Distance in the forest fire model how far are you from Eve?

Varun Kanade; Reut Levi; Zvi Lotker; Prederik Mallmann-Trenn; Claire Mathieu

doi:10.1137/1.9781611974331.ch109

Distance in the forest fire model how far are you from Eve?

Varun Kanade, Reut Levi, Zvi Lotker, Prederik Mallmann-Trenn, Claire Mathieu

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

1 Scopus citations

Abstract

Leskovec, Kleinberg and Faloutsos (2005) observed that many social networks exhibit properties such as shrinking (i.e. bounded) diameter, densification, and (power-law) heavy tail degree distributions. To explain these phenomena, they introduced a generative model, called the Forest Fire model, and using simulations showed that this model indeed exhibited these properties; however, proving this rigorously was left as an open problem. In this paper, we analyse one of these properties, shrinking diameter. We define a restricted version of their model that incorporates the main features that seem to contribute towards this property, and prove that the graphs generated by this model exhibit shrinking distance to the seed graph. We prove that an even simpler model, the random walk model, already exhibits this phenomenon.

Original language	English
Title of host publication	27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Editors	Robert Krauthgamer
Publisher	Association for Computing Machinery
Pages	1602-1620
Number of pages	19
ISBN (Electronic)	9781510819672
DOIs	https://doi.org/10.1137/1.9781611974331.ch109
State	Published - 2016
Externally published	Yes
Event	27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 - Arlington, United States Duration: 10 Jan 2016 → 12 Jan 2016

Publication series

Name	Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume	3

Conference

Conference	27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016
Country/Territory	United States
City	Arlington
Period	10/01/16 → 12/01/16

Bibliographical note

Publisher Copyright:
© (2016) by SIAM: Society for Industrial and Applied Mathematics.

Access to Document

10.1137/1.9781611974331.ch109

Cite this

Kanade, V., Levi, R., Lotker, Z., Mallmann-Trenn, P., & Mathieu, C. (2016). Distance in the forest fire model how far are you from Eve? In R. Krauthgamer (Ed.), 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 (pp. 1602-1620). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 3). Association for Computing Machinery. https://doi.org/10.1137/1.9781611974331.ch109

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title = "Distance in the forest fire model how far are you from Eve?",

abstract = "Leskovec, Kleinberg and Faloutsos (2005) observed that many social networks exhibit properties such as shrinking (i.e. bounded) diameter, densification, and (power-law) heavy tail degree distributions. To explain these phenomena, they introduced a generative model, called the Forest Fire model, and using simulations showed that this model indeed exhibited these properties; however, proving this rigorously was left as an open problem. In this paper, we analyse one of these properties, shrinking diameter. We define a restricted version of their model that incorporates the main features that seem to contribute towards this property, and prove that the graphs generated by this model exhibit shrinking distance to the seed graph. We prove that an even simpler model, the random walk model, already exhibits this phenomenon.",

author = "Varun Kanade and Reut Levi and Zvi Lotker and Prederik Mallmann-Trenn and Claire Mathieu",

note = "Publisher Copyright: {\textcopyright} (2016) by SIAM: Society for Industrial and Applied Mathematics.; 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016 ; Conference date: 10-01-2016 Through 12-01-2016",

year = "2016",

doi = "10.1137/1.9781611974331.ch109",

language = "אנגלית",

series = "Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms",

publisher = "Association for Computing Machinery",

pages = "1602--1620",

editor = "Robert Krauthgamer",

booktitle = "27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016",

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Kanade, V, Levi, R, Lotker, Z, Mallmann-Trenn, P & Mathieu, C 2016, Distance in the forest fire model how far are you from Eve? in R Krauthgamer (ed.), 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 3, Association for Computing Machinery, pp. 1602-1620, 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, United States, 10/01/16. https://doi.org/10.1137/1.9781611974331.ch109

Distance in the forest fire model how far are you from Eve? / Kanade, Varun; Levi, Reut; Lotker, Zvi et al.
27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016. ed. / Robert Krauthgamer. Association for Computing Machinery, 2016. p. 1602-1620 (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. 3).

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