Viral processes by random walks on random regular graphs

Authors:
Mohammed Abdullah;Colin Cooper;Moez Draief
Affiliations:
Department of Informatics, King's College London;Department of Informatics, King's College London;Department of Electrical and Electronic Engineering, Imperial College London
Venue:
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Year:
2011

Citing 12
Cited 0

On spreading a rumor

SIAM Journal on Applied Mathematics
One, Two and Three Times log n/n for Paths in a Complete Graph with Random Weights

Combinatorics, Probability and Computing
The Cover Time of Random Regular Graphs

SIAM Journal on Discrete Mathematics
The infection time of graphs

Discrete Applied Mathematics
Impact of Human Mobility on Opportunistic Forwarding Algorithms

IEEE Transactions on Mobile Computing
The cover time of the giant component of a random graph

Random Structures & Algorithms
Parsimonious flooding in dynamic graphs

Proceedings of the 28th ACM symposium on Principles of distributed computing
Epidemics and Rumours in Complex Networks

Epidemics and Rumours in Complex Networks
Multiple Random Walks in Random Regular Graphs

SIAM Journal on Discrete Mathematics
A random walk model for infection on graphs: spread of epidemics & rumours with mobile agents

Discrete Event Dynamic Systems
Tight bounds on information dissemination in sparse mobile networks

Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Mobile geometric graphs: detection, coverage and percolation

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the SIR epidemic model with infections carried by k particles making independent random walks on a random regular graph. We give a edge-weighted graph reduction of the dynamics of the process that allows us to apply standard results of Erdös-Renyi random graphs on the particle set. In particular, we show how the parameters of the model produce two phase transitions: In the subcritical regime, O(ln k) particles are infected. In the supercritical regime, for a constant C determined by the parameters of the model, Ck get infected with probability C, and O(ln k) get infected with probability (1-C). Finally, there is a regime in which all k particles are infected. Furthermore, the edge weights give information about when a particle becomes infected. We demonstrate how this can be exploited to determine the completion time of the process by applying a result of Janson on randomly edge weighted graphs.