa{\l}},
  title =	{{Treewidth of Outer k-Planar Graphs}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.28},
  URN =		{urn:nbn:de:0030-drops-250141},
  doi =		{10.4230/LIPIcs.GD.2025.28},
  annote =	{Keywords: treewidth, outer k-planar graphs, outer min-k-planar graphs, separation number}
}
Document
DOI: 10.4230/LIPIcs.DISC.2025.41
Natural Calamities Demand More Rescuers: Exploring Connectivity Time Dynamic Graphs

Authors: Ashish Saxena and Kaushik Mondal

Published in: LIPIcs, Volume 356, 39th International Symposium on Distributed Computing (DISC 2025)

Abstract
We study the exploration problem by mobile agents in Connectivity Time dynamic graphs. The Connectivity Time model was introduced by Michail et al. [JPDC 2014] and is arguably one of the weakest dynamic graph connectivity models. We prove that exploration is impossible in such graphs using ((n-1)(n-2))/2 mobile agents starting from an arbitrary initial configuration, even when agents have full knowledge of system parameters, global communication, full visibility, and infinite memory. We then present an exploration algorithm that uses ((n-1)(n-2))/2 + 1 agents equipped with global communication, 1-hop visibility and O(log n) memory.
Cite as

Ashish Saxena and Kaushik Mondal. Natural Calamities Demand More Rescuers: Exploring Connectivity Time Dynamic Graphs. In 39th International Symposium on Distributed Computing (DISC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 356, pp. 41:1-41:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{saxena_et_al:LIPIcs.DISC.2025.41,
  author =	{Saxena, Ashish and Mondal, Kaushik},
  title =	{{Natural Calamities Demand More Rescuers: Exploring Connectivity Time Dynamic Graphs}},
  booktitle =	{39th International Symposium on Distributed Computing (DISC 2025)},
  pages =	{41:1--41:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-402-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{356},
  editor =	{Kowalski, Dariusz R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2025.41},
  URN =		{urn:nbn:de:0030-drops-248585},
  doi =		{10.4230/LIPIcs.DISC.2025.41},
  annote =	{Keywords: Mobile agents, Anonymous graphs, Exploration, Dynamic graphs, Deterministic algorithm}
}
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.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
DOI: 10.4230/LIPIcs.SEA.2025.6
Planar Network Diversion

Authors: Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, and Steinar Simonnes

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Network Diversion is a graph problem that has been extensively studied in both the network-analysis and operations-research communities as a measure of how robust a network is against adversarial disruption. In Network Diversion we want to enforce all s-t-paths through a specific edge b by removing edges from G. This problem is especially well motivated in transportation networks, which are often assumed to be planar. Motivated by this and recent theoretical advances for Network Diversion on planar input graphs, we develop a fast O(n log n) time algorithm and present a practical implementation of this algorithm that is able to solve instances with millions of vertices in a matter of seconds.
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Matthias Bentert, Pål Grønås Drange, Fedor V. Fomin, and Steinar Simonnes. Planar Network Diversion. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bentert_et_al:LIPIcs.SEA.2025.6,
  author =	{Bentert, Matthias and Drange, P\r{a}l Gr{\o}n\r{a}s and Fomin, Fedor V. and Simonnes, Steinar},
  title =	{{Planar Network Diversion}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.6},
  URN =		{urn:nbn:de:0030-drops-232448},
  doi =		{10.4230/LIPIcs.SEA.2025.6},
  annote =	{Keywords: Minimal cuts, Bridges, Network interdiction, Algorithm engineering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.8
Identifying Approximate Minimizers Under Stochastic Uncertainity

Authors: Hessa Al-Thani and Viswanath Nagarajan

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

Abstract
We study a fundamental stochastic selection problem involving n independent random variables, each of which can be queried at some cost. Given a tolerance level δ, the goal is to find a δ-approximately minimum (or maximum) value over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a δ-minimum value or a δ-minimizer. When all query costs are uniform, we provide a 4-approximation algorithm for both variants. When query costs are non-uniform, we provide a 5.83-approximation algorithm for the δ-minimum value and a 7.47-approximation for the δ-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding "adaptivity" gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties.
Cite as

Hessa Al-Thani and Viswanath Nagarajan. Identifying Approximate Minimizers Under Stochastic Uncertainity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{althani_et_al:LIPIcs.ICALP.2025.8,
  author =	{Al-Thani, Hessa and Nagarajan, Viswanath},
  title =	{{Identifying Approximate Minimizers Under Stochastic Uncertainity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{8:1--8:18},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-233854},
  doi =		{10.4230/LIPIcs.ICALP.2025.8},
  annote =	{Keywords: Approximation algorithms, stochastic optimization, selection problem}
}
Document
DOI: 10.4230/LIPIcs.SAND.2025.12
Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs

Authors: Kamran Ayoubi and Lata Narayanan

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

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

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

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@InProceedings{ayoubi_et_al:LIPIcs.SAND.2025.12,
  author =	{Ayoubi, Kamran and Narayanan, Lata},
  title =	{{Restless Exploration and Token Dissemination in Vertex-Permuted Temporal Graphs}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.12},
  URN =		{urn:nbn:de:0030-drops-230658},
  doi =		{10.4230/LIPIcs.SAND.2025.12},
  annote =	{Keywords: Temporal graphs, Vertex permuted graphs, Restless exploration, Periodic graphs, Token dissemination}
}
Document
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
Brief Announcement
DOI: 10.4230/LIPIcs.SAND.2025.18
Brief Announcement: The Shortest Temporal Exploration Problem

Authors: Stefan Balev, Éric Sanlaville, and Antoine Toullalan

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

Abstract
A temporal graph is a graph for which the edge set can change from one time step to the next. This paper considers undirected temporal graphs defined over L time steps and connected at each time step. We study the Shortest Temporal Exploration Problem (STEXP) that, given the evolution of the graph, asks for a temporal walk that starts at a given vertex, moves over at most one edge at each time step, visits all the vertices, takes at most L time steps and traverses the smallest number of edges. We prove that every constantly connected temporal graph with n vertices can be explored with O(n^{1.5}) edges traversed if L is O(n^{3.5}) time steps. This result improves the upper bound of O(n²) edges when L is Ω(n²). Moreover, we study the case where the graph has a diameter bounded by a parameter k at each time step and we prove that there exists an exploration which takes O(kn²) time steps and traverses O(kn) edges. Finally, the case where the underlying graph is a cycle is studied and tight linear bounds are provided on the number of edges traversed in the worst-case.
Cite as

Stefan Balev, Éric Sanlaville, and Antoine Toullalan. Brief Announcement: The Shortest Temporal Exploration Problem. In 4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 330, pp. 18:1-18:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balev_et_al:LIPIcs.SAND.2025.18,
  author =	{Balev, Stefan and Sanlaville, \'{E}ric and Toullalan, Antoine},
  title =	{{Brief Announcement: The Shortest Temporal Exploration Problem}},
  booktitle =	{4th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2025)},
  pages =	{18:1--18:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-368-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{330},
  editor =	{Meeks, Kitty and Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2025.18},
  URN =		{urn:nbn:de:0030-drops-230716},
  doi =		{10.4230/LIPIcs.SAND.2025.18},
  annote =	{Keywords: Graph Theory, Temporal Graph, Temporal Graph Exploration}
}
Document
Academic Track
DOI: 10.4230/OASIcs.SAIA.2024.15
AI Assessment in Practice: Implementing a Certification Scheme for AI Trustworthiness (Academic Track)

Authors: Carmen Frischknecht-Gruber, Philipp Denzel, Monika Reif, Yann Billeter, Stefan Brunner, Oliver Forster, Frank-Peter Schilling, Joanna Weng, and Ricardo Chavarriaga

Published in: OASIcs, Volume 126, Symposium on Scaling AI Assessments (SAIA 2024)

Abstract
The trustworthiness of artificial intelligence systems is crucial for their widespread adoption and for avoiding negative impacts on society and the environment. This paper focuses on implementing a comprehensive certification scheme developed through a collaborative academic-industry project. The scheme provides practical guidelines for assessing and certifying the trustworthiness of AI-based systems. The implementation of the scheme leverages aspects from Machine Learning Operations and the requirements management tool Jira to ensure continuous compliance and efficient lifecycle management. The integration of various high-level frameworks, scientific methods, and metrics supports the systematic evaluation of key aspects of trustworthiness, such as reliability, transparency, safety and security, and human oversight. These methods and metrics were tested and assessed on real-world use cases to dependably verify means of compliance with regulatory requirements and evaluate criteria and detailed objectives for each of these key aspects. Thus, this certification framework bridges the gap between ethical guidelines and practical application, ensuring the safe and effective deployment of AI technologies.
Cite as

Carmen Frischknecht-Gruber, Philipp Denzel, Monika Reif, Yann Billeter, Stefan Brunner, Oliver Forster, Frank-Peter Schilling, Joanna Weng, and Ricardo Chavarriaga. AI Assessment in Practice: Implementing a Certification Scheme for AI Trustworthiness (Academic Track). In Symposium on Scaling AI Assessments (SAIA 2024). Open Access Series in Informatics (OASIcs), Volume 126, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{frischknechtgruber_et_al:OASIcs.SAIA.2024.15,
  author =	{Frischknecht-Gruber, Carmen and Denzel, Philipp and Reif, Monika and Billeter, Yann and Brunner, Stefan and Forster, Oliver and Schilling, Frank-Peter and Weng, Joanna and Chavarriaga, Ricardo},
  title =	{{AI Assessment in Practice: Implementing a Certification Scheme for AI Trustworthiness}},
  booktitle =	{Symposium on Scaling AI Assessments (SAIA 2024)},
  pages =	{15:1--15:18},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-357-7},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{126},
  editor =	{G\"{o}rge, Rebekka and Haedecke, Elena and Poretschkin, Maximilian and Schmitz, Anna},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SAIA.2024.15},
  URN =		{urn:nbn:de:0030-drops-227554},
  doi =		{10.4230/OASIcs.SAIA.2024.15},
  annote =	{Keywords: AI Assessment, Certification Scheme, Artificial Intelligence, Trustworthiness of AI systems, AI Standards, AI Safety}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.55
Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous

Authors: Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Temporal graphs are dynamic graphs where the edge set can change in each time step, while the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been widely studied. In this paper, we extend the concept of graph automorphisms from static graphs to temporal graphs and show for the first time that symmetries enable faster exploration: We prove that a connected temporal graph with n vertices and orbit number r (i.e., r is the number of automorphism orbits) can be explored in O(r n^{1+ε}) time steps, for any fixed ε > 0. For r = O(n^c) for constant c < 1, this is a significant improvement over the known tight worst-case bound of Θ(n²) time steps for arbitrary connected temporal graphs. We also give two lower bounds for temporal exploration, showing that Ω(n log n) time steps are required for some inputs with r = O(1) and that Ω(rn) time steps are required for some inputs for any r with 1 ≤ r ≤ n. Moreover, we show that the techniques we develop for fast exploration can be used to derive the following result for rendezvous: Two agents with different programs and without communication ability are placed by an adversary at arbitrary vertices and given full information about the connected temporal graph, except that they do not have consistent vertex labels. Then the two agents can meet at a common vertex after O(n^{1+ε}) time steps, for any constant ε > 0. For some connected temporal graphs with the orbit number being a constant, we also present a complementary lower bound of Ω(nlog n) time steps.
Cite as

Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.. Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dogeas_et_al:LIPIcs.ICALP.2024.55,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Kammer, Frank and Meintrup, Johannes and Moses Jr., William K.},
  title =	{{Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.55},
  URN =		{urn:nbn:de:0030-drops-201989},
  doi =		{10.4230/LIPIcs.ICALP.2024.55},
  annote =	{Keywords: dynamic graphs, parameterized algorithms, algorithmic graph theory, graph automorphism, orbit number}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAND.2024.1
Exploration and Rendezvous in Temporal Graphs (Invited Talk)

Authors: Thomas Erlebach

Published in: LIPIcs, Volume 292, 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)

Abstract
Given a temporal graph 𝒢 and a start vertex v in 𝒢, the temporal exploration problem (TEXP) is the problem of determining a temporal walk that starts at v and visits all vertices of 𝒢, with the objective of minimizing the time when the last unvisited vertex is reached. Studies have investigated the (parameterized) complexity and approximability of TEXP and the worst-case number of time steps required to complete an exploration. While many upper and lower bounds have been obtained for different settings, there are still some large gaps that pose interesting open problems. In this talk, we will give an overview of known results and techniques as well as open problems. Furthermore, we will discuss recent results (from joint work with Konstantinos Dogeas, Frank Kammer, Johannes Meintrup, and William K. Moses Jr) about exploiting symmetries in temporal graphs to get faster exploration. We view the number of automorphism orbits of the temporal graph as a new parameter, termed the orbit number, that may also be useful in other contexts. Finally, we show how a subroutine for quickly exploring a single orbit of the graph can be exploited to solve a certain rendezvous problem with two agents using a near-linear number of time steps in every always-connected temporal graph.
Cite as

Thomas Erlebach. Exploration and Rendezvous in Temporal Graphs (Invited Talk). In 3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 292, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{erlebach:LIPIcs.SAND.2024.1,
  author =	{Erlebach, Thomas},
  title =	{{Exploration and Rendezvous in Temporal Graphs}},
  booktitle =	{3rd Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2024)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-315-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{292},
  editor =	{Casteigts, Arnaud and Kuhn, Fabian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2024.1},
  URN =		{urn:nbn:de:0030-drops-198797},
  doi =		{10.4230/LIPIcs.SAND.2024.1},
  annote =	{Keywords: Dynamic graphs, parameterized algorithms, orbit number}
}
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