Revisiting Volgenant-Jonker for Approximating Graph Edit Distance

  • William JonesEmail author
  • Aziem Chawdhary
  • Andy King
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9069)


Although it is agreed that the Volgenant-Jonker (VJ) algorithm provides a fast way to approximate graph edit distance (GED), until now nobody has reported how the VJ algorithm can be tuned for this task. To this end, we revisit VJ and propose a series of refinements that improve both the speed and memory footprint without sacrificing accuracy in the GED approximation. We quantify the effectiveness of these optimisations by measuring distortion between control-flow graphs: a problem that arises in malware matching. We also document an unexpected behavioural property of VJ in which the time required to find shortest paths to unassigned nodes decreases as graph size increases, and explain how this phenomenon relates to the birthday paradox.


Cost Matrix Edit Operation Memory Footprint Cost Range Graph Edit Distance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Balasn, E., Miller, D., Pekny, J., Toth, P.: A parallel shortest augmenting path algorithm for the assignment problem. JACM 38(4), 985–1004 (1991)CrossRefGoogle Scholar
  2. 2.
    Bourquin, M., King, A., Robbins, E.: BinSlayer: Accurate Comparison of Binary Executables. In: Proceedings of Program Protection and Reverse Engineering Workshop. ACM (2013)Google Scholar
  3. 3.
    Burkard, R.E., Cela, E.: Linear Assignment Problems and Extensions. Springer (1999)Google Scholar
  4. 4.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty Years of Graph Matching in Pattern Recognition. International Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2004)CrossRefGoogle Scholar
  5. 5.
    Gao, X., Xiao, B., Tao, D., Li, X.: A Survey of Graph Edit Distance. Pattern Analysis and Applications 13(1), 113–129 (2010)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Jonker, R., Volgenant, A.: A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems. Computing 38(4), 325–340 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Myers, R., Wison, R.C., Hancock, E.R.: Bayesian graph edit distance. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(6), 628–635 (2000)CrossRefGoogle Scholar
  8. 8.
    Riesen, K., Bunke, H.: Approximate Graph Edit Distance computation by means of Bipartite Graph Matching. Image and Vision Computing 27(7), 950–959 (2009)CrossRefGoogle Scholar
  9. 9.
    Serratosa, F.: Fast computation of bipartite graph matching. Pattern Recognition Letters 45, 244–250 (2014)CrossRefGoogle Scholar
  10. 10.
    Serratosa, F., Cortés, X.: Edit Distance Computed by Fast Bipartite Graph Matching, pp. 253–262 (2014)Google Scholar
  11. 11.
    Zeng, Z., Tung, A.K.H., Wang, J., Feng, J., Zhou, L.: Comparing Stars: On Approximating Graph Edit Distance. VLDB Endowment 2(1), 25–36 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of KentCanterburyUK

Personalised recommendations