Pattern Recognition Letters ( IF 3.9 ) Pub Date : 2018-05-03 , DOI: 10.1016/j.patrec.2018.05.002 David B. Blumenthal , Johann Gamper
The graph edit distance is a widely used distance measure for labelled graph. However, the standard approach for its exact computation, suffers from huge runtime and memory requirements. Recently, three better performing algorithms have been proposed: The general algorithms and and the algorithm which only works for uniform edit costs. All newly proposed algorithms outperform the standard approach . However, cross-comparisons are lacking. This paper consolidates and extends these recent advances. To this purpose, we present all existing algorithms in a unified way and show that the slightly different definitions of the graph edit distance underlying and on the one side, and on the other side, can be harmonised. This harmonisation allows us to develop a generalisation of to non-uniform edit cost. Moreover, we present a speed-up of and for uniform edit costs, which build upon the fact that, in the uniform case, a continuously used subroutine can be implemented to run in linear rather than cubic time. We also suggest an algorithm which builds upon a very compact new mixed integer linear programming formulation. Finally, we carry out a thorough empirical evaluation, which, for the first time, compares all existing exact algorithms.
中文翻译：
关于图形编辑距离的精确计算
图形编辑距离是标记图形广泛使用的距离度量。然而，精确计算的标准方法遭受巨大的运行时和内存需求。最近，提出了三种性能更好的算法：通用算法 和 和算法 仅适用于统一的编辑费用。所有新提出的算法均优于标准方法。但是，缺乏交叉比较。本文巩固并扩展了这些最新进展。为此，我们以统一的方式介绍了所有现有算法，并表明图编辑距离的基本定义略有不同 和 一方面， 另一方面，可以协调。这种统一使我们能够对费用不一致。此外，我们提出了 和 在统一情况下，可以实现连续使用的子例程以线性而不是三次时间运行的事实，从而获得统一的编辑成本。我们还建议一种算法它基于非常紧凑的新混合整数线性规划公式。最后，我们进行了全面的经验评估，这是首次将所有现有的精确算法进行比较。
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