## Abstract

This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially except the information source which is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample path based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for g-regular trees such that gq > 1, where g is the node degree and q is the infection probability, the estimator is within a constant distance from the actual source with high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic.

Original language | English (US) |
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Title of host publication | 2013 Information Theory and Applications Workshop, ITA 2013 - Conference Proceedings |

Pages | 486-494 |

Number of pages | 9 |

DOIs | |

State | Published - 2013 |

Event | 2013 Information Theory and Applications Workshop, ITA 2013 - San Diego, CA, United States Duration: Feb 10 2013 → Feb 15 2013 |

### Other

Other | 2013 Information Theory and Applications Workshop, ITA 2013 |
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Country/Territory | United States |

City | San Diego, CA |

Period | 2/10/13 → 2/15/13 |

## ASJC Scopus subject areas

- Computer Science Applications
- Information Systems