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Introducing VF3: A New Algorithm for Subgraph Isomorphism

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Graph-Based Representations in Pattern Recognition (GbRPR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10310))

Abstract

Several graph-based applications require to detect and locate occurrences of a pattern graph within a larger target graph. Subgraph isomorphism is a widely adopted formalization of this problem. While subgraph isomorphism is NP-Complete in the general case, there are algorithms that can solve it in a reasonable time on the average graphs that are encountered in specific real-world applications. In 2015 we introduced one such algorithm, VF2Plus, that was specifically designed for the large graphs encountered in bioinformatics applications. VF2Plus was an evolution of VF2, which had been considered for many years one of the fastest available algorithms. In turn, VF2Plus proved to be significantly faster than its predecessor, and among the fastest algorithms on bioinformatics graphs. In this paper we propose a further evolution, named VF3, that adds new improvements specifically targeted at enhancing the performance on graphs that are at the same time large and dense, that are currently the most problematic case for the state-of-the-art algorithms. The effectiveness of VF3 has been experimentally validated using several publicly available datasets, showing a significant speedup with respect to its predecessor and to the other most advanced state-of-the-art algorithms.

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References

  1. RCSB: Protein data bank web site (2017). http://www.rcsb.org/pdb

  2. Aittokallio, T., Schwikowski, B.: Graph-based methods for analysing networks in cell biology. Brief. Bioinform. 7(3), 243 (2006). http://dx.doi.org/10.1093/bib/bbl022

    Article  Google Scholar 

  3. Bonnici, V., Giugno, R.: On the variable ordering in subgraph isomorphism algorithms. IEEE/ACM Trans. Comput. Biol. Bioinform. PP(99) (2016)

    Google Scholar 

  4. Carletti, V., Foggia, P., Vento, M., Jiang, X.: Report on the first contest on graph matching algorithms for pattern search in biological databases. In: Liu, C.-L., Luo, B., Kropatsch, W.G., Cheng, J. (eds.) GbRPR 2015. LNCS, vol. 9069, pp. 178–187. Springer, Cham (2015). doi:10.1007/978-3-319-18224-7_18

    Chapter  Google Scholar 

  5. 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). doi:10.1007/978-3-642-41190-8_44

    Chapter  Google Scholar 

  6. Carletti, V., Foggia, P., Vento, M.: VF2 plus: an improved version of VF2 for biological graphs. In: Liu, C.-L., Luo, B., Kropatsch, W.G., Cheng, J. (eds.) GbRPR 2015. LNCS, vol. 9069, pp. 168–177. Springer, Cham (2015). doi:10.1007/978-3-319-18224-7_17

    Chapter  Google Scholar 

  7. Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI 18(3), 265–298 (2004)

    Google Scholar 

  8. Cordella, L., Foggia, P., Sansone, C., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Anal. Mach. Intell. 26, 1367–1372 (2004)

    Article  Google Scholar 

  9. Foggia, P., Percannella, G., Vento, M.: Graph matching and learning in pattern recognition on the last ten years. J. Pattern Recognit. 28(1), 1450001 (2014)

    Article  MathSciNet  Google Scholar 

  10. Han, W., Lee, J.h., Lee, J.: TurboISO: towards ultrafast and robust subgraph isomorphism search in large graph databases. In: Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data, pp. 337–348 (2013)

    Google Scholar 

  11. Huan, J., et al.: Comparing graph representations of protein structure for mining family-specific residue-based packing motif. J. Comput. Biol. 12(6), 657–671 (2005)

    Article  Google Scholar 

  12. Lacroix, V., Fernandez, C., Sagot, M.: Motif search in graphs: application to metabolic networks. Trans. Computat. Biol. Bioinform. 4, 360–368 (2006)

    Article  Google Scholar 

  13. Lehmann, J., Isele, R., Jakob, M., Jentzsch, A., Kontokostas, D., Mendes, P.N., Hellmann, S., Morsey, M., van Kleef, P., Auer, S., Bizer, C.: DBpedia - a large-scale, multilingual knowledge base extracted from Wikipedia. Semant. Web J. 6(2), 167–195 (2015)

    Article  Google Scholar 

  14. McGregor, J.: Relational consistency algorithms and their application in finding subgraph and graph isomorphisms. Inf. Sci. 19(3), 229–250 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  15. Solnon, C.: Alldifferent-based filtering for subgraph isomorphism. Artif. Intell. 174(12–13), 850–864 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ullmann, J.R.: An algorithm for subgraph isomorphism. J. Assoc. Comput. Mach. 23, 31–42 (1976)

    Article  MathSciNet  Google Scholar 

  17. Ullmann, J.: Bit-vector algorithms for binary constraint satisfaction and subgraph isomorphism. J. Exp. Algorithm. (JEA) 15(1) (2010)

    Google Scholar 

  18. Vento, M.: A long trip in the charming world of graphs for pattern recognition. Pattern Recognit. 48(1), 11 (2014)

    MathSciNet  Google Scholar 

  19. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications, vol. 8. Cambridge University Press, Cambridge (1994)

    Book  MATH  Google Scholar 

  20. Zampelli, S., Deville, Y., Solnon, C.: Solving subgraph isomorphism problems with constraint programming. Constraints 15(3), 327–353 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang, S., Li, S., Yang, J.: GADDI: Distance Index Based Subgraph Matching In Biological Networks. In: Proceedings of the 12th International Conference on Extending Database Technology: Advances in Database Technology (2009)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Salerno, Italy

    Vincenzo Carletti, Pasquale Foggia, Alessia Saggese & Mario Vento

Authors
  1. Vincenzo Carletti
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  2. Pasquale Foggia
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  3. Alessia Saggese
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  4. Mario Vento
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Corresponding author

Correspondence to Vincenzo Carletti .

Editor information

Editors and Affiliations

  1. Università degli Studi di Salerno, Fisciano, Italy

    Pasquale Foggia

  2. Chinese Academy of Sciences, Beijing, China

    Cheng-Lin Liu

  3. Università degli Studi di Salerno, Fisciano, Italy

    Mario Vento

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Carletti, V., Foggia, P., Saggese, A., Vento, M. (2017). Introducing VF3: A New Algorithm for Subgraph Isomorphism. In: Foggia, P., Liu, CL., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2017. Lecture Notes in Computer Science(), vol 10310. Springer, Cham. https://doi.org/10.1007/978-3-319-58961-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-58961-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58960-2

  • Online ISBN: 978-3-319-58961-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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