Fast Breadth-First Search Approximation for Epidemic Source Inference

Abstract

Detecting the epidemic source has applications to computational epidemiology of infectious diseases and rumor source detection in online social networks. The problem of epidemic source inference was first studied in the seminal work by Shah and Zaman using maximum likelihood (ML) estimation and solved optimally only for the case of degree-regular trees. In this paper, we study the problem for the general graph setting, which is challenging due to the combinatorial complexity and problem scale. As a first step, we study the ML estimator on almost degree-regular trees with a single irregular node. By demonstrating how the probability of spreading permutation affects the likelihood, we propose a fast Breadth-First Search algorithm and a greedy algorithm to approximate the solution for general irregular trees, and then extend the methods to cactus graphs. Our performance evaluation results demonstrate that the algorithms improve over prior heuristics in the literature and serve as a basis for designing data-driven health response analytics to combat the epidemic.