AI 中文总结
本文针对多图对齐与相关性检测，提出基于最后匹配的方法，将两图逆界扩展至多图，推导了高斯与Erdos-Renyi模型下的相关逆界。
AI 中文摘要
本文聚焦于m个相关图的对齐以及m个图间相关性检测的信息论逆界。对于m≥3的简单思路是，若m-1个图的对齐作为额外信息（例如由精灵提供）被揭示，仍需完成剩余1个图与其他图的对齐，即必须完成最后匹配。对于高斯模型和Erdos-Renyi模型，最后匹配问题等价于仅含两个观测图的问题，为将m=2时的逆界扩展至更大的m提供了途径。尽管该方法对图对齐而言相当直观，但本文证明其也可用于推导相关性弱检测的逆界。
英文摘要
The paper focuses on information theoretic converse bounds for the alignment of $m$ correlated graphs and for the detection of correlation among $m$ graphs. A simple idea for $m\geq 3$ is that if the alignment of $m-1$ of the graphs is revealed as extra information (by a genie for example) then it is still necessary to produce the alignment between the one remaining graph and the others, i.e. the last matching must be accomplished. For both Gaussian and Erdos-Renyi models, the last-matching problem is equivalent to one with two observed graphs, providing a path to extend converse bounds for $m=2$ to larger $m$. While the method is rather obvious for alignment, we show that the method can also be used to derive converse bounds for weak detection of correlation.
