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 under the seeded Erd\H{o}s--R\'{e}nyi graph pair model, the proposed algorithms extends the best known feasible region for exact alignment by polynomial-time algorithms.

翻译：图对齐旨在寻找两个相关图之间的顶点对应关系，这是社交网络分析等图挖掘应用中频繁出现的任务。属性图对齐是图对齐的一种变体，其中利用公开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经验性能。这促使我们研究具有理论性能保证的高效算法。本文提出两种多项式时间算法，它们能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。当特化为种子Erdős–Rényi图对模型下的种子图对齐问题时，所提算法通过多项式时间算法扩展了已知的最佳精确对齐可行域。