Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

中文翻译：

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二次图中的近似图形编辑距离。

图形编辑距离是可用的最灵活和通用的图形匹配模型之一。但是，图形编辑距离的主要缺点是其计算复杂性，限制了其对相当小尺寸的图形的适用性。最近，本文的作者介绍了一种用于图编辑距离问题的通用逼近框架。该特定算法的基本思想是首先计算独立局部图结构的最佳分配（包括节点和边的替换，删除和插入）。相对于两个图的所涉及节点，此最佳分配是完整且一致的，因此可用于在O（n3）时间内立即导出原始图编辑距离问题的可允许（但次优）解决方案。但是，对于大型图形或图形集，立方时间复杂度可能仍然太高。因此，我们建议使用二次时间而不是三次时间的次优算法来解决基本分配问题。特别是，在图编辑距离近似的背景下，本文介绍了五种不同的贪婪分配算法。在实验评估中，我们表明这些方法具有进一步加速图形编辑距离计算的巨大潜力，而近似距离仍足以针对基于图形的图案分类提供足够的准确性。在图编辑距离近似的背景下，本文介绍了五种不同的贪婪分配算法。在实验评估中，我们表明这些方法具有进一步加速图形编辑距离计算的巨大潜力，而近似距离仍足以针对基于图形的图案分类提供足够的准确性。在图编辑距离近似的背景下，本文介绍了五种不同的贪婪分配算法。在实验评估中，我们表明这些方法具有进一步加速图形编辑距离计算的巨大潜力，而近似距离仍足以针对基于图形的图案分类提供足够的准确性。