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A Hungarian Algorithm for Error-Correcting Graph Matching

  • Sébastien BougleuxEmail author
  • Benoit Gaüzère
  • Luc Brun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10310)

Abstract

Bipartite graph matching algorithms become more and more popular to solve error-correcting graph matching problems and to approximate the graph edit distance of two graphs. However, the memory requirements and execution times of this method are respectively proportional to \((n+m)^2\) and \((n+m)^3\) where n and m are the order of the graphs. Subsequent developments reduced these complexities. However, these improvements are valid only under some constraints on the parameters of the graph edit distance. We propose in this paper a new formulation of the bipartite graph matching algorithm designed to solve efficiently the associated graph edit distance problem. The resulting algorithm requires \(\mathcal {O}(nm)\) memory space and \(\mathcal {O}(\min (n,m)^2\max (n,m))\) execution times.

Keywords

Graph edit distance Bipartite matching Error-correcting matching Hungarian algorithm 

References

  1. 1.
    Bougleux, S., Brun, L.: Linear sum assignment with edition. Technical report, Normandie Univ, GREYC UMR 6072, Caen (2016)Google Scholar
  2. 2.
    Bougleux, S., Brun, L., Carletti, V., Foggia, P., Gaüzère, B., Vento, M.: Graph edit distance as a quadratic assignment problem. Pattern Recognit. Lett. 87, 38–46 (2017)CrossRefGoogle Scholar
  3. 3.
    Bougleux, S., Gaüzère, B., Brun, L.: Graph edit distance as a quadratic program. In: International Conference on Pattern Recognition. IEEE (2016)Google Scholar
  4. 4.
    Bourgeois, F., Lassalle, J.: An extension of the Munkres algorithm for the assignment problem to rectangular matrices. Commun. ACM 14, 802–804 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Burkard, R., Dell’Amico, M., Martello, S.: Assignment Problems. SIAM, Philadelphia (2009)CrossRefzbMATHGoogle Scholar
  6. 6.
    Gaüzère, B., Bougleux, S., Riesen, K., Brun, L.: Approximate graph edit distance guided by bipartite matching of bags of walks. In: Fränti, P., Brown, G., Loog, M., Escolano, F., Pelillo, M. (eds.) S+SSPR 2014. LNCS, vol. 8621, pp. 73–82. Springer, Heidelberg (2014). doi: 10.1007/978-3-662-44415-3_8 Google Scholar
  7. 7.
    Jones, W., Chawdhary, A., King, A.: Revisiting Volgenant-Jonker for approximating graph edit distance. In: Liu, C.-L., Luo, B., Kropatsch, W.G., Cheng, J. (eds.) GbRPR 2015. LNCS, vol. 9069, pp. 98–107. Springer, Cham (2015). doi: 10.1007/978-3-319-18224-7_10 Google Scholar
  8. 8.
    Jonker, R., Volgenant, A.: Improving the Hungarian assignment algorithm. Oper. Res. Lett. 5, 171–175 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lawler, E.: Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New York (1976)zbMATHGoogle Scholar
  10. 10.
    Leordeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: Advances in Neural Information Processing Systems, vol. 22, pp. 1114–1122 (2009)Google Scholar
  11. 11.
    Neuhaus, M., Bunke, H.: A quadratic programming approach to the graph edit distance problem. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 92–102. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-72903-7_9 CrossRefGoogle Scholar
  12. 12.
    Riesen, K., Bunke, H.: Approximate graph edit distance computation by means of bipartite graph matching. Image Vis. Comput. 27, 950–959 (2009)CrossRefGoogle Scholar
  13. 13.
    Serratosa, F.: Fast computation of bipartite graph matching. Pattern Recognit. Lett. 45, 244–250 (2014)CrossRefGoogle Scholar
  14. 14.
    Serratosa, F.: Speeding up fast bipartite graph matching through a new cost matrix. Int. J. Pattern Recognit. 29(2), 1550010 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Sébastien Bougleux
    • 1
    Email author
  • Benoit Gaüzère
    • 2
  • Luc Brun
    • 1
  1. 1.Normandie Univ, CNRS - ENSICAEN - UNICAENCaenFrance
  2. 2.Normandie Univ, INSA de RouenRouenFrance

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