Electronic Communications in Probability

Rumor source detection for rumor spreading on random increasing trees

Michael Fuchs and Pei-Duo Yu

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

rumor spreading rumor center detection probability random increasing trees

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


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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  • Barabasi, Albert-Laszlo; Albert, Reka. Emergence of scaling in random networks. Science 286 (1999), no. 5439, 509–512.
  • Bergeron, Francois; Flajolet, Philippe; Salvy, Bruno. Varieties of increasing trees, CAAP '92, Rennes, 1992, 24–48, Lecture Notes in Comput. Sci., 581, Springer, Berlin, 1992.
  • Feng, Qunqiang; Mahmoud, Hosam M. On the variety of shapes on the fringe of a random recursive tree. J. Appl. Probab. 47 (2010), no. 1, 191–200.
  • Fill, James Allen. On the distribution of binary search trees under the random permutation model. Random Structures Algorithms 8 (1996), no. 1, 1–25.
  • Flajolet, Philippe; Sedgewick, Robert. Analytic combinatorics. Cambridge University Press, Cambridge, 2009, xiv+810 pp. ISBN: 978-0-521-89806-5
  • Kuba, Markus; Panholzer, Alois. On the degree distribution of the nodes in increasing trees. J. Combin. Theory Ser. A 114 (2007), no. 4, 597–618.
  • Kuba, Markus; Panholzer, Alois. On moment sequences and mixed Poisson distributions, arXiv:1403.2712.
  • Moon, J. W. The distance between nodes in recursive trees, Combinatorics Proc. British Combinatorial Conf., Univ. Coll. Wales, Aberystwyth, 1973, pp. 125–132, London Math. Soc. Lecture Note Ser., No. 13, Cambridge Univ. Press, London, 1974.
  • Panholzer, Alois; Prodinger, Helmut. Level of nodes in increasing trees revisited. Random Structures Algorithms 31 (2007), no. 2, 203–226.
  • Shah, Devavrat; Zaman, Tauhid. Finding sources of computer viruses in networks: Theory and experiment, in Proc. ACM Sigmetrics 15 (2010), 5249–5262.
  • Shah, Devavrat; Zaman, Tauhid. Rumors in a network: who's the culprit? IEEE Trans. Inform. Theory 57 (2011), no. 8, 5163–5181.
  • Shah. Devavrat; Zaman, Tauhid. Finding rumor sources on random graphs, arXiv:1110.6230.