Electronic Communications in Probability

Rumor source detection for rumor spreading on random increasing trees

Michael Fuchs and Pei-Duo Yu

Full-text: Open access

Abstract

In a recent paper, Shah and Zaman proposed the rumor center as an effective rumor source estimator for rumor spreading on random graphs. They proved for a very general random tree model that the detection probability remains positive as the number of nodes to which the rumor has spread tends to infinity. Moreover, they derived explicit asymptotic formulas for the detection probability of random $d$-regular trees and random geometric trees. In this paper, we derive asymptotic formulas for the detection probability of grown simple families of random increasing trees. These families of random trees contain important random tree models as special cases, e.g., binary search trees, recursive trees and plane-oriented recursive trees. Our results show that the detection probability varies from $0$ to $1$ across these families. Moreover, a brief discussion of the rumor center for unordered trees is given as well.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 2, 12 pp.

Dates
Accepted: 6 January 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465320929

Digital Object Identifier
doi:10.1214/ECP.v20-3743

Mathematical Reviews number (MathSciNet)
MR3304408

Zentralblatt MATH identifier
1306.05223

Subjects
Primary: 05C80: Random graphs [See also 60B20]
Secondary: 60C05: Combinatorial probability

Keywords
rumor spreading rumor center detection probability random increasing trees

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Fuchs, Michael; Yu, Pei-Duo. Rumor source detection for rumor spreading on random increasing trees. Electron. Commun. Probab. 20 (2015), paper no. 2, 12 pp. doi:10.1214/ECP.v20-3743. https://projecteuclid.org/euclid.ecp/1465320929


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