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GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism

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Graph-Based Representations in Pattern Recognition (GbRPR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9069))

Abstract

The substitution-tolerant subgraph isomorphism is a particular error-tolerant subgraph matching that allows label substitutions for both vertices and edges. Such a matching is often required in pattern recognition applications since graphs extracted from images are generally labeled with features vectors computed from raw data which are naturally subject to noise. This paper describes an extended version of a Binary Linear Program (BLP) for solving this class of graph matching problem. The paper also presents GEM++, a software framework that implements the BLP and that we have made available for the research community. GEM++ allows the processing of different sub-problems (induced isomorphism or not, directed graphs or not) with complex labelling of vertices and edges. We also present some datasets available for evaluating future contributions in this field.

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References

  1. Cordella, L.P., Foggia, P., Sansone, C., Vento, M.: Performance evaluation of the VF graph matching algorithm. In: Proc. of the Int’l Conf. on Image Analys. and Proc., pp. 1172–1177 (1999)

    Google Scholar 

  2. Cordella, L.P., Foggia, P., Sansone, C., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. on PAMI 26(10), 1367–1372 (2004)

    Article  Google Scholar 

  3. Danna, E., Fenelon, M., Gu, Z., Wunderling, R.: Generating multiple solutions for mixed integer programming problems. In: Fischetti, M., Williamson, D.P. (eds.) IPCO 2007. LNCS, vol. 4513, pp. 280–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. De Santo, M., Foggia, P., Sansone, C., Vento, M.: A large database of graphs and its use for benchmarking graph isomorphism algorithms. Pattern Recogn. Lett. 24(8), 1067–1079 (2003)

    Article  MATH  Google Scholar 

  5. Erdös, P., Rényi, A.: On random graphs. Public. Mathemat. 6, 290–297 (1959)

    MATH  Google Scholar 

  6. Foggia, P., Sansone, C., Vento, M.: A database of graphs for isomorphism and sub-graph isomorphism benchmarking. In: Proc. Third IAPR TC-15 Int’l Workshop Graph Based Representations, pp. 176–187 (2001)

    Google Scholar 

  7. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman & Co. (1979)

    Google Scholar 

  8. Ghahraman, D.E., Wong, A.K.C., Au, T.: Graph optimal monomorphism algorithms. IEEE Transactions on System, Man and Cybernetics 10, 181–188 (1980)

    Article  MATH  Google Scholar 

  9. Le Bodic, P., Héroux, P., Adam, S., Lecourtier, Y.: An integer linear program for substitution-tolerant subgraph isomorphism and its use for symbol spotting in technical drawings. Pattern Recognition 45(12), 4214–4224 (2012)

    Article  Google Scholar 

  10. Le Bodic, P., Locteau, H., Adam, S., Héroux, P., Lecourtier, Y., Knippel, A.: Symbol detection using region adjacency graphs and integer linear programming. In: Proc. of the Int’l Conf. on Doc. Analys. and Recog., pp. 1320–1324 (2009)

    Google Scholar 

  11. Solnon, C.: Alldifferent-based filtering for subgraph isomorphism. Artificial Intelligence 174(12-13), 850–864 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ullmann, J.R.: An algorithm for subgraph isomorphism. J. ACM 23(1), 31–42 (1976)

    Article  MathSciNet  Google Scholar 

  13. Wong, A.K.C., You, M., Chan, S.C.: An algorithm for graph optimal monomorphism. IEEE Transactions on System, Man and Cybernetics 20(3), 628–638 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Julien Lerouge .

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© 2015 Springer International Publishing Switzerland

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Lerouge, J., Le Bodic, P., Héroux, P., Adam, S. (2015). GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism. In: Liu, CL., Luo, B., Kropatsch, W., Cheng, J. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2015. Lecture Notes in Computer Science(), vol 9069. Springer, Cham. https://doi.org/10.1007/978-3-319-18224-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-18224-7_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18223-0

  • Online ISBN: 978-3-319-18224-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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