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.2021.68
URN: urn:nbn:de:0030-drops-146496
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14649/
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Mathieu, Claire ; Zhou, Hang

A Simple Algorithm for Graph Reconstruction

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LIPIcs-ESA-2021-68.pdf (0.9 MB)

Abstract

How efficiently can we find an unknown graph using distance queries between its vertices? We assume that the unknown graph is connected, unweighted, and has bounded degree. The goal is to find every edge in the graph. This problem admits a reconstruction algorithm based on multi-phase Voronoi-cell decomposition and using Õ(n^{3/2}) distance queries [Kannan et al., 2018].
In our work, we analyze a simple reconstruction algorithm. We show that, on random Δ-regular graphs, our algorithm uses Õ(n) distance queries. As by-products, we can reconstruct those graphs using O(log² n) queries to an all-distances oracle or Õ(n) queries to a betweenness oracle, and we bound the metric dimension of those graphs by log² n.
Our reconstruction algorithm has a very simple structure, and is highly parallelizable. On general graphs of bounded degree, our reconstruction algorithm has subquadratic query complexity.

BibTeX - Entry

@InProceedings{mathieu_et_al:LIPIcs.ESA.2021.68,
  author =	{Mathieu, Claire and Zhou, Hang},
  title =	{{A Simple Algorithm for Graph Reconstruction}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{68:1--68:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14649},
  URN =		{urn:nbn:de:0030-drops-146496},
  doi =		{10.4230/LIPIcs.ESA.2021.68},
  annote =	{Keywords: reconstruction, network topology, random regular graphs, metric dimension}
}

Keywords: reconstruction, network topology, random regular graphs, metric dimension
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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