### Abstract

This paper studies information source detection in networks under the independent cascade (IC) model. Assume the spread of information starts from a single source in a network and a complete snapshot of the network is obtained at some time. The goal is to identify the source based on the observation. We derive the maximum a posterior (MAP) estimator of the source for tree networks and propose a Short-Fat Tree (SFT) algorithm for general networks based on the MAP estimator. The algorithm selects the Jordan infection center [1] and breaks ties according the degree of boundary infected nodes. Loosely speaking, the algorithm selects the node such that the breadth-first search (BFS) tree from it has the minimum depth but the maximum number of leaf nodes. On the Erdos-Renyi (ER) random graph, we establish the following possibility and impossibility results: (i) when the infection duration 0.5, SFT identifies the source with probability 1 (w.p.1) asymptotically (as network size increases to infinity), where n is the network size and μ is the average node degree; (ii) when the infection duration > [log n/ log μ ] + 2, the probability of identifying the source approaches zero asymptotically under any algorithm; and (iii) when infection duration < 0, asymptotically, at least 1-δ fraction of the nodes on the BFS tree starting from the source are leaf-nodes, where δ = 3√log n/μ, i.e., the BFS tree starting from the actual source is a fat tree. 1Numerical experiments on tree networks, the ER random graphs and real world networks with different evaluation metrics show that the SFT algorithm outperforms existing algorithms.

Original language | English (US) |
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Title of host publication | IEEE INFOCOM 2016 - 35th Annual IEEE International Conference on Computer Communications |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Volume | 2016-July |

ISBN (Electronic) | 9781467399531 |

DOIs | |

State | Published - Jul 27 2016 |

Event | 35th Annual IEEE International Conference on Computer Communications, IEEE INFOCOM 2016 - San Francisco, United States Duration: Apr 10 2016 → Apr 14 2016 |

### Other

Other | 35th Annual IEEE International Conference on Computer Communications, IEEE INFOCOM 2016 |
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Country | United States |

City | San Francisco |

Period | 4/10/16 → 4/14/16 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Electrical and Electronic Engineering

### Cite this

*IEEE INFOCOM 2016 - 35th Annual IEEE International Conference on Computer Communications*(Vol. 2016-July). [7524363] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/INFOCOM.2016.7524363

**Information source detection in networks : Possibility and impossibility results.** / Zhu, Kai; Ying, Lei.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE INFOCOM 2016 - 35th Annual IEEE International Conference on Computer Communications.*vol. 2016-July, 7524363, Institute of Electrical and Electronics Engineers Inc., 35th Annual IEEE International Conference on Computer Communications, IEEE INFOCOM 2016, San Francisco, United States, 4/10/16. https://doi.org/10.1109/INFOCOM.2016.7524363

}

TY - GEN

T1 - Information source detection in networks

T2 - Possibility and impossibility results

AU - Zhu, Kai

AU - Ying, Lei

PY - 2016/7/27

Y1 - 2016/7/27

N2 - This paper studies information source detection in networks under the independent cascade (IC) model. Assume the spread of information starts from a single source in a network and a complete snapshot of the network is obtained at some time. The goal is to identify the source based on the observation. We derive the maximum a posterior (MAP) estimator of the source for tree networks and propose a Short-Fat Tree (SFT) algorithm for general networks based on the MAP estimator. The algorithm selects the Jordan infection center [1] and breaks ties according the degree of boundary infected nodes. Loosely speaking, the algorithm selects the node such that the breadth-first search (BFS) tree from it has the minimum depth but the maximum number of leaf nodes. On the Erdos-Renyi (ER) random graph, we establish the following possibility and impossibility results: (i) when the infection duration 0.5, SFT identifies the source with probability 1 (w.p.1) asymptotically (as network size increases to infinity), where n is the network size and μ is the average node degree; (ii) when the infection duration > [log n/ log μ ] + 2, the probability of identifying the source approaches zero asymptotically under any algorithm; and (iii) when infection duration < 0, asymptotically, at least 1-δ fraction of the nodes on the BFS tree starting from the source are leaf-nodes, where δ = 3√log n/μ, i.e., the BFS tree starting from the actual source is a fat tree. 1Numerical experiments on tree networks, the ER random graphs and real world networks with different evaluation metrics show that the SFT algorithm outperforms existing algorithms.

AB - This paper studies information source detection in networks under the independent cascade (IC) model. Assume the spread of information starts from a single source in a network and a complete snapshot of the network is obtained at some time. The goal is to identify the source based on the observation. We derive the maximum a posterior (MAP) estimator of the source for tree networks and propose a Short-Fat Tree (SFT) algorithm for general networks based on the MAP estimator. The algorithm selects the Jordan infection center [1] and breaks ties according the degree of boundary infected nodes. Loosely speaking, the algorithm selects the node such that the breadth-first search (BFS) tree from it has the minimum depth but the maximum number of leaf nodes. On the Erdos-Renyi (ER) random graph, we establish the following possibility and impossibility results: (i) when the infection duration 0.5, SFT identifies the source with probability 1 (w.p.1) asymptotically (as network size increases to infinity), where n is the network size and μ is the average node degree; (ii) when the infection duration > [log n/ log μ ] + 2, the probability of identifying the source approaches zero asymptotically under any algorithm; and (iii) when infection duration < 0, asymptotically, at least 1-δ fraction of the nodes on the BFS tree starting from the source are leaf-nodes, where δ = 3√log n/μ, i.e., the BFS tree starting from the actual source is a fat tree. 1Numerical experiments on tree networks, the ER random graphs and real world networks with different evaluation metrics show that the SFT algorithm outperforms existing algorithms.

UR - http://www.scopus.com/inward/record.url?scp=84983315337&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983315337&partnerID=8YFLogxK

U2 - 10.1109/INFOCOM.2016.7524363

DO - 10.1109/INFOCOM.2016.7524363

M3 - Conference contribution

VL - 2016-July

BT - IEEE INFOCOM 2016 - 35th Annual IEEE International Conference on Computer Communications

PB - Institute of Electrical and Electronics Engineers Inc.

ER -