VF2 Plus: An Improved version of VF2 for Biological Graphs

  • Vincenzo CarlettiEmail author
  • Pasquale Foggia
  • Mario Vento
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9069)


Subgraph isomorphism is a common problem in several application fields where graphs are the best suited data representation, but it is known to be an NP-Complete problem. However, several algorithms exist that are fast enough on commonly encountered graphs so as to be practically usable; among them, for more than a decade VF2 has been the state of the art algorithm used to solve this problem and it is still the reference algorithm for many applications. Nevertheless, VF2 has been designed and implemented ten years ago when the structural features of the commonly used graphs were considerably different. Hence a renovation is required to make the algorithm able to compete in the challenges arisen in the last years, such as the use of graph matching on the very large graphs coming from bioinformatics applications. In this paper we propose a significant set of enhancements to the original VF2 algorithm that enable it to compete with more recently proposed graph matching techniques. Finally, we evaluate the effectiveness of these enhancement by comparing the matching performance both with the original VF2 and with several recent algorithms, using both the widely known MIVIA graph database and another public graph dataset containing real-world graphs from bioinformatics applications.


Resource Description Framework Constraint Programming Graph Match Sparse Graph Graph Isomorphism 
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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  1. 1.
    Bonnici, V., Giugno, R., Pulvirenti, A., Shasha, D., Ferro, A.: A subgraph isomorphism algorithm and its application to biochemical data. BMC Bioinformatics 14 (2013)Google Scholar
  2. 2.
    Carletti, V., Foggia, P., Vento, M.: Performance Comparison of Five Exact Graph Matching Algorithms on Biological Databases. In: Petrosino, A., Maddalena, L., Pala, P. (eds.) ICIAP 2013. LNCS, vol. 8158, pp. 409–417. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in Pattern Recognition. IJPRAI 18(3), 265–298 (2004)Google Scholar
  4. 4.
    Cordella, L., Foggia, P., Sansone, C., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 26, 1367–1372 (2004)CrossRefGoogle Scholar
  5. 5.
    Dahm, N., Bunke, H., Caelli, T., Gao, Y.: Efficient subgraph matching using topological node feature constraints. Pattern Recognition (June 2014)Google Scholar
  6. 6.
    Foggia, P., Percannella, G., Vento, M.: Graph Matching And Learning In Pattern Recognition On The Last Ten Years. …Journal of Pattern Recognition …(2014)Google Scholar
  7. 7.
    Han, W.S., Lee, J.H., Lee, J.H.: Turbo Iso: Towards Ultrafast And Robust Subgraph Isomorphism Search In Large Graph Databases. In: …of the 2013 International Conference on …, pp. 337–348 (2013)Google Scholar
  8. 8.
    He, H., Singh, A.K.: Graphs-At-A-Time: Query Language And Access Methods For Graph Databases. In: Proceedings of the 2008 ACM SIGMOD International …, pp. 405–417 (2008)Google Scholar
  9. 9.
    Huan, J., et al: Comparing graph representations of protein structure for mining family-specific residue-based packing motif. Journal of Computational Biology (2005)Google Scholar
  10. 10.
    Lacroix, V., Fernandez, C., Sagot, M.: Motif search in graphs: Application to metabolic networks. Transactions on computational biology and bioinformatics (Dicember 2006)Google Scholar
  11. 11.
    Larrosa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Mathematical Structures in Computer Science 12, 403–422 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    McGregor, J.: Relational consistency algorithms and their application in finding subgraph and graph isomorphisms. Information Sciences 19(3), 229–250 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    RCSB: Protein data bank web site (June 2015),
  14. 14.
    Shang, H., Zhang, Y., Lin, X., Yu, J.X.: Taming Verification Hardness: An Efficient Algorithm for Testing Subgraph Isomorphism, pp. 364–375 (2008)Google Scholar
  15. 15.
    Solnon, C.: Alldifferent-based filtering for subgraph isomorphism. Artificial Intelligence 174(12-13), 850–864 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Ullman, J.R.: An algorithm for subgraph isomorphism. J. Assoc. Comput. Mach. 23, 31–42 (1976)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Ullmann, J.: Bit-Vector Algorithms For Binary Constraint Satisfaction And Subgraph Isomorphism. Journal of Experimental Algorithmics (JEA) 15(1) (2010)Google Scholar
  18. 18.
    Vento, M.: A Long Tri. In: The Charming World Of Graphs For Pattern Recognition. Pattern Recognition, 1–11 (January 2014)Google Scholar
  19. 19.
    Vento, M., Jiang, X., Foggia, P.: International contest on pattern search in biological databases (June 2015),
  20. 20.
    Zampelli, S., Deville, Y., Solnon, C.: Solving subgraph isomorphism problems with constraint programming. Constraints 15(3), 327–353 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Zhang, S., Li, S., Yang, J.: GADDI: Distance Index Based Subgraph Matching In Biological Networks. In: …of the 12th International Conference on …(2009)Google Scholar
  22. 22.
    Zhao, P., Han, J.: On Graph Query Optimization In Large Networks. Proceedings of the VLDB Endowment 3(1-2), 340–351 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Vincenzo Carletti
    • 1
    Email author
  • Pasquale Foggia
    • 1
  • Mario Vento
    • 1
  1. 1.DIEM, Department of Information Engineering, Electrical Engineering and Applied MathematicsUniversity of SalernoSalernoItaly

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