An Efficient Heuristic for Graph Edit Distance

Xiaoyang Chen, Yujia Wang, Hongwei Huo, Jeffrey Scott Vitter

Abstract: The graph edit distance (GED) is a flexible distance measure widely used in many applications. Existing GED computation methods are usually based upon the tree-based search algorithm that explores all possible vertex (or edge) mappings between two compared graphs. During this process, various GED lower bounds are adopted as heuristic estimations to accelerate the tree-based search algorithm. For the first time, we analyze the relationship among three state-of-the-art GED lower bounds, label edit distance (LED), Hausdorff edit distance (HED), and branch edit distance (BED). Specifically, we demonstrate that BED(G, Q) ≥ HED(G, Q) and BED(G, Q) ≥ LED(G, Q) for any two undirected graphs G and Q. Furthermore, for BED we propose an efficient heuristic BED^+ for improving the tree-based search algorithm. Extensive experiments on real and synthetic datasets confirm that BED^+ achieves smaller deviation and larger solvable ratios than LED, HED and BED when they are employed as heuristic estimations. The source code is available online.

External IDs:dblp:conf/birthday/ChenWHV25