TY - JOUR

T1 - Graph reconstruction in the congested clique

AU - Montealegre, P.

AU - Perez-Salazar, S.

AU - Rapaport, I.

AU - Todinca, I.

N1 - Funding Information:
This work has been partially supported by CONICYT via PIA/Apoyo a Centros Científicos y Tecnológicos de Excelencia AFB 170001 (P.M. and I.R.), FONDECYT 1170021 (I.R.), FONDECYT 11190482 (P.M.) and PAI + Convocatoria Nacional Subvención a la Incorporación en la Academia Año 2017 + PAI77170068 (P.M.).
Publisher Copyright:
© 2020 Elsevier Inc.

PY - 2020/11

Y1 - 2020/11

N2 - In this paper we study the reconstruction problem in the congested clique model. Given a class of graphs G, the problem is defined as follows: if G∉G, then every node must reject; if G∈G, then every node must end up knowing all the edges of G. The cost of an algorithm is the total number of bits received by any node through one link. It is not difficult to see that the cost of any algorithm that solves this problem is Ω(log|Gn|/n), where Gn is the subclass of all n-node labeled graphs in G. We prove that the lower bound is tight and that it is possible to achieve it with only 2 rounds.

AB - In this paper we study the reconstruction problem in the congested clique model. Given a class of graphs G, the problem is defined as follows: if G∉G, then every node must reject; if G∈G, then every node must end up knowing all the edges of G. The cost of an algorithm is the total number of bits received by any node through one link. It is not difficult to see that the cost of any algorithm that solves this problem is Ω(log|Gn|/n), where Gn is the subclass of all n-node labeled graphs in G. We prove that the lower bound is tight and that it is possible to achieve it with only 2 rounds.

KW - Congested clique

KW - Distributed computing

KW - Graph classes

KW - Reconstruction problem

KW - Round complexity

UR - http://www.scopus.com/inward/record.url?scp=85089433092&partnerID=8YFLogxK

U2 - 10.1016/j.jcss.2020.04.004

DO - 10.1016/j.jcss.2020.04.004

M3 - Article

AN - SCOPUS:85089433092

VL - 113

SP - 1

EP - 17

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

ER -