This paper studies a variation of the classic network alignment problem, named diffusion-network alignment. The goal is to align the vertices of a rooted diffusion tree to the vertices of a network, where the diffusion tree could be from a communication trace or contact tracing, and the network could be an online or offline social network. Different from the classic network alignment where both networks are fully observed, this model captures the information asymmetry of two networks. To solve this problem, this paper presents an efficient algorithm based on tree correlation tests to extract alignment information from local neighborhoods. We analyze the performance of the algorithm in the sparse graph regime and show that with high probability, all matched pairs are correct. Furthermore, for each vertex on the diffusion tree, this paper establishes an explicit lower bound on the probability that the vertex is correctly matched. These lower bounds are depth-dependent and increase as vertices get closer to the root.

翻译：本文研究经典网络对齐问题的一个变体，称为扩散-网络对齐。其目标是将有根扩散树的顶点与网络的顶点进行对齐，其中扩散树可能来自通信轨迹或接触追踪，而网络则可能是在线或离线社交网络。与经典网络对齐中两个网络均被完全观测不同，该模型捕捉了两个网络间的信息不对称性。为解决此问题，本文提出一种基于树相关性检验的高效算法，从局部邻域中提取对齐信息。我们分析了该算法在稀疏图机制下的性能，并证明所有匹配对均以高概率正确。此外，对于扩散树上的每个顶点，本文建立了该顶点被正确匹配的概率显式下界。这些下界具有深度依赖性，并随着顶点靠近根节点而增大。