随机超立方体中的篡改检测
Detecting Tampering in a Random Hypercube
摘要：
考虑从超立方体$H_2^n$中删除任意给定边得到的随机超立方体$H_2^n(p_n)$，该边的概率为$1-p_n$，与所有其他边无关。$H_2^n$中的直径路径是$H_2^n$中的最长测地线路径。考虑以下两种篡改随机图$H_2^n(p_n)$的方法：（i）随机选择一条直径路径，并将其所有边邻接到$H_2^n(p_n)$ ;（ii）从那些从$0=(0,..., 0)$开始的直径路径中随机选择一条直径路径，并将其所有边邻接到$H_2^n(p_n)$。我们研究的问题，这些篡改是否渐近检测为$n\to\infty$。
英文摘要：
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 $0=(0,..., 0)$, and adjoin all of its edges to $H_2^n(p_n)$. We study the question of whether these tamperings are detectable asymptotically as $n\to\infty$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
