On the Feasible Region of Efficient Algorithms for Attributed Graph Alignment

TL;DR

This paper introduces two polynomial-time algorithms for attributed graph alignment that achieve near-optimal feasible regions, extending the known limits and improving the theoretical guarantees for exact vertex correspondence recovery.

Contribution

The paper proposes two efficient algorithms with theoretical guarantees for attributed graph alignment, expanding the feasible region close to information-theoretic limits.

Findings

Algorithms recover vertex correspondence with high probability.

Feasible region is near optimal compared to theoretical limits.

Extends the best known feasible region for seeded graph alignment.

Abstract

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.