The graph edit distance (GED) is a flexible distance measure which is widely used for inexact graph matching. Since its exact computation is 𝒩𝒫-hard, heuristics are used in practice. A popular approach is to obtain upper bounds for GED via transformations to the linear sum assignment problem with error-correction (LSAPE). Typically, local structures and distances between them are employed for carrying out this transformation, but recently also machine learning techniques have been used. In this paper, we formally define a unifying framework LSAPE-GED for transformations from GED to LSAPE. We also introduce rings, a new kind of local structures designed for graphs where most information resides in the topology rather than in the node labels. Furthermore, we propose two new ring-based heuristics RING and RING-ML, which instantiate LSAPE-GED using the traditional and the machine learning-based approach for transforming GED to LSAPE, respectively. Extensive experiments show that using rings for upper bounding GED significantly improves the state of the art on datasets where most information resides in the graphs’ topologies. This closes the gap between fast but rather inaccurate LSAPE-based heuristics and more accurate but significantly slower GED algorithms based on local search.

中文翻译：

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基于环和机器学习的上边界图编辑距离

图编辑距离（GED）是一种灵活的距离度量，广泛用于不精确的图匹配。因为它的精确计算是𝒩𝒫-hard，启发式在实践中使用。一种流行的方法是通过对具有纠错的线性和分配问题 (LSAPE) 的转换来获得 GED 的上限。通常，使用局部结构和它们之间的距离来执行这种转换，但最近也使用了机器学习技术。在本文中，我们正式定义了一个统一的框架LSAPE-GED用于从 GED 到 LSPE 的转换。我们还介绍了环，这是一种为图设计的新型局部结构，其中大多数信息位于拓扑中而不是节点标签中。此外，我们提出了两种新的基于环的启发式算法戒指和环-ML, 实例化LSAPE-GED分别使用传统和基于机器学习的方法将 GED 转换为 LSAPE。大量实验表明，使用环作为上限 GED 显着提高了大多数信息位于图形拓扑中的数据集的最新技术。这缩小了快速但相当不准确的基于 LSAPE 的启发式算法与更准确但明显较慢的基于本地搜索的 GED 算法之间的差距。