Locating the Source of Diffusion in Large-Scale Networks

TL;DR

This paper introduces an optimal method for localizing the source of diffusion in large-scale networks using sparse observations, with efficient algorithms and analysis of factors affecting accuracy.

Contribution

It presents a novel, optimal source localization strategy applicable to arbitrary trees and graphs, with efficient implementations and comprehensive case study analysis.

Findings

Optimal localization probability achieved for arbitrary trees.

Complexity of the implementation is O(N^{eta}) with eta=1 or 3.

Localization accuracy depends on network structure, observer density, and cascade count.

Abstract

How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.