Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 28, 12 pp.
Detecting tampering in a random hypercube
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 $n\to\infty$.
Electron. J. Probab., Volume 18 (2013), paper no. 28, 12 pp.
Accepted: 18 February 2013
First available in Project Euclid: 4 June 2016
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Pinsky, Ross. Detecting tampering in a random hypercube. Electron. J. Probab. 18 (2013), paper no. 28, 12 pp. doi:10.1214/EJP.v18-2290. https://projecteuclid.org/euclid.ejp/1465064253