Flexible Graph Similarity Computation With A Proactive Optimization Strategy

Graph Edit Distance (GED) is an important similarity measure in graph retrieval, which quantifies the minimum cost of transforming one graph into another through edit operations, and offers flexibility by allowing customizable operation costs. Recent learning-based approaches approximate GEDs with the distances between representations in vector spaces. However, these methods often struggle with varying operation costs due to neglecting the impact of these costs on determining optimal graph mappings. Furthermore, they rely on isolated node distances as guidance, necessitating inefficient reactive refinements of mappings. To address these issues, we propose Graph Edit Network (GEN), a novel learning-based approach for flexible GED computation. By identifying the limitations of existing methods in capturing flexibility of GED, we introduce a principled yet simple solution that incorporates the operation costs before establishing mappings. To improve matching efficiency, we propose a strategy that proactively optimizes guidance from a graph perspective. This strategy initializes guidance as each node's alignment difficulty and captures the interdependencies between matches within and across graphs through a difficulty propagation mechanism, enabling more informed decisions. As a result, GEN selects optimal matches in a single step, minimizing the need for costly refinements. Results on real-world and synthetic datasets demonstrate the effectiveness, time efficiency, and adaptability of GEN, achieving up to 37.8\% error reduction and 72.7\% inference time reduction compared with state-of-the-art models, while performing robustly under varying cost settings and graph sizes.