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Archaeology of random recursive dags and Cooper-Frieze random networks

Part of: Graph theory Combinatorial probability

Published online by Cambridge University Press:  13 June 2023

Simon Briend ,
Francisco Calvillo  and
Gábor Lugosi
Simon Briend
Affiliation:
Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay, CNRS, Orsay, France
Francisco Calvillo
Affiliation:
Department of Mathematics and Applications, École Normale Supérieure, Paris, France
Gábor Lugosi*
Affiliation:
Department of Economics and Business, Pompeu Fabra University, Barcelona, Spain Barcelona Graduate School of Economics, ICREA, Barcelona, Spain
*
Corresponding author: Gábor Lugosi; Email: gabor.lugosi@gmail.com
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Abstract

We study the problem of finding the root vertex in large growing networks. We prove that it is possible to construct confidence sets of size independent of the number of vertices in the network that contain the root vertex with high probability in various models of random networks. The models include uniform random recursive dags and uniform Cooper-Frieze random graphs.

Keywords

Combinatorial statisticsNetwork archaeology

MSC classification

Primary: 05C80: Random graphs
Secondary: 60C05: Combinatorial probability
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 32 , Issue 6 , November 2023 , pp. 859 - 873
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

*

This research was supported by a Huawei Technologies Co., Ltd. grant. Simon Briend acknowledges the support of Région Ile de France. Gábor Lugosi acknowledges the support of Ayudas Fundación BBVA a Proyectos de Investigación Científica 2021 and the Spanish Ministry of Economy and Competitiveness, Grant PGC2018-101643-B-I00 and FEDER, EU.

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