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An Efficient Heuristic for Graph Edit Distance

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

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Subject Classification

ACM Subject Classification
  • Information systems → Query optimization
Keywords
  • Graph edit distance
  • Label edit distance
  • Hausdorff edit distance
  • Branch edit distance
  • Tree-based search
  • Heuristics

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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.

Cite As Get BibTex

Xiaoyang Chen, Yujia Wang, Hongwei Huo, and Jeffrey Scott Vitter. An Efficient Heuristic for Graph Edit Distance. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/OASIcs.Grossi.1

Author Details

Xiaoyang Chen
  • Department of Computer Science, Xidian University, Xi'an, China
Yujia Wang
  • Department of Computer Science, Xidian University, Xi'an, China
Hongwei Huo
  • Department of Computer Science, Xidian University, Xi'an, China
Jeffrey Scott Vitter
  • Department of Computer Science, Tulane University, New Orleans, LA, USA
  • The University of Mississippi, MS, USA

Funding

This work was supported in part by the National Natural Science Foundation of China under Grant No. 62272358.

Supplementary Materials

References

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