License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.OPODIS.2021.22
URN: urn:nbn:de:0030-drops-157970
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15797/
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Bousquet, Nicolas ; Feuilloley, Laurent ; Pierron, Théo

Local Certification of Graph Decompositions and Applications to Minor-Free Classes

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LIPIcs-OPODIS-2021-22.pdf (0.7 MB)

Abstract

Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes received a considerable attention. The goal is to certify that a graph G belongs to a given graph class ?. Such certifications with labels of size O(log n) (where n is the size of the network) exist for trees, planar graphs and graphs embedded on surfaces. Feuilloley et al. ask if this can be extended to any class of graphs defined by a finite set of forbidden minors.
In this work, we develop new decomposition tools for graph certification, and apply them to show that for every small enough minor H, H-minor-free graphs can indeed be certified with labels of size O(log n). We also show matching lower bounds using a new proof technique.

BibTeX - Entry

@InProceedings{bousquet_et_al:LIPIcs.OPODIS.2021.22,
  author =	{Bousquet, Nicolas and Feuilloley, Laurent and Pierron, Th\'{e}o},
  title =	{{Local Certification of Graph Decompositions and Applications to Minor-Free Classes}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{22:1--22:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15797},
  URN =		{urn:nbn:de:0030-drops-157970},
  doi =		{10.4230/LIPIcs.OPODIS.2021.22},
  annote =	{Keywords: Local certification, proof-labeling schemes, locally checkable proofs, graph decompositions, minor-free graphs}
}

Keywords: Local certification, proof-labeling schemes, locally checkable proofs, graph decompositions, minor-free graphs
Collection: 25th International Conference on Principles of Distributed Systems (OPODIS 2021)
Issue Date: 2022
Date of publication: 28.02.2022

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