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
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)
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)
Bron, C., Kerbosch, J.: Finding all cliques of an undirected graph. Communication of the ACM 16(9), 575–579 (1973)
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI 18(3), 265–298 (2004)
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)
Harary, F.: Graph Theory. Addison-Wesley, Reading (1969)
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)
Koch, I.: Enumerating all connected maximal common subgraphs in two graphs. Theoretical Computer Science 250, 1–30 (2001)
Laburthe, F., Jussien, N.: Jchoco: A java library for constraint satisfaction problems, http://choco.sourceforge.net
Larossa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Math. Struct. Comput. Sci. 12(4), 403–422 (2002)
Levi, G.: A note on the derivation of maximal common subgraphs of two directed or undirected graphs. Calcolo 9(4), 341–352 (1972)
McGregor, J.J.: Backtrack search algorithms and the maximal common subgraph problem. Software Practice and Experience 12, 23–34 (1982)
Meseguer, P., Rossi, F., Schiex, T.: Soft constraints. In: Rossi, et al. (eds.) [16], pp. 281–328
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)
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)
Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier, Amsterdam (2006)
Whitney, H.: Congruent graphs and the connectivity of graphs. Am. J. Math. 54, 150–168 (1932)
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)
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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
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