Marked subgraph isomorphism of ordered graphs

  • Xiaoyi Jiang
  • Horst Bunke
Structural Matching and Grammatical Inference
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1451)


Recently, the concept of ordered graphs has been introduced and it was shown that isomorphism of ordered graphs can be solved in quadratic time. In the present paper we consider a special case of the subgraph isomorphism problem for ordered graphs, called marked subgraph isomorphism. An algorithm of O(m1m2) complexity is developed for finding all marked subgraph isomorphisms from a graph G1 to another graph G2, where m1 and m2 are the number of edges in G1 and G2, respectively. We demonstrate the usefulness of our algorithm by applying it to solving the subcircuit extraction problem. It turns out that our approach is much more efficient than traditional methods based on general subgraph isomorphism techniques.


  1. 1.
    P. Dublish, Some comments on the subtree isomorphism problem for ordered trees, Information Processing Letters, 36: 273–275, 1990.CrossRefGoogle Scholar
  2. 2.
    M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, Freeman and Co., 1979.Google Scholar
  3. 3.
    J.E. Hopcroft and J.K. Wong, Linear time algorithm for isomorphism of planar graphs, Proc. of 6th Annual ACM Symposium on Theory of Computing, 172–184, 1974.Google Scholar
  4. 4.
    X. Jiang and H. Bunke, A simple and efficient algorithm for determining the symmetries of polyhedra, Graphical Models and Image Processing, 54(1):91–95, 1992.CrossRefGoogle Scholar
  5. 5.
    X. Jiang, K. Yu, and H. Bunke, Detection of rotational and involutational symmetries and congruity of polyhedra, The Visual Computer, 12(4): 193–201, 1996.Google Scholar
  6. 6.
    X. Jiang and H. Bunke, Including geometry in graph representations: A quadratictime graph isomorphism algorithm and its applications, In Advances in Structural and Syntactical Pattern Recognition (P. Perner, P. Wang, A. Rosenfeld, Eds.), Lectures Notes in Computer Science 1121, Springer-Verlag, 110–119, 1996.Google Scholar
  7. 7.
    X. Jiang and H. Bunke, On the coding of ordered graphs, Computing, 1998. (to appear)Google Scholar
  8. 8.
    S. Kasif, L. Kitchen, and A. Rosenfeld, A Hough transform technique for subgraph isomorphism, Pattern Recognition Letters, 2: 83–88, 1983.CrossRefGoogle Scholar
  9. 9.
    E.M. Luks, Isomorphism of graphs of bounded valence can be tested in polynomial time, Journal of Computer and System Science, 25: 42–65, 1982.CrossRefGoogle Scholar
  10. 10.
    M. Ohlrich et al., SubGemini: Identifying subcircuits using a fast subgraph isomorphism algorithm, Proc. of 30th ACM1IEEE Design Automation Conference, 31–37, 1993.Google Scholar
  11. 11.
    N. Vijaykrishnan and N. Ranganathan, SUBGEN: A genetic approach for subcircuit extraction, Proc. of Int. Conf. on VLSI Design, Bangalore, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Xiaoyi Jiang
    • 1
  • Horst Bunke
    • 1
  1. 1.Department of Computer ScienceUniversity of BernBernSwitzerland

Personalised recommendations