






























In the graph shotgun assembly problem, we are given the balls of radius $r$ around each vertex of a graph and asked to reconstruct the graph. We study the shotgun assembly of the Erdős-Rényi random graph $\mathcal G(n,p)$ for a wide range of values of $r$. We determine the threshold for reconstructibility for each $r\geq 3$, extending and improving substantially on results of Mossel and Ross for $r=3$. For $r=2$, we give upper and lower bounds that improve on results of Gaudio and Mossel by polynomial factors. We also give a sharpening of a result of Huang and Tikhomirov for $r=1$.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。