A First Step Towards Exact Graph Edit Distance Using Bipartite Graph Matching

  • Miquel FerrerEmail author
  • Francesc Serratosa
  • Kaspar Riesen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9069)


In recent years, a powerful approximation framework for graph edit distance computation has been introduced. This particular approximation is based on an optimal assignment of local graph structures which can be established in polynomial time. However, as this approach considers the local structural properties of the graphs only, it yields sub-optimal solutions that overestimate the true edit distance in general. Recently, several attempts for reducing this overestimation have been made. The present paper is a starting point towards the study of sophisticated heuristics that can be integrated in these reduction strategies. These heuristics aim at further improving the overall distance quality while keeping the low computation time of the approximation framework. We propose an iterative version of one of the existing improvement strategies. An experimental evaluation clearly shows that there is large space for further substantial reductions of the overestimation in the existing approximation framework.


Search Tree Edit Distance Tree Node Iterative Version Edit Operation 
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.
    Sanfeliu, A., Fu, K.-S.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man and Cybernetics SMC-13(3), 353–362 (1983)CrossRefGoogle Scholar
  2. 2.
    Bunke, H., Allermann, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)CrossRefzbMATHGoogle Scholar
  3. 3.
    Neuhaus, M., Bunke, H.: A graph matching based approach to fingerprint classification using directional variance. In: Kanade, T., Jain, A., Ratha, N.K. (eds.) AVBPA 2005. LNCS, vol. 3546, pp. 191–200. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Robles-Kelly, A., Hancock, E.R.: Graph edit distance from spectral seriation. IEEE Trans. Pattern Anal. Mach. Intell. 27(3), 365–378 (2005)CrossRefGoogle Scholar
  5. 5.
    Gao, X., Xiao, B., Tao, D., Li, X.: A survey of graph edit distance. Pattern Anal. Appl. 13(1), 113–129 (2010)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Boeres, M.C., Ribeiro, C.C., Bloch, I.: A randomized heuristic for scene recognition by graph matching. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 100–113. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Sorlin, S., Solnon, C.: Reactive tabu search for measuring graph similarity. In: Brun, L., Vento, M. (eds.) GbRPR 2005. LNCS, vol. 3434, pp. 172–182. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Justice, D., Hero, A.O.: A binary linear programming formulation of the graph edit distance. IEEE Trans. PAMI 28(8), 1200–1214 (2006)CrossRefGoogle Scholar
  9. 9.
    Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR&SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vision Comput. 27(7), 950–959 (2009)CrossRefGoogle Scholar
  11. 11.
    Serratosa, F.: Fast computation of bipartite graph matching. Pattern Recognition Letters 45, 244–250 (2014)CrossRefGoogle Scholar
  12. 12.
    Burkard, R.E., Dell’Amico, M., Martello, S.: Assignment Problems. SIAM (2009)Google Scholar
  13. 13.
    Riesen, K., Fischer, A., Bunke, H.: Combining bipartite graph matching and beam search for graph edit distance approximation. In: El Gayar, N., Schwenker, F., Suen, C. (eds.) ANNPR 2014. LNCS, vol. 8774, pp. 117–128. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  14. 14.
    Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: da Vitoria Lobo, et al. (eds.) [15], pp. 287–297Google Scholar
  15. 15.
    da Vitoria Lobo, N., Kasparis, T., Roli, F., Kwok, J.T., Georgiopoulos, M., Anagnostopoulos, G.C., Loog, M. (eds.): SSPR&SPR 2008. LNCS, vol. 5342. Springer, Heidelberg (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Miquel Ferrer
    • 1
    Email author
  • Francesc Serratosa
    • 2
  • Kaspar Riesen
    • 1
  1. 1.Institute for Information SystemsUniversity of Applied Sciences and ArtsOltenSwitzerland
  2. 2.Departament d’Enginyeria Informàtica i MatemàtiquesUniversitat Rovira i VirgiliTarragonaSpain

Personalised recommendations