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Documents authored by Stagni, Henrique

Document
DOI: 10.4230/LIPIcs.ITCS.2020.43
Testing Linear Inequalities of Subgraph Statistics

Authors: Lior Gishboliner, Asaf Shapira, and Henrique Stagni

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ? and those that are far from satisfying it. Since these algorithms operate by inspecting a small randomly selected portion of the input, the most natural property one would like to be able to test is whether the input does not contain certain forbidden small substructures. In the setting of graphs, such a result was obtained by Alon et al., who proved that for any finite family of graphs ℱ, the property of being induced ℱ-free (i.e. not containing an induced copy of any F ∈ ℱ) is testable. It is natural to ask if one can go one step further and prove that more elaborate properties involving induced subgraphs are also testable. One such generalization of the result of Alon et al. was formulated by Goldreich and Shinkar who conjectured that for any finite family of graphs ℱ, and any linear inequality involving the densities of the graphs F ∈ ℱ in the input graph, the property of satisfying this inequality can be tested in a certain restricted model of graph property testing. Our main result in this paper disproves this conjecture in the following strong form: some properties of this type are not testable even in the classical (i.e. unrestricted) model of graph property testing. The proof deviates significantly from prior non-testability results in this area. The main idea is to use a linear inequality relating induced subgraph densities in order to encode the property of being a pseudo-random graph.
Cite as

Lior Gishboliner, Asaf Shapira, and Henrique Stagni. Testing Linear Inequalities of Subgraph Statistics. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 43:1-43:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gishboliner_et_al:LIPIcs.ITCS.2020.43,
  author =	{Gishboliner, Lior and Shapira, Asaf and Stagni, Henrique},
  title =	{{Testing Linear Inequalities of Subgraph Statistics}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{43:1--43:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.43},
  URN =		{urn:nbn:de:0030-drops-117287},
  doi =		{10.4230/LIPIcs.ITCS.2020.43},
  annote =	{Keywords: graph property testing, subgraph statistics}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2016.35
Estimating Parameters Associated with Monotone Properties

Authors: Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann, and Henrique Stagni

Published in: LIPIcs, Volume 60, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)

Abstract
There has been substantial interest in estimating the value of a graph parameter, i.e., of a real function defined on the set of finite graphs, by sampling a randomly chosen substructure whose size is independent of the size of the input. Graph parameters that may be successfully estimated in this way are said to be testable or estimable, and the sample complexity q_z=q_z(epsilon) of an estimable parameter z is the size of the random sample required to ensure that the value of z(G) may be estimated within error epsilon with probability at least 2/3. In this paper, we study the sample complexity of estimating two graph parameters associated with a monotone graph property, improving previously known results. To obtain our results, we prove that the vertex set of any graph that satisfies a monotone property P may be partitioned equitably into a constant number of classes in such a way that the cluster graph induced by the partition is not far from satisfying a natural weighted graph generalization of P}. Properties for which this holds are said to be recoverable, and the study of recoverable properties may be of independent interest.
Cite as

Carlos Hoppen, Yoshiharu Kohayakawa, Richard Lang, Hanno Lefmann, and Henrique Stagni. Estimating Parameters Associated with Monotone Properties. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 60, pp. 35:1-35:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{hoppen_et_al:LIPIcs.APPROX-RANDOM.2016.35,
  author =	{Hoppen, Carlos and Kohayakawa, Yoshiharu and Lang, Richard and Lefmann, Hanno and Stagni, Henrique},
  title =	{{Estimating Parameters Associated with Monotone Properties}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2016)},
  pages =	{35:1--35:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-018-7},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{60},
  editor =	{Jansen, Klaus and Mathieu, Claire and Rolim, Jos\'{e} D. P. and Umans, Chris},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2016.35},
  URN =		{urn:nbn:de:0030-drops-66588},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2016.35},
  annote =	{Keywords: parameter estimation, parameter testing, edit distance to monotone graph properties, entropy of subgraph classes, speed of subgraph classes}
}
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