GTED: Graph Traversal Edit Distance

  • Ali Ebrahimpour Boroojeny
  • Akash Shrestha
  • Ali Sharifi-Zarchi
  • Suzanne Renick Gallagher
  • S. Cenk Sahinalp
  • Hamidreza ChitsazEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10812)


Many problems in applied machine learning deal with graphs (also called networks), including social networks, security, web data mining, protein function prediction, and genome informatics. The kernel paradigm beautifully decouples the learning algorithm from the underlying geometric space, which renders graph kernels important for the aforementioned applications.

In this paper, we give a new graph kernel which we call graph traversal edit distance (GTED). We introduce the GTED problem and give the first polynomial time algorithm for it. Informally, the graph traversal edit distance is the minimum edit distance between two strings formed by the edge labels of respective Eulerian traversals of the two graphs. Also, GTED is motivated by and provides the first mathematical formalism for sequence co-assembly and de novo variation detection in bioinformatics.

We demonstrate that GTED admits a polynomial time algorithm using a linear program in the graph product space that is guaranteed to yield an integer solution. To the best of our knowledge, this is the first approach to this problem. We also give a linear programming relaxation algorithm for a lower bound on GTED. We use GTED as a graph kernel and evaluate it by computing the accuracy of an SVM classifier on a few datasets in the literature. Our results suggest that our kernel outperforms many of the common graph kernels in the tested datasets. As a second set of experiments, we successfully cluster viral genomes using GTED on their assembly graphs obtained from de novo assembly of next generation sequencing reads. Our GTED implementation can be downloaded from


Edit Distance Eulerian Traversal Graph Kernels Assembly Graph Generation Sequencing Reads 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ali Ebrahimpour Boroojeny
    • 1
  • Akash Shrestha
    • 1
  • Ali Sharifi-Zarchi
    • 1
    • 2
    • 3
  • Suzanne Renick Gallagher
    • 1
  • S. Cenk Sahinalp
    • 4
  • Hamidreza Chitsaz
    • 1
    Email author
  1. 1.Colorado State UniversityFort CollinsUSA
  2. 2.Royan InstituteTehranIran
  3. 3.Sharif University of TechnologyTehranIran
  4. 4.Indiana UniversityBloomingtonUSA

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