论文标题
随机几何图的shot弹枪装配
Shotgun Assembly of Random Geometric Graphs
论文作者
论文摘要
在最近的一项工作中，Huang和Tikhomirov考虑了ERD \ H OS-Rényi图形的shot弹枪装配$ \ MATHCAL G（N，P_N）$带有$ p_n = n = n^{ - α} $，并显示该图是可重构的，如果$ 0 <α<α<\ frac {1} $ rconct $ \ frac {1} {2} <α<1 $从其$ 1 $ -neighbourhoods。在本文中，我们考虑了随机的几何图$ g（n，r）$，其中$ r^2 = n^{ - α} $和$ 0 <α<1 $，在扁平圆环上。有趣的是，与ERD \ H OS-Rényi随机图的结果不同，我们表明随机几何图始终可以从其1-纽布时重建。
In a recent work, Huang and Tikhomirov considered the shotgun assembly for Erd\H os-Rényi graphs $\mathcal G(n,p_n)$ with $p_n=n^{-α}$, and showed that the graph is reconstructable if $0<α< \frac{1}{2}$ and not reconstructable if $\frac{1}{2}<α<1$ from its $1$-neighbourhoods. In this article, we consider random geometric graphs $G(n,r)$, where $r^2=n^{-α}$ and $ 0<α<1$, on flat torus. Interestingly, unlike the results for the Erd\H os-Rényi random graphs, we show that the random geometric graph is always reconstructable from its 1-neighbourhoods.
