7 Search Results for "Norin, Sergey"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.26
Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set

Authors: Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond

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

Abstract
The paper deals with the Feedback Vertex Set problem parameterized by the solution size. Given a graph G and a parameter k, one has to decide if there is a set S of at most k vertices such that G-S is acyclic. Assuming the Exponential Time Hypothesis, it is known that FVS cannot be solved in time 2^{o(k)}n^{𝒪(1)} in general graphs. To overcome this, many recent results considered FVS restricted to particular intersection graph classes and provided such 2^{o(k)}n^{𝒪(1)} algorithms. In this paper we provide generic conditions on a graph class for the existence of an algorithm solving FVS in subexponential FPT time, i.e. time 2^k^ε poly(n), for some ε < 1, where n denotes the number of vertices of the instance and k the parameter. On the one hand this result unifies algorithms that have been proposed over the years for several graph classes such as planar graphs, map graphs, unit-disk graphs, pseudo-disk graphs, and string graphs of bounded edge-degree. On the other hand it extends the tractability horizon of FVS to new classes that are not amenable to previously used techniques, in particular intersection graphs of "thin" objects like segment graphs or more generally s-string graphs.
Cite as

Gaétan Berthe, Marin Bougeret, Daniel Gonçalves, and Jean-Florent Raymond. Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berthe_et_al:LIPIcs.ICALP.2025.26,
  author =	{Berthe, Ga\'{e}tan and Bougeret, Marin and Gon\c{c}alves, Daniel and Raymond, Jean-Florent},
  title =	{{Pushing the Frontiers of Subexponential FPT Time for Feedback Vertex Set}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{26:1--26:15},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-234036},
  doi =		{10.4230/LIPIcs.ICALP.2025.26},
  annote =	{Keywords: Subexponential FPT algorithms, geometric intersection graphs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.129
An Upper Bound on the Weisfeiler-Leman Dimension

Authors: Thomas Schneider and Pascal Schweitzer

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

Abstract
The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a parameterized family: for each k ∈ ℕ there is a corresponding k-dimensional algorithm WLk. The algorithms become increasingly powerful with increasing dimension, but at the same time the running time increases. The WL-dimension of a graph G is the smallest k ∈ ℕ for which WLk correctly decides isomorphism between G and every other graph. In some sense, the WL-dimension measures how difficult it is to test isomorphism of one graph to others using a fairly general class of combinatorial algorithms. Nowadays, it is a standard measure in descriptive complexity theory for the structural complexity of a graph. We prove that the WL-dimension of a graph on n vertices is at most 3/20 ⋅ n + o(n) = 0.15 ⋅ n + o(n). Reducing the question to coherent configurations, the proof develops various techniques to analyze their structure. This includes sufficient conditions under which a fiber can be restored uniquely up to isomorphism if it is removed, a recursive proof exploiting a degree reduction and treewidth bounds, as well as an exhaustive analysis of interspaces involving small fibers. As a base case, we also analyze the dimension of coherent configurations with small fiber size and thereby graphs with small color class size.
Cite as

Thomas Schneider and Pascal Schweitzer. An Upper Bound on the Weisfeiler-Leman Dimension. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 129:1-129:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schneider_et_al:LIPIcs.ICALP.2025.129,
  author =	{Schneider, Thomas and Schweitzer, Pascal},
  title =	{{An Upper Bound on the Weisfeiler-Leman Dimension}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{129:1--129:18},
  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.2025.129},
  URN =		{urn:nbn:de:0030-drops-235065},
  doi =		{10.4230/LIPIcs.ICALP.2025.129},
  annote =	{Keywords: Weisfeiler-Leman dimension, descriptive complexity, coherent configurations}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.36
Strongly Sublinear Separators and Bounded Asymptotic Dimension for Sphere Intersection Graphs

Authors: James Davies, Agelos Georgakopoulos, Meike Hatzel, and Rose McCarty

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
In this paper, we consider the class 𝒞^d of sphere intersection graphs in R^d for d ≥ 2. We show that for each integer t, the class of all graphs in 𝒞^d that exclude K_{t,t} as a subgraph has strongly sublinear separators. We also prove that 𝒞^d has asymptotic dimension at most 2d+2.
Cite as

James Davies, Agelos Georgakopoulos, Meike Hatzel, and Rose McCarty. Strongly Sublinear Separators and Bounded Asymptotic Dimension for Sphere Intersection Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{davies_et_al:LIPIcs.SoCG.2025.36,
  author =	{Davies, James and Georgakopoulos, Agelos and Hatzel, Meike and McCarty, Rose},
  title =	{{Strongly Sublinear Separators and Bounded Asymptotic Dimension for Sphere Intersection Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.36},
  URN =		{urn:nbn:de:0030-drops-231881},
  doi =		{10.4230/LIPIcs.SoCG.2025.36},
  annote =	{Keywords: Intersection graphs, strongly sublinear separators, asymptotic dimension}
}
Document
DOI: 10.4230/LIPIcs.STACS.2025.56
Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs

Authors: Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt

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

Abstract
Some of the most important open problems for linear layouts of graphs ask for the relation between a graph’s queue number and its stack number or mixed number. In such, we seek a vertex order and edge partition of G into parts with pairwise non-crossing edges (a stack) or with pairwise non-nesting edges (a queue). Allowing only stacks, only queues, or both, the minimum number of required parts is the graph’s stack number sn(G), queue number qn(G), and mixed number mn(G), respectively. Already in 1992, Heath and Rosenberg asked whether qn(G) is bounded in terms of sn(G), that is, whether stacks "can be transformed into" queues. This is equivalent to bipartite 3-stack graphs having bounded queue number (Dujmović and Wood, 2005). Recently, Alam et al. asked whether qn(G) is bounded in terms of mn(G), which we show to also be equivalent to the previous questions. We approach the problem by considering separated linear layouts of bipartite graphs. In this natural setting all vertices of one part must precede all vertices of the other part. Separated stack and queue numbers coincide, and for fixed vertex orders, graphs with bounded separated stack/queue number can be characterized and efficiently recognized, whereas the separated mixed layouts are more challenging. In this work, we thoroughly investigate the relationship between separated and non-separated, mixed and pure linear layouts.
Cite as

Julia Katheder, Michael Kaufmann, Sergey Pupyrev, and Torsten Ueckerdt. Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 56:1-56:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{katheder_et_al:LIPIcs.STACS.2025.56,
  author =	{Katheder, Julia and Kaufmann, Michael and Pupyrev, Sergey and Ueckerdt, Torsten},
  title =	{{Transforming Stacks into Queues: Mixed and Separated Layouts of Graphs}},
  booktitle =	{42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025)},
  pages =	{56:1--56:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-365-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{327},
  editor =	{Beyersdorff, Olaf and Pilipczuk, Micha{\l} and Pimentel, Elaine and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2025.56},
  URN =		{urn:nbn:de:0030-drops-228819},
  doi =		{10.4230/LIPIcs.STACS.2025.56},
  annote =	{Keywords: Separated linear Layouts, Stack Number, Queue Number, mixed Number, bipartite Graphs}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.21
Adjacency Labeling Schemes for Small Classes

Authors: Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
A graph class admits an implicit representation if, for every positive integer n, its n-vertex graphs have a O(log n)-bit (adjacency) labeling scheme, i.e., their vertices can be labeled by binary strings of length O(log n) such that the presence of an edge between any pair of vertices can be deduced solely from their labels. The famous Implicit Graph Conjecture posited that every hereditary (i.e., closed under taking induced subgraphs) factorial (i.e., containing 2^O(n log n) n-vertex graphs) class admits an implicit representation. The conjecture was recently refuted [Hatami and Hatami, FOCS '22], and does not even hold among monotone (i.e., closed under taking subgraphs) factorial classes [Bonnet et al., ICALP '24]. However, monotone small (i.e., containing at most n! cⁿ many n-vertex graphs for some constant c) classes do admit implicit representations. This motivates the Small Implicit Graph Conjecture: Every hereditary small class admits an O(log n)-bit labeling scheme. We provide evidence supporting the Small Implicit Graph Conjecture. First, we show that every small weakly sparse (i.e., excluding some fixed bipartite complete graph as a subgraph) class has an implicit representation. This is a consequence of the following fact of independent interest proved in the paper: Every weakly sparse small class has bounded expansion (hence, in particular, bounded degeneracy). Second, we show that every hereditary small class admits an O(log³ n)-bit labeling scheme, which provides a substantial improvement of the best-known polynomial upper bound of n^(1-ε) on the size of adjacency labeling schemes for such classes. This is a consequence of another fact of independent interest proved in the paper: Every small class has neighborhood complexity O(n log n).
Cite as

Édouard Bonnet, Julien Duron, John Sylvester, and Viktor Zamaraev. Adjacency Labeling Schemes for Small Classes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 21:1-21:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonnet_et_al:LIPIcs.ITCS.2025.21,
  author =	{Bonnet, \'{E}douard and Duron, Julien and Sylvester, John and Zamaraev, Viktor},
  title =	{{Adjacency Labeling Schemes for Small Classes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{21:1--21:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.21},
  URN =		{urn:nbn:de:0030-drops-226493},
  doi =		{10.4230/LIPIcs.ITCS.2025.21},
  annote =	{Keywords: Adjacency labeling, degeneracy, weakly sparse classes, small classes, implicit graph conjecture}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.58
Testability and Local Certification of Monotone Properties in Minor-Closed Classes

Authors: Louis Esperet and Sergey Norin

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
The main problem in the area of graph property testing is to understand which graph properties are testable, which means that with constantly many queries to any input graph G, a tester can decide with good probability whether G satisfies the property, or is far from satisfying the property. Testable properties are well understood in the dense model and in the bounded degree model, but little is known in sparse graph classes when graphs are allowed to have unbounded degree. This is the setting of the sparse model. We prove that for any proper minor-closed class 𝒢, any monotone property (i.e., any property that is closed under taking subgraphs) is testable for graphs from 𝒢 in the sparse model. This extends a result of Czumaj and Sohler (FOCS'19), who proved it for monotone properties with finitely many forbidden subgraphs. Our result implies for instance that for any integers k and t, k-colorability of K_t-minor free graphs is testable in the sparse model. Elek recently proved that monotone properties of bounded degree graphs from minor-closed classes that are closed under disjoint union can be verified by an approximate proof labeling scheme in constant time. We show again that the assumption of bounded degree can be omitted in his result.
Cite as

Louis Esperet and Sergey Norin. Testability and Local Certification of Monotone Properties in Minor-Closed Classes. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 58:1-58:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{esperet_et_al:LIPIcs.ICALP.2022.58,
  author =	{Esperet, Louis and Norin, Sergey},
  title =	{{Testability and Local Certification of Monotone Properties in Minor-Closed Classes}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{58:1--58:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.58},
  URN =		{urn:nbn:de:0030-drops-163997},
  doi =		{10.4230/LIPIcs.ICALP.2022.58},
  annote =	{Keywords: Property testing, sparse model, local certification, minor-closed classes}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.78
Large Supports are Required for Well-Supported Nash Equilibria

Authors: Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, and Hehui Wu

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
We prove that for any constant k and any epsilon < 1, there exist bimatrix win-lose games for which every epsilon-WSNE requires supports of cardinality greater than k. To do this, we provide a graph-theoretic characterization of win-lose games that possess epsilon-WSNE with constant cardinality supports. We then apply a result in additive number theory of Haight to construct win-lose games that do not satisfy the requirements of the characterization. These constructions disprove graph theoretic conjectures of Daskalakis, Mehta and Papadimitriou and Myers.
Cite as

Yogesh Anbalagan, Hao Huang, Shachar Lovett, Sergey Norin, Adrian Vetta, and Hehui Wu. Large Supports are Required for Well-Supported Nash Equilibria. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 78-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{anbalagan_et_al:LIPIcs.APPROX-RANDOM.2015.78,
  author =	{Anbalagan, Yogesh and Huang, Hao and Lovett, Shachar and Norin, Sergey and Vetta, Adrian and Wu, Hehui},
  title =	{{Large Supports are Required for Well-Supported Nash Equilibria}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{78--84},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.78},
  URN =		{urn:nbn:de:0030-drops-52959},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.78},
  annote =	{Keywords: bimatrix games, well-supported Nash equilibria}
}
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