A Comparison of Algorithms for Maximum Common Subgraph on Randomly Connected Graphs

  • Horst Bunke
  • Pasquale Foggia
  • Corrado Guidobaldi
  • Carlo Sansone
  • Mario Vento
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2396)

Abstract

A graph g is called a maximum common subgraph of two graphs, g 1 and g 2, if there exists no other common subgraph of g 1 and g 2 that has more nodes than g. For the maximum common subgraph problem, exact and inexact algorithms are known from the literature. Nevertheless, until now no effort has been done for characterizing their performance. In this paper, two exact algorithms for maximum common subgraph detection are described. Moreover a database containing randomly connected pairs of graphs, having a maximum common graph of at least two nodes, is presented, and the performance of the two algorithms is evaluated on this database.

References

  1. 1.
    J.R. Ullmann, “An Algorithm for Subgraph Isomorphism”, Journal of the Association for Computing Machinery, vol. 23, pp. 31–42, 1976.MathSciNetGoogle Scholar
  2. 2.
    L.P. Cordella, P. Foggia C. Sansone, M. Vento, “An Improved Algorithm for Matching Large Graphs”, Proc. of the 3rd IAPR-TC-15 International Workshop on Graph-based Representations, Italy, pp. 149–159, 2001.Google Scholar
  3. 3.
    H. Bunke X. Jiang and A. Kandel, “On the Minimum Supergraph of Two Graphs”, Computing 65, Nos. 13–25, pp. 13–25, 2000.MATHMathSciNetGoogle Scholar
  4. 4.
    H. Bunke and K. Sharer, “A Graph Distance Metric Based on the Maximal Common Subgraph”, Pattern Recognition Letters, Vol. 19, Nos. 3–4, pp. 255–259, 1998.MATHCrossRefGoogle Scholar
  5. 5.
    G. Levi, “A Note on the Derivation of Maximal Common Subgraphs of Two Directed or Undirected Graphs”, Calcolo, Vol. 9, pp. 341–354, 1972.CrossRefMathSciNetGoogle Scholar
  6. 6.
    M. M. Cone, Rengachari Venkataraghven, and F. W. McLafferty, “Molecular Structure Comparison Program for the Identification of Maximal Common Substructures”, Journal of Am. Chem. Soc, 99(23), pp. 7668–7671 1977.CrossRefGoogle Scholar
  7. 7.
    J.J. McGregor, “Backtrack Search Algorithms and the Maximal Common Subgraph Problem”, Software Practice and Experience, Vol. 12, pp. 23–34, 1982.MATHCrossRefGoogle Scholar
  8. 8.
    C. Bron and J. Kerbosch, “Finding All the Cliques in an Undirected Graph”, Communication of the Association for Computing Machinery 16, pp. 575–577, 1973.MATHGoogle Scholar
  9. 9.
    B. T. Messmer, “Efficient Graph Matching Algorithms for Preprocessed Model Graphs”, Ph.D. Thesis, Inst. of Comp. Science and Appl. Mathematics, University of Bern, 1996.Google Scholar
  10. 10.
    M. R. Garey, D. S. Johnson, “Computers and Intractability: A Guide to the Theory of NP-Completeness”, Freeman & Co, New York, 1979.MATHGoogle Scholar
  11. 11.
    I. M. Bomze, M. Budinich, P. M. Pardalos, and M. Pelillo, “The Maximum Clique Problem”, Handbook of Combinatorial Optimization, vol. 4, Kluwer Academy Pub., 1999.Google Scholar
  12. 12.
    P. J. Durand, R. Pasari, J. W. Baker, and Chun-che Tsai, “An Efficient Algorithm for Similarity Analysis of Molecules ”, Internet Journal of Chemistry, vol. 2, 1999.Google Scholar
  13. 13.
    N. J. Nilsson, “Principles of Artificial Intelligence”, Springer-Verlag, 1982.Google Scholar
  14. 14.
    P. Foggia, C. Sansone, M. Vento, “A Database of Graphs for Isomorphism and Sub-Graph Isomorphism Benchmarking”, Proc. of the 3rd IAPR TC-15 International Workshop on Graph-based Representations, Italy, pp. 176–187, 2001.Google Scholar
  15. 15.
    H. Bunke, M. Gori, M. Hagenbuchner C. Irniger, A.C. Tsoi, “Generation of Images Databases using Attributed Plex Grammars”, Proc. of the 3rd IAPR TC-15 International Workshop on Graph-based Representations, Italy, pp. 200–209, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Horst Bunke
    • 1
  • Pasquale Foggia
    • 2
  • Corrado Guidobaldi
    • 1
    • 2
  • Carlo Sansone
    • 2
  • Mario Vento
    • 3
  1. 1.Institut für Informatik und angwandte MathematikUniversität BernBernSwitzerland
  2. 2.Dipartimento di Informatica e SistemisticaUniversità di Napoli “Federico II”NapoliItaly
  3. 3.Dipartimento di Ingegneria dell’Informazione ed Ingegneria ElettricaUniversità di SalernoFiscianoItaly

Personalised recommendations