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Finding Maximum Common Connected Subgraphs Using Clique Detection or Constraint Satisfaction Algorithms

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Modelling, Computation and Optimization in Information Systems and Management Sciences (MCO 2008)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 14))

Abstract

This paper investigates the problem of Maximum Common Connected Subgraph (MCCS) which is not necessarily an induced subgraph. This problem has so far been neglected by the literature which is mainly devoted to the MCIS problem. Two reductions of the MCCS problem to a MCCIS problem are explored: a classic method based on linegraphs and an original approach using subdivision graphs. Then we propose a method to solve MCCS that searchs for a maximum clique in a compatibility graph. To compare with backtrack approach we explore the applicability of Constraint Satisfaction framework to the MCCS problem for both reductions.

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References

  1. Akutsu, T.: A polynomial time algorithm for finding a largest common subgraph of almost trees of bounded degree. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E76-A(9) (1993)

    Google Scholar 

  2. Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillo, M.: The maximum clique problem. In: Du, D.-Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization (Supplement vol. A), pp. 1–74. Kluwer Academic, Dordrecht (1999)

    Chapter  Google Scholar 

  3. Bron, C., Kerbosch, J.: Finding all cliques of an undirected graph. Communication of the ACM 16(9), 575–579 (1973)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  5. Dooms, G., Deville, Y., Dupont, P.: Cp(graph): Introducing a graph computation domain in constraint programming. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)

    MATH  Google Scholar 

  7. Johnston, H.C.: Cliques of a graph-variations on the bron-kerbosch algorithm. International Journal of Computer and Information Sciences 5(3), 209–238 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. Koch, I.: Enumerating all connected maximal common subgraphs in two graphs. Theoretical Computer Science 250, 1–30 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Laburthe, F., Jussien, N.: Jchoco: A java library for constraint satisfaction problems, http://choco.sourceforge.net

  10. Larossa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Math. Struct. Comput. Sci. 12(4), 403–422 (2002)

    MathSciNet  MATH  Google Scholar 

  11. Levi, G.: A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9(4), 341–352 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  12. McGregor, J.J.: Backtrack search algorithms and the maximal common subgraph problem. Software Practice and Experience 12, 23–34 (1982)

    Article  MATH  Google Scholar 

  13. Meseguer, P., Rossi, F., Schiex, T.: Soft constraints. In: Rossi, et al. (eds.) [16], pp. 281–328

    Google Scholar 

  14. Raymond, J.W., Willett, P.: Maximum common subgraph isomorphism algorithms for the matching of chemical structures. Journal of Computer-Aided Molecular Design 16(7), 521–533 (2002)

    Article  Google Scholar 

  15. Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: AAAI 1994, Proceedings of the National Conference on Artificial Intelligence, Seattle, Washington, pp. 362–367 (1994)

    Google Scholar 

  16. Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  17. Whitney, H.: Congruent graphs and the connectivity of graphs. Am. J. Math. 54, 150–168 (1932)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yamaguchi, A., Mamitsuka, H., Aoki, K.F.: Finding the maximum common subgraph of a partial k-tree and a graph with a polynomially bounded number of spanning trees. Information Processing Letters 92(2), 57–63 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. LIRMM, 161 rue Ada, 34392, Montpellier Cedex 5, France

    Philippe Vismara & Benoît Valery

  2. LASB - Montpellier SupAgro, 2 place Pierre Viala, 34060, Montpellier Cedex 1, France

    Philippe Vismara

Authors
  1. Philippe Vismara
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  2. Benoît Valery
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Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, UFR MIM,, Paul Verlaine University of Metz, Metz, France

    Hoai An Le Thi

  2. Faculty of Sciences, Technology and Communications, University of Luxembourg, Luxembourg

    Pascal Bouvry

  3. Laboratory of Mathematics, National Institute for Applied Sciences, Rouen Mont, Saint Aignan, France

    Tao Pham Dinh

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© 2008 Springer-Verlag Berlin Heidelberg

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Vismara, P., Valery, B. (2008). Finding Maximum Common Connected Subgraphs Using Clique Detection or Constraint Satisfaction Algorithms. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. MCO 2008. Communications in Computer and Information Science, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87477-5_39

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  • DOI: https://doi.org/10.1007/978-3-540-87477-5_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87476-8

  • Online ISBN: 978-3-540-87477-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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