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.ESA.2023.100
URN: urn:nbn:de:0030-drops-187536
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18753/
Go to the corresponding LIPIcs Volume Portal

Verbitsky, Oleg ; Zhukovskii, Maksim

Canonization of a Random Graph by Two Matrix-Vector Multiplications

pdf-format:
LIPIcs-ESA-2023-100.pdf (0.6 MB)

Abstract

We show that a canonical labeling of a random n-vertex graph can be obtained by assigning to each vertex x the triple (w₁(x),w₂(x),w₃(x)), where w_k(x) is the number of walks of length k starting from x. This takes time ?(n²), where n² is the input size, by using just two matrix-vector multiplications. The linear-time canonization of a random graph is the classical result of Babai, Erdős, and Selkow. For this purpose they use the well-known combinatorial color refinement procedure, and we make a comparative analysis of the two algorithmic approaches.

BibTeX - Entry

@InProceedings{verbitsky_et_al:LIPIcs.ESA.2023.100,
  author =	{Verbitsky, Oleg and Zhukovskii, Maksim},
  title =	{{Canonization of a Random Graph by Two Matrix-Vector Multiplications}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{100:1--100:13},
  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.dagstuhl.de/opus/volltexte/2023/18753},
  URN =		{urn:nbn:de:0030-drops-187536},
  doi =		{10.4230/LIPIcs.ESA.2023.100},
  annote =	{Keywords: Graph Isomorphism, canonical labeling, random graphs, walk matrix, color refinement, linear time}
}

Keywords: Graph Isomorphism, canonical labeling, random graphs, walk matrix, color refinement, linear time
Collection: 31st Annual European Symposium on Algorithms (ESA 2023)
Issue Date: 2023
Date of publication: 30.08.2023

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI