Expansion and Flooding in Dynamic Random Networks with Node Churn

07/29/2020
โˆ™
by   Luca Becchetti, et al.
โˆ™
0
โˆ™

We study expansion and information diffusion in dynamic networks, that is in networks in which nodes and edges are continuously created and destroyed. We consider information diffusion by flooding, the process by which, once a node is informed, it broadcasts its information to all its neighbors. We study models in which the network is sparse, meaning that it has ๐’ช(n) edges, where n is the number of nodes, and in which edges are created randomly, rather than according to a carefully designed distributed algorithm. In our models, when a node is "born", it connects to d=๐’ช(1) random other nodes. An edge remains alive as long as both its endpoints do. If no further edge creation takes place, we show that, although the network will have ฮฉ_d(n) isolated nodes, it is possible, with large constant probability, to inform a 1-exp(-ฮฉ(d)) fraction of nodes in ๐’ช(log n) time. Furthermore, the graph exhibits, at any given time, a "large-set expansion" property. We also consider models with edge regeneration, in which if an edge (v,w) chosen by v at birth goes down because of the death of w, the edge is replaced by a fresh random edge (v,z). In models with edge regeneration, we prove that the network is, with high probability, a vertex expander at any given time, and flooding takes ๐’ช(log n) time. The above results hold both for a simple but artificial streaming model of node churn, in which at each time step one node is born and the oldest node dies, and in a more realistic continuous-time model in which the time between births is Poisson and the lifetime of each node follows an exponential distribution.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
โˆ™ 10/27/2020

Improved Algorithms for Edge Colouring in the W-Streaming Model

In the W-streaming model, an algorithm is given O(n polylog n) space and...
research
โˆ™ 05/16/2020

Tight Analysis of Asynchronous Rumor Spreading in Dynamic Networks

The asynchronous rumor algorithm spreading propagates a piece of informa...
research
โˆ™ 06/10/2019

Latent Channel Networks

Latent Euclidean embedding models a given network by representing each n...
research
โˆ™ 07/29/2021

The Complexity of Growing a Graph

Motivated by biological processes, we introduce here the model of growin...
research
โˆ™ 01/30/2018

A Dynamic Process Interpretation of the Sparse ERGM Reference Model

Exponential family random graph models (ERGMs) can be understood in term...
research
โˆ™ 11/09/2020

Characterizing the head of the degree distributions of growing networks

The analysis in this paper helps to explain the formation of growing net...
research
โˆ™ 07/01/2020

On the Distributed Construction of Stable Networks in Polylogarithmic Parallel Time

We study the class of networks which can be created in polylogarithmic p...

Please sign up or login with your details

Forgot password? Click here to reset