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Documents authored by Norin, Sergey

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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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