Graph reconstruction in the congested clique

Abstract

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.