Graph alignment aims at finding the vertex correspondence between two correlated graphs, a task that frequently occurs in graph mining applications such as social network analysis. Attributed graph alignment is a variant of graph alignment, in which publicly available side information or attributes are exploited to assist graph alignment. Existing studies on attributed graph alignment focus on either theoretical performance without computational constraints or empirical performance of efficient algorithms. This motivates us to investigate efficient algorithms with theoretical performance guarantee. In this paper, we propose two polynomial-time algorithms that exactly recover the vertex correspondence with high probability. The feasible region of the proposed algorithms is near optimal compared to the information-theoretic limits. When specialized to the seeded graph alignment problem, the proposed algorithms strictly improve the best known feasible region for exact alignment by polynomial-time algorithms.

翻译：图对齐旨在发现两个相关图之间的顶点对应关系，这一任务频繁出现在社交网络分析等图挖掘应用中。属性图对齐是图对齐的一种变体，其中利用公开可用的辅助信息或属性来辅助图对齐。现有关于属性图对齐的研究要么关注无计算约束的理论性能，要么关注高效算法的实证性能。这促使我们研究具有理论性能保证的高效算法。本文提出了两种多项式时间算法，能够以高概率精确恢复顶点对应关系。与信息论极限相比，所提算法的可行域接近最优。当专门用于种子图对齐问题时，所提算法严格改进了已有通过多项式时间算法实现精确对齐的最佳可行域。