59 Search Results for "M�ller, Sebastian"


Document
Treewidth Is NP-Complete on Cubic Graphs

Authors: Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
In this paper, we show that Treewidth is NP-complete for cubic graphs, thereby improving the result by Bodlaender and Thilikos from 1997 that Treewidth is NP-complete on graphs with maximum degree at most 9. We add a new and simpler proof of the NP-completeness of treewidth, and show that Treewidth remains NP-complete on subcubic induced subgraphs of the infinite 3-dimensional grid.

Cite as

Hans L. Bodlaender, Édouard Bonnet, Lars Jaffke, Dušan Knop, Paloma T. Lima, Martin Milanič, Sebastian Ordyniak, Sukanya Pandey, and Ondřej Suchý. Treewidth Is NP-Complete on Cubic Graphs. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bodlaender_et_al:LIPIcs.IPEC.2023.7,
  author =	{Bodlaender, Hans L. and Bonnet, \'{E}douard and Jaffke, Lars and Knop, Du\v{s}an and Lima, Paloma T. and Milani\v{c}, Martin and Ordyniak, Sebastian and Pandey, Sukanya and Such\'{y}, Ond\v{r}ej},
  title =	{{Treewidth Is NP-Complete on Cubic Graphs}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{7:1--7:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.7},
  URN =		{urn:nbn:de:0030-drops-194263},
  doi =		{10.4230/LIPIcs.IPEC.2023.7},
  annote =	{Keywords: Treewidth, cubic graphs, degree, NP-completeness}
}
Document
Parameterized Complexity Classification for Interval Constraints

Authors: Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, Marcin Pilipczuk, and Roohani Sharma

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
Constraint satisfaction problems form a nicely behaved class of problems that lends itself to complexity classification results. From the point of view of parameterized complexity, a natural task is to classify the parameterized complexity of MinCSP problems parameterized by the number of unsatisfied constraints. In other words, we ask whether we can delete at most k constraints, where k is the parameter, to get a satisfiable instance. In this work, we take a step towards classifying the parameterized complexity for an important infinite-domain CSP: Allen’s interval algebra (IA). This CSP has closed intervals with rational endpoints as domain values and employs a set A of 13 basic comparison relations such as "precedes" or "during" for relating intervals. IA is a highly influential and well-studied formalism within AI and qualitative reasoning that has numerous applications in, for instance, planning, natural language processing and molecular biology. We provide an FPT vs. W[1]-hard dichotomy for MinCSP(Γ) for all Γ ⊆ A. IA is sometimes extended with unions of the relations in A or first-order definable relations over A, but extending our results to these cases would require first solving the parameterized complexity of Directed Symmetric Multicut, which is a notorious open problem. Already in this limited setting, we uncover connections to new variants of graph cut and separation problems. This includes hardness proofs for simultaneous cuts or feedback arc set problems in directed graphs, as well as new tractable cases with algorithms based on the recently introduced flow augmentation technique. Given the intractability of MinCSP(A) in general, we then consider (parameterized) approximation algorithms. We first show that MinCSP(A) cannot be polynomial-time approximated within any constant factor and continue by presenting a factor-2 fpt-approximation algorithm. Once again, this algorithm has its roots in flow augmentation.

Cite as

Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, Marcin Pilipczuk, and Roohani Sharma. Parameterized Complexity Classification for Interval Constraints. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dabrowski_et_al:LIPIcs.IPEC.2023.11,
  author =	{Dabrowski, Konrad K. and Jonsson, Peter and Ordyniak, Sebastian and Osipov, George and Pilipczuk, Marcin and Sharma, Roohani},
  title =	{{Parameterized Complexity Classification for Interval Constraints}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.11},
  URN =		{urn:nbn:de:0030-drops-194306},
  doi =		{10.4230/LIPIcs.IPEC.2023.11},
  annote =	{Keywords: (minimum) constraint satisfaction problem, Allen’s interval algebra, parameterized complexity, cut problems}
}
Document
From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem

Authors: Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formulated as classical graph problems on induced subgraphs of powers of partially-defined hypercubes. In this paper, we follow up on this recent direction by investigating the Independent Set problem on this graph class, which has been studied in the data science setting under the name Diversity. We obtain a comprehensive picture of the problem’s parameterized complexity and establish its fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube. Given that several such FO-definable problems have been shown to be fixed-parameter tractable on the considered graph class, one may ask whether fixed-parameter tractability could be extended to capture all FO-definable problems. We answer this question in the negative by showing that FO model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general graphs.

Cite as

Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider. From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{eiben_et_al:LIPIcs.IPEC.2023.16,
  author =	{Eiben, Eduard and Ganian, Robert and Kanj, Iyad and Ordyniak, Sebastian and Szeider, Stefan},
  title =	{{From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{16:1--16:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.16},
  URN =		{urn:nbn:de:0030-drops-194357},
  doi =		{10.4230/LIPIcs.IPEC.2023.16},
  annote =	{Keywords: Independent Set, Powers of Hypercubes, Diversity, Parameterized Complexity, Incomplete Data}
}
Document
Dynamic Programming on Bipartite Tree Decompositions

Authors: Lars Jaffke, Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
We revisit a graph width parameter that we dub bipartite treewidth, along with its associated graph decomposition that we call bipartite tree decomposition. Bipartite treewidth can be seen as a common generalization of treewidth and the odd cycle transversal number. Intuitively, a bipartite tree decomposition is a tree decomposition whose bags induce almost bipartite graphs and whose adhesions contain at most one vertex from the bipartite part of any other bag, while the width of such decomposition measures how far the bags are from being bipartite. Adapted from a tree decomposition originally defined by Demaine, Hajiaghayi, and Kawarabayashi [SODA 2010] and explicitly defined by Tazari [Theor. Comput. Sci. 2012], bipartite treewidth appears to play a crucial role for solving problems related to odd-minors, which have recently attracted considerable attention. As a first step toward a theory for solving these problems efficiently, the main goal of this paper is to develop dynamic programming techniques to solve problems on graphs of small bipartite treewidth. For such graphs, we provide a number of para-NP-completeness results, FPT-algorithms, and XP-algorithms, as well as several open problems. In particular, we show that K_t-Subgraph-Cover, Weighted Vertex Cover/Independent Set, Odd Cycle Transversal, and Maximum Weighted Cut are FPT parameterized by bipartite treewidth. We also provide the following complexity dichotomy when H is a 2-connected graph, for each of the H-Subgraph-Packing, H-Induced-Packing, H-Scattered-Packing, and H-Odd-Minor-Packing problems: if H is bipartite, then the problem is para-NP-complete parameterized by bipartite treewidth while, if H is non-bipartite, then the problem is solvable in XP-time. Beyond bipartite treewidth, we define 1-ℋ-treewidth by replacing the bipartite graph class by any graph class ℋ. Most of the technology developed here also works for this more general parameter.

Cite as

Lars Jaffke, Laure Morelle, Ignasi Sau, and Dimitrios M. Thilikos. Dynamic Programming on Bipartite Tree Decompositions. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 26:1-26:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{jaffke_et_al:LIPIcs.IPEC.2023.26,
  author =	{Jaffke, Lars and Morelle, Laure and Sau, Ignasi and Thilikos, Dimitrios M.},
  title =	{{Dynamic Programming on Bipartite Tree Decompositions}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{26:1--26:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.26},
  URN =		{urn:nbn:de:0030-drops-194455},
  doi =		{10.4230/LIPIcs.IPEC.2023.26},
  annote =	{Keywords: tree decomposition, bipartite graphs, dynamic programming, odd-minors, packing, maximum cut, vertex cover, independent set, odd cycle transversal}
}
Document
PACE Solver Description
PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth

Authors: Max Bannach and Sebastian Berndt

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
This article is a report by the challenge organizers on the 8th Parameterized Algorithms and Computational Experiments Challenge (PACE 2023). As was common in previous iterations of the competition, this year’s iteration implemented an exact and heuristic track for a parameterized problem that has gained attention in the theory community. This year, the problem was to compute the twinwidth of a graph, a recently introduced width parameter that measures the similarity of a graph to a cograph. In the exact track, the competition participants were asked to develop an exact algorithm that can solve as many instances as possible from a benchmark set of 100 instances - with a time limit of 30 minutes per instance. The same task must be accomplished within 5 minutes in the heuristic track. However, the result in this track is not required to be optimal. As in previous iterations, the organizers handed out awards to the best solutions in both tracks and to the best student submissions. New this year is a dedicated theory award that appreciates new theoretical insights found by the participants during the development of their tools.

Cite as

Max Bannach and Sebastian Berndt. PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bannach_et_al:LIPIcs.IPEC.2023.35,
  author =	{Bannach, Max and Berndt, Sebastian},
  title =	{{PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.35},
  URN =		{urn:nbn:de:0030-drops-194548},
  doi =		{10.4230/LIPIcs.IPEC.2023.35},
  annote =	{Keywords: Twinwidth, Algorithm Engineering, FPT, Kernelization}
}
Document
New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines

Authors: Sebastian Berndt, Hauke Brinkop, Klaus Jansen, Matthias Mnich, and Tobias Stamm

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the minimum number of non-zero integer variables in an optimal solution. A hallmark result by Eisenbrand and Shmonin (Oper. Res. Lett. , 2006) shows that any feasible integer linear program (ILP) has a solution with support size s ≤ 2m⋅log(4mΔ), where m is the number of constraints, and Δ is the largest absolute coefficient in any constraint. Our main combinatorial result are improved support size bounds for ILPs. We show that any ILP has a solution with support size s ≤ m⋅(log(3A_max)+√{log(A_max)}), where A_max≔ ‖A‖₁ denotes the 1-norm of the constraint matrix A. Furthermore, we show support bounds in the linearized form s ≤ 2m⋅log(1.46 A_max). Our upper bounds also hold with A_max replaced by √mΔ, which improves on the previously best constants in the linearized form. Our main algorithmic result are the fastest known approximation schemes for fundamental scheduling problems, which use the improved support bounds as one ingredient. We design an efficient approximation scheme (EPTAS) for makespan minimization on uniformly related machines (Q||C_{max}). Our EPTAS yields a (1+ε)-approximation for Q||C_{max} on N jobs in time 2^𝒪(1/ε log³(1/ε)log(log(1/ε))) + 𝒪(N), which improves over the previously fastest algorithm by Jansen, Klein and Verschae (Math. Oper. Res., 2020) with run time 2^𝒪(1/ε log⁴(1/ε)) + N^𝒪(1). Arguably, our approximation scheme is also simpler than all previous EPTASes for Q||C_max, as we reduce the problem to a novel MILP formulation which greatly benefits from the small support.

Cite as

Sebastian Berndt, Hauke Brinkop, Klaus Jansen, Matthias Mnich, and Tobias Stamm. New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{berndt_et_al:LIPIcs.ISAAC.2023.13,
  author =	{Berndt, Sebastian and Brinkop, Hauke and Jansen, Klaus and Mnich, Matthias and Stamm, Tobias},
  title =	{{New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.13},
  URN =		{urn:nbn:de:0030-drops-193155},
  doi =		{10.4230/LIPIcs.ISAAC.2023.13},
  annote =	{Keywords: Integer programming, scheduling algorithms, uniformly related machines, makespan minimization}
}
Document
Funnelselect: Cache-Oblivious Multiple Selection

Authors: Gerth Stølting Brodal and Sebastian Wild

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We present the algorithm funnelselect, the first optimal randomized cache-oblivious algorithm for the multiple-selection problem. The algorithm takes as input an unsorted array of N elements and q query ranks r_1 < ⋯ < r_q, and returns in sorted order the q input elements of rank r_1, …, r_q, respectively. The algorithm uses expected and with high probability O(∑_{i = 1}^{q+1} Δ_i/B ⋅ log_{M/B} N/(Δ_i) + N/B) I/Os, where B is the external memory block size, M ≥ B^{1+ε} is the internal memory size, for some constant ε > 0, and Δ_i = r_i - r_{i-1} (assuming r_0 = 0 and r_{q+1} = N + 1). This is the best possible I/O bound in the cache-oblivious and external memory models. The result is achieved by reversing the computation of the cache-oblivious sorting algorithm funnelsort by Frigo, Leiserson, Prokop and Ramachandran [FOCS 1999], using randomly selected pivots for distributing elements, and pruning computations that with high probability are not expected to contain any query ranks.

Cite as

Gerth Stølting Brodal and Sebastian Wild. Funnelselect: Cache-Oblivious Multiple Selection. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 25:1-25:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{brodal_et_al:LIPIcs.ESA.2023.25,
  author =	{Brodal, Gerth St{\o}lting and Wild, Sebastian},
  title =	{{Funnelselect: Cache-Oblivious Multiple Selection}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{25:1--25:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.25},
  URN =		{urn:nbn:de:0030-drops-186789},
  doi =		{10.4230/LIPIcs.ESA.2023.25},
  annote =	{Keywords: Multiple selection, cache-oblivious algorithm, randomized algorithm, entropy bounds}
}
Document
Bootstrapping Dynamic Distance Oracles

Authors: Sebastian Forster, Gramoz Goranci, Yasamin Nazari, and Antonis Skarlatos

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Designing approximate all-pairs distance oracles in the fully dynamic setting is one of the central problems in dynamic graph algorithms. Despite extensive research on this topic, the first result breaking the O(√n) barrier on the update time for any non-trivial approximation was introduced only recently by Forster, Goranci and Henzinger [SODA'21] who achieved m^{1/ρ+o(1)} amortized update time with a O(log n)^{3ρ-2} factor in the approximation ratio, for any parameter ρ ≥ 1. In this paper, we give the first constant-stretch fully dynamic distance oracle with small polynomial update and query time. Prior work required either at least a poly-logarithmic approximation or much larger update time. Our result gives a more fine-grained trade-off between stretch and update time, for instance we can achieve constant stretch of O(1/(ρ²))^{4/ρ} in amortized update time Õ(n^{ρ}), and query time Õ(n^{ρ/8}) for any constant parameter 0 < ρ < 1. Our algorithm is randomized and assumes an oblivious adversary. A core technical idea underlying our construction is to design a black-box reduction from decremental approximate hub-labeling schemes to fully dynamic distance oracles, which may be of independent interest. We then apply this reduction repeatedly to an existing decremental algorithm to bootstrap our fully dynamic solution.

Cite as

Sebastian Forster, Gramoz Goranci, Yasamin Nazari, and Antonis Skarlatos. Bootstrapping Dynamic Distance Oracles. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 50:1-50:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{forster_et_al:LIPIcs.ESA.2023.50,
  author =	{Forster, Sebastian and Goranci, Gramoz and Nazari, Yasamin and Skarlatos, Antonis},
  title =	{{Bootstrapping Dynamic Distance Oracles}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{50:1--50:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.50},
  URN =		{urn:nbn:de:0030-drops-187031},
  doi =		{10.4230/LIPIcs.ESA.2023.50},
  annote =	{Keywords: Dynamic graph algorithms, Distance Oracles, Shortest Paths}
}
Document
Track A: Algorithms, Complexity and Games
Efficient Data Structures for Incremental Exact and Approximate Maximum Flow

Authors: Gramoz Goranci and Monika Henzinger

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
We show an (1+ε)-approximation algorithm for maintaining maximum s-t flow under m edge insertions in m^{1/2+o(1)} ε^{-1/2} amortized update time for directed, unweighted graphs. This constitutes the first sublinear dynamic maximum flow algorithm in general sparse graphs with arbitrarily good approximation guarantee. Furthermore we give an algorithm that maintains an exact maximum s-t flow under m edge insertions in an n-node graph in Õ(n^{5/2}) total update time. For sufficiently dense graphs, this gives to the first exact incremental algorithm with sub-linear amortized update time for maintaining maximum flows.

Cite as

Gramoz Goranci and Monika Henzinger. Efficient Data Structures for Incremental Exact and Approximate Maximum Flow. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 69:1-69:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{goranci_et_al:LIPIcs.ICALP.2023.69,
  author =	{Goranci, Gramoz and Henzinger, Monika},
  title =	{{Efficient Data Structures for Incremental Exact and Approximate Maximum Flow}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.69},
  URN =		{urn:nbn:de:0030-drops-181212},
  doi =		{10.4230/LIPIcs.ICALP.2023.69},
  annote =	{Keywords: dynamic graph algorithms, maximum flow, data structures}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes

Authors: Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they generalize notions such as nowhere denseness, bounded cliquewidth, and bounded twinwidth. Our main result is the - to the best of our knowledge first - purely combinatorial characterization of monadically stable classes of graphs, in terms of a property dubbed flip-flatness. A class C of graphs is flip-flat if for every fixed radius r, every sufficiently large set of vertices of a graph G ∈ C contains a large subset of vertices with mutual distance larger than r, where the distance is measured in some graph G' that can be obtained from G by performing a bounded number of flips that swap edges and non-edges within a subset of vertices. Flip-flatness generalizes the notion of uniform quasi-wideness, which characterizes nowhere dense classes and had a key impact on the combinatorial and algorithmic treatment of nowhere dense classes. To obtain this result, we develop tools that also apply to the more general monadically NIP classes, based on the notion of indiscernible sequences from model theory. We show that in monadically stable and monadically NIP classes indiscernible sequences impose a strong combinatorial structure on their definable neighborhoods. All our proofs are constructive and yield efficient algorithms.

Cite as

Jan Dreier, Nikolas Mählmann, Sebastian Siebertz, and Szymon Toruńczyk. Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 125:1-125:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{dreier_et_al:LIPIcs.ICALP.2023.125,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Siebertz, Sebastian and Toru\'{n}czyk, Szymon},
  title =	{{Indiscernibles and Flatness in Monadically Stable and Monadically NIP Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{125:1--125:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.125},
  URN =		{urn:nbn:de:0030-drops-181779},
  doi =		{10.4230/LIPIcs.ICALP.2023.125},
  annote =	{Keywords: stability, NIP, combinatorial characterization, first-order model checking}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Flipper Games for Monadically Stable Graph Classes

Authors: Jakub Gajarský, Nikolas Mählmann, Rose McCarty, Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, Sebastian Siebertz, Marek Sokołowski, and Szymon Toruńczyk

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
A class of graphs C is monadically stable if for every unary expansion Ĉ of C, one cannot encode - using first-order transductions - arbitrarily long linear orders in graphs from C. It is known that nowhere dense graph classes are monadically stable; these include classes of bounded maximum degree and classes that exclude a fixed topological minor. On the other hand, monadic stability is a property expressed in purely model-theoretic terms that is also suited for capturing structure in dense graphs. In this work we provide a characterization of monadic stability in terms of the Flipper game: a game on a graph played by Flipper, who in each round can complement the edge relation between any pair of vertex subsets, and Localizer, who in each round is forced to restrict the game to a ball of bounded radius. This is an analog of the Splitter game, which characterizes nowhere dense classes of graphs (Grohe, Kreutzer, and Siebertz, J. ACM '17). We give two different proofs of our main result. The first proof is based on tools borrowed from model theory, and it exposes an additional property of monadically stable graph classes that is close in spirit to definability of types. Also, as a byproduct, we show that monadic stability for graph classes coincides with monadic stability of existential formulas with two free variables, and we provide another combinatorial characterization of monadic stability via forbidden patterns. The second proof relies on the recently introduced notion of flip-flatness (Dreier, Mählmann, Siebertz, and Toruńczyk, arXiv 2206.13765) and provides an efficient algorithm to compute Flipper’s moves in a winning strategy.

Cite as

Jakub Gajarský, Nikolas Mählmann, Rose McCarty, Pierre Ohlmann, Michał Pilipczuk, Wojciech Przybyszewski, Sebastian Siebertz, Marek Sokołowski, and Szymon Toruńczyk. Flipper Games for Monadically Stable Graph Classes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 128:1-128:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2023.128,
  author =	{Gajarsk\'{y}, Jakub and M\"{a}hlmann, Nikolas and McCarty, Rose and Ohlmann, Pierre and Pilipczuk, Micha{\l} and Przybyszewski, Wojciech and Siebertz, Sebastian and Soko{\l}owski, Marek and Toru\'{n}czyk, Szymon},
  title =	{{Flipper Games for Monadically Stable Graph Classes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{128:1--128:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.128},
  URN =		{urn:nbn:de:0030-drops-181804},
  doi =		{10.4230/LIPIcs.ICALP.2023.128},
  annote =	{Keywords: Stability theory, structural graph theory, games}
}
Document
Artifact
From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS (Artifact)

Authors: Sebastian Altmeyer, Étienne André, Silvano Dal Zilio, Loïc Fejoz, Michael González Harbour, Susanne Graf, J. Javier Gutiérrez, Rafik Henia, Didier Le Botlan, Giuseppe Lipari, Julio Medina, Nicolas Navet, Sophie Quinton, Juan M. Rivas, and Youcheng Sun

Published in: DARTS, Volume 9, Issue 1, Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)


Abstract
We propose here solutions to the FMTV 2015 challenge of a distributed video processing system using four different formalisms, as well as the description of the challenge itself. This artifact contains several solutions to various subchallenges, and instructions and scripts to reproduce these results smoothly.

Cite as

Sebastian Altmeyer, Étienne André, Silvano Dal Zilio, Loïc Fejoz, Michael González Harbour, Susanne Graf, J. Javier Gutiérrez, Rafik Henia, Didier Le Botlan, Giuseppe Lipari, Julio Medina, Nicolas Navet, Sophie Quinton, Juan M. Rivas, and Youcheng Sun. From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS (Artifact). In Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 1, pp. 4:1-4:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@Article{altmeyer_et_al:DARTS.9.1.4,
  author =	{Altmeyer, Sebastian and Andr\'{e}, \'{E}tienne and Dal Zilio, Silvano and Fejoz, Lo\"{i}c and Harbour, Michael Gonz\'{a}lez and Graf, Susanne and Guti\'{e}rrez, J. Javier and Henia, Rafik and Le Botlan, Didier and Lipari, Giuseppe and Medina, Julio and Navet, Nicolas and Quinton, Sophie and Rivas, Juan M. and Sun, Youcheng},
  title =	{{From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS (Artifact)}},
  pages =	{4:1--4:6},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2023},
  volume =	{9},
  number =	{1},
  editor =	{Altmeyer, Sebastian and Andr\'{e}, \'{E}tienne and Dal Zilio, Silvano and Fejoz, Lo\"{i}c and Harbour, Michael Gonz\'{a}lez and Graf, Susanne and Guti\'{e}rrez, J. Javier and Henia, Rafik and Le Botlan, Didier and Lipari, Giuseppe and Medina, Julio and Navet, Nicolas and Quinton, Sophie and Rivas, Juan M. and Sun, Youcheng},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DARTS.9.1.4},
  URN =		{urn:nbn:de:0030-drops-180257},
  doi =		{10.4230/DARTS.9.1.4},
  annote =	{Keywords: Verification challenge, industrial use case, end-to-end latency, real-time systems, response time analysis}
}
Document
Invited Paper
From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS (Invited Paper)

Authors: Sebastian Altmeyer, Étienne André, Silvano Dal Zilio, Loïc Fejoz, Michael González Harbour, Susanne Graf, J. Javier Gutiérrez, Rafik Henia, Didier Le Botlan, Giuseppe Lipari, Julio Medina, Nicolas Navet, Sophie Quinton, Juan M. Rivas, and Youcheng Sun

Published in: LIPIcs, Volume 262, 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)


Abstract
We present here the main features and lessons learned from the first edition of what has now become the ECRTS industrial challenge, together with the final description of the challenge and a comparative overview of the proposed solutions. This verification challenge, proposed by Thales, was first discussed in 2014 as part of a dedicated workshop (FMTV, a satellite event of the FM 2014 conference), and solutions were discussed for the first time at the WATERS 2015 workshop. The use case for the verification challenge is an aerial video tracking system. A specificity of this system lies in the fact that periods are constant but known with a limited precision only. The first part of the challenge focuses on the video frame processing system. It consists in computing maximum values of the end-to-end latency of the frames sent by the camera to the display, for two different buffer sizes, and then the minimum duration between two consecutive frame losses. The second challenge is about computing end-to-end latencies on the tracking and camera control for two different values of jitter. Solutions based on five different tools - Fiacre/Tina, CPAL (simulation and analysis), IMITATOR, UPPAAL and MAST - were submitted for discussion at WATERS 2015. While none of these solutions provided a full answer to the challenge, a combination of several of them did allow to draw some conclusions.

Cite as

Sebastian Altmeyer, Étienne André, Silvano Dal Zilio, Loïc Fejoz, Michael González Harbour, Susanne Graf, J. Javier Gutiérrez, Rafik Henia, Didier Le Botlan, Giuseppe Lipari, Julio Medina, Nicolas Navet, Sophie Quinton, Juan M. Rivas, and Youcheng Sun. From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS (Invited Paper). In 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 262, pp. 19:1-19:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{altmeyer_et_al:LIPIcs.ECRTS.2023.19,
  author =	{Altmeyer, Sebastian and Andr\'{e}, \'{E}tienne and Dal Zilio, Silvano and Fejoz, Lo\"{i}c and Harbour, Michael Gonz\'{a}lez and Graf, Susanne and Guti\'{e}rrez, J. Javier and Henia, Rafik and Le Botlan, Didier and Lipari, Giuseppe and Medina, Julio and Navet, Nicolas and Quinton, Sophie and Rivas, Juan M. and Sun, Youcheng},
  title =	{{From FMTV to WATERS: Lessons Learned from the First Verification Challenge at ECRTS}},
  booktitle =	{35th Euromicro Conference on Real-Time Systems (ECRTS 2023)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-280-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{262},
  editor =	{Papadopoulos, Alessandro V.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2023.19},
  URN =		{urn:nbn:de:0030-drops-180486},
  doi =		{10.4230/LIPIcs.ECRTS.2023.19},
  annote =	{Keywords: Verification challenge, industrial use case, end-to-end latency}
}
Document
Cut Paths and Their Remainder Structure, with Applications

Authors: Massimo Cairo, Shahbaz Khan, Romeo Rizzi, Sebastian Schmidt, Alexandru I. Tomescu, and Elia C. Zirondelli

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)


Abstract
In a strongly connected graph G = (V,E), a cut arc (also called strong bridge) is an arc e ∈ E whose removal makes the graph no longer strongly connected. Equivalently, there exist u,v ∈ V, such that all u-v walks contain e. Cut arcs are a fundamental graph-theoretic notion, with countless applications, especially in reachability problems. In this paper we initiate the study of cut paths, as a generalisation of cut arcs, which we naturally define as those paths P for which there exist u,v ∈ V, such that all u-v walks contain P as subwalk. We first prove various properties of cut paths and define their remainder structures, which we use to present a simple O(m)-time verification algorithm for a cut path (|V| = n, |E| = m). Secondly, we apply cut paths and their remainder structures to improve several reachability problems from bioinformatics, as follows. A walk is called safe if it is a subwalk of every node-covering closed walk of a strongly connected graph. Multi-safety is defined analogously, by considering node-covering sets of closed walks instead. We show that cut paths provide simple O(m)-time algorithms verifying if a walk is safe or multi-safe. For multi-safety, we present the first linear time algorithm, while for safety, we present a simple algorithm where the state-of-the-art employed complex data structures. Finally we show that the simultaneous computation of remainder structures of all subwalks of a cut path can be performed in linear time, since they are related in a structured way. These properties yield an O(mn)-time algorithm outputting all maximal multi-safe walks, improving over the state-of-the-art algorithm running in time O(m²+n³). The results of this paper only scratch the surface in the study of cut paths, and we believe a rich structure of a graph can be revealed, considering the perspective of a path, instead of just an arc.

Cite as

Massimo Cairo, Shahbaz Khan, Romeo Rizzi, Sebastian Schmidt, Alexandru I. Tomescu, and Elia C. Zirondelli. Cut Paths and Their Remainder Structure, with Applications. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 17:1-17:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cairo_et_al:LIPIcs.STACS.2023.17,
  author =	{Cairo, Massimo and Khan, Shahbaz and Rizzi, Romeo and Schmidt, Sebastian and Tomescu, Alexandru I. and Zirondelli, Elia C.},
  title =	{{Cut Paths and Their Remainder Structure, with Applications}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{17:1--17:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.17},
  URN =		{urn:nbn:de:0030-drops-176690},
  doi =		{10.4230/LIPIcs.STACS.2023.17},
  annote =	{Keywords: reachability, cut arc, strong bridge, covering walk, safety, persistence, essentiality, genome assembly}
}
Document
Combinatorial and Algorithmic Aspects of Monadic Stability

Authors: Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)


Abstract
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory, generalize nowhere dense classes and close them under transductions, i.e. transformations defined by colorings and simple first-order interpretations. In this work we aim to extend some combinatorial and algorithmic properties of nowhere dense classes to monadically stable classes of finite graphs. We prove the following results. - For every monadically stable class C and fixed integer s ≥ 3, the Ramsey numbers R_C(s,t) are bounded from above by 𝒪(t^{s-1-δ}) for some δ > 0, improving the bound R(s,t) ∈ 𝒪(t^{s-1}/(log t)^{s-1}) known for the class of all graphs and the bounds known for k-stable graphs when s ≤ k. - For every monadically stable class C and every integer r, there exists δ > 0 such that every graph G ∈ C that contains an r-subdivision of the biclique K_{t,t} as a subgraph also contains K_{t^δ,t^δ} as a subgraph. This generalizes earlier results for nowhere dense graph classes. - We obtain a stronger regularity lemma for monadically stable classes of graphs. - Finally, we show that we can compute polynomial kernels for the independent set and dominating set problems in powers of nowhere dense classes. Formerly, only fixed-parameter tractable algorithms were known for these problems on powers of nowhere dense classes.

Cite as

Jan Dreier, Nikolas Mählmann, Amer E. Mouawad, Sebastian Siebertz, and Alexandre Vigny. Combinatorial and Algorithmic Aspects of Monadic Stability. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{dreier_et_al:LIPIcs.ISAAC.2022.11,
  author =	{Dreier, Jan and M\"{a}hlmann, Nikolas and Mouawad, Amer E. and Siebertz, Sebastian and Vigny, Alexandre},
  title =	{{Combinatorial and Algorithmic Aspects of Monadic Stability}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{11:1--11:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.11},
  URN =		{urn:nbn:de:0030-drops-172961},
  doi =		{10.4230/LIPIcs.ISAAC.2022.11},
  annote =	{Keywords: Monadic Stability, Structural Graph Theory, Ramsey Numbers, Regularity, Kernels}
}
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