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A binary linear programming formulation of the graph edit distance.

Derek Justice1, Alfred Hero

  • 1Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue, Ann Arbor, MI 48109-2122, USA. justiced@umich.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 5, 2006
PubMed
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This study introduces a new graph edit distance metric using binary linear programming for comparing graphs with attributes. This method effectively addresses graph recognition challenges in chemical information systems.

Area of Science:

  • Computer Science
  • Graph Theory
  • Computational Chemistry

Background:

  • Graph edit distance (GED) is crucial for comparing graph structures.
  • Existing GED methods may not efficiently handle graphs with vertex attributes.
  • Graph recognition tasks require robust and scalable comparison metrics.

Purpose of the Study:

  • To develop a novel binary linear programming formulation for graph edit distance.
  • To ensure the derived graph edit distance satisfies metric properties.
  • To apply and evaluate this new metric in a chemical graph recognition problem.

Main Methods:

  • Formulated graph edit distance using binary linear programming for unweighted, undirected graphs with vertex attributes.
  • Proved the derived graph edit distance is a metric under specific cost function conditions.

Related Experiment Videos

  • Developed polynomial-time methods for calculating upper and lower bounds of the binary program solution.
  • Utilized a minimum normalized variance criterion for optimizing edit operation costs.

    • Main Results:

    • The binary linear programming formulation provides a computable graph edit distance.
    • Efficient algorithms for bounding the solution were derived.
    • The new metric demonstrated strong performance in chemical graph recognition tasks.
    • The method outperformed existing metrics on a database of chemical graphs.

    Conclusions:

    • The proposed binary linear programming approach offers an effective method for calculating graph edit distance.
    • This metric is suitable for graph recognition, particularly in cheminformatics.
    • The approach provides a scalable and accurate solution for comparing graphs with attributes.