@inproceedings{eec71929521c4375a124852a97068a7b,
title = "A simple algorithm for graph reconstruction",
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 {\~O}(n3/2) distance queries [27]. In our work, we analyze a simple reconstruction algorithm. We show that, on random ∆-regular graphs, our algorithm uses {\~O}(n) distance queries. As by-products, we can reconstruct those graphs using O(log2 n) queries to an all-distances oracle or {\~O}(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.",
keywords = "Metric dimension, Network topology, Random regular graphs, Reconstruction",
author = "Claire Mathieu and Hang Zhou",
note = "Publisher Copyright: {\textcopyright} Claire Mathieu and Hang Zhou; licensed under Creative Commons License CC-BY 4.0; 29th Annual European Symposium on Algorithms, ESA 2021 ; Conference date: 06-09-2021 Through 08-09-2021",
year = "2021",
month = sep,
day = "1",
doi = "10.4230/LIPIcs.ESA.2021.68",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Petra Mutzel and Rasmus Pagh and Grzegorz Herman",
booktitle = "29th Annual European Symposium on Algorithms, ESA 2021",
}