Open Access
2013 Detecting tampering in a random hypercube
Ross Pinsky
Author Affiliations +
Electron. J. Probab. 18: 1-12 (2013). DOI: 10.1214/EJP.v18-2290


Consider the random hypercube $H_2^n(p_n)$ obtained from the hypercube $H_2^n$ by deleting any given edge with probabilty $1 -p_n$, independently of all the other edges. A diameter path in $H_2^n$ is a longest geodesic path in $H_2^n$. Consider the following two ways of tampering with the random graph $H_2^n(p_n)$: (i) choose a diameter path at random and adjoin all of its edges to $H_2^n(p_n)$; (ii) choose a diameter path at random from among those that start at $0=(0,\cdots, 0)$, and adjoin all of its edges to $H_2^n(p_n)$. We study the question of whether these tamperings are detectable asymptotically as $n\to\infty$.


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Ross Pinsky. "Detecting tampering in a random hypercube." Electron. J. Probab. 18 1 - 12, 2013.


Accepted: 18 February 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1282.05199
MathSciNet: MR3035756
Digital Object Identifier: 10.1214/EJP.v18-2290

Primary: 05C80
Secondary: 60C05

Keywords: Detection , random graph , random hypercube , total variation norm

Vol.18 • 2013
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