Finding the Maximum Common Subgraph of a Partial k-Tree and a Graph with a Polynomially Bounded Number of Spanning Trees

  • Atsuko Yamaguchi
  • Hiroshi Mamitsuka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2906)


The maximum common subgraph problem is NP-hard even if the two input graphs are partial k-trees. We present a polynomial time algorithm for finding the maximum common connected induced subgraph of two bounded degree graphs G1 and G2, where G1 is a partial k-tree and G2 is a graph whose possible spanning trees are polynomially bounded. The key idea of our algorithm is that for each spanning tree generated from G2, a candidate for the maximum common connected induced subgraph is generated in polynomial time since a subgraph of a partial k-tree is also a partial k-tree. Among all of these candidates, we can find the maximum common connected induced subgraph for G1 and G2.


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  1. 1.
    Akutsu, T.: A polynomial time algorithm for finding a largest common subgraph of almost trees of bounded degree. IEICE Trans. Fundamentals E76-A, 1488–1493 (1993)Google Scholar
  2. 2.
    Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. on Algebraic and Discrete Methods 8, 277–284 (1987)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arnborg, S., Proskurowski, A.: Linear time algorithms for NP-hard problems on graphs embedded in k-trees. Discrete Appl. Math. 23, 11–24 (1989)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25, 1305–1317 (1996)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bayada, D.M., Simpson, R.W., Johnson, A.P.: An algorithm for the multiple common subgraph problem. J. Chem. Inf. Comput. Sci. 32, 680–685 (1992)Google Scholar
  6. 6.
    Ding, G.: Graphs with not too many spanning trees. Networks 25, 193–197 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman (1987)Google Scholar
  8. 8.
    Gupta, A., Nishimura, N.: The complexity of subgraph isomorphisms for classes of partial k-trees. Theoret. Comput. Sci. 30, 402–404 (2002)Google Scholar
  9. 9.
    Goto, S., Okuno, Y., Hattori, M., Nishioka, T., Kanehisa, M.: LIGAND: database of chemical compounds and reactions in biological pathways. Nucleic Acids Res. 30, 402–404 (2002)CrossRefGoogle Scholar
  10. 10.
    Kann, V.: On the approximability of the maximum common subgraph problem. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 377–388. Springer, Heidelberg (1992)Google Scholar
  11. 11.
    van Leeuwen, J.: Handbook of Theoretical Computer Science. Algorithm and Complexity, vol. A. Elsevier Science Pub., Amsterdam (1990)Google Scholar
  12. 12.
    Matoušek, J., Thomas, R.: On the complexity of finding iso- and other morphisms for partial k-trees. Discrete Math. 108, 343–364 (1992)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sanders, D.: On linear recognition of tree-width at most four. SIAM J. Discrete Math. 108, 343–364 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Atsuko Yamaguchi
    • 1
  • Hiroshi Mamitsuka
    • 1
  1. 1.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityGokasho, UjiJapan

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