A New Error-Correcting Distance for Attributed Relational Graph Problems

  • Yasser El-Sonbaty
  • M. A. Ismail
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)


In this paper a new distance for attributed relational graphs is proposed. The main idea of the new algorithm is to decompose the graphs to be matched into smaller subgraphs. The matching process is then done at the level of the decomposed subgraphs based on the concept of error-correcting transformations. The distance between two graphs is found to be the minimum of a weighted bipartite graph constructed from the decomposed subgraphs. The average computational complexity of the proposed distance is found to be O(N 4), which is much better than many techniques.


Input Graph Graph Match Graph Isomorphism Graph Grammar Subgraph Isomorphism 
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  1. 1-.
    Sanfeliu A., Fu K. S.: A Distance Between Attributed Relational Graphs for Pattern Recognition, IEEE Trans, on Sys., Man and Cybernetics, Vol. 13, No. 3, (1983) 353–362.zbMATHGoogle Scholar
  2. 2-.
    El-Sonbaty Yasser, Ismail, M. A.: A New Algorithm for Subgraph Optimal Isomorphism, Pattern Recognition, Vol. 31, No. 2. (1998) 205–218.CrossRefGoogle Scholar
  3. 3-.
    Wong, A. K. C., You, M, Chan, S. C.: An Algorithm for Graph Optimal Monomorphism, IEEE Tran, on Sys., Man and Cybernetics, Vol. 20, No. 3, (1990) 628–636.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4-.
    Shapiro, L. G. Haralick, R. M.: Structural Descriptions and Inexact Matching, Tech. Rep. CS-79011-R, Virginia Polytech. Inst. and State Univ., Blacksburg VA, (Nov. 1979).Google Scholar
  5. 5-.
    Kitchen, L.: Relaxation Applied to Matching Quantitative Relational Structures, IEEE Tran, on Sys., Man and Cybernetics, Vol. 10, No. 2, (1980).Google Scholar
  6. 6-.
    Ghahraman, D. E., Wong, A. K. C., Au, T.: Graph Optimal Monomorphism Algorithms, IEEE Tran, on Sys., Man and Cybernetics, Vol. 10, No. 4, (1980).Google Scholar
  7. 7-.
    Tsai, W., Fu, K. S.: Subgraph Error-Correcting Isomorphisms for Syntactic Pattern Recognition, IEEE Tran, on Sys., Man and Cybernetics, Vol. 13, No. 1, (1983) 48–62.zbMATHMathSciNetGoogle Scholar
  8. 8-.
    Suganthan, P., Teoh, E., Mital, D.: Pattern Recognition by Graph Matching Using the Potts MFT Neural Networks Pattern Recognition, Vol. 28, (1995) 997–1009.Google Scholar
  9. 9-.
    Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching, IEEE Trans, on PAMI, Vol. 18, No. 4, (1996) 377–388.Google Scholar
  10. 10-.
    Depiero, F., Trivedi, M., Serbin, S.: Graph Matching Using a Direct Classification of Node Attendance Pattern Recognition, Vol. 29, No. 6, (1996) 1031–1048.Google Scholar
  11. 11-.
    Umeyama, S.: An Eigendecomposition Approach to Weighted Graph Matching Problems, IEEE Trans, on PAMI, Vol. 10, No. 5, (1988) 695–703.zbMATHGoogle Scholar
  12. 12-.
    Almohamad, H. A.: A Polynomial Transform for Matching Pairs of Weighted Graphs, J. Applied Math. Modeling, Vol. 15, No. 4, (1991).Google Scholar
  13. 13-.
    Almohamad, H. A., Duffuaa, S. O.: A Linear Programming Approach for the Weighted Graph Matching Problem, IEEE Trans, on PAMI, Vol 15, No. 5.(1993).Google Scholar
  14. 14-.
    Tsai W. H., Fu K. S.: Error-Correcting Isomorphism of Attributed Relational Graphs for Pattern Rec, IEEE Trans, on Sys., Man, and Cybernetics, Vol. 9, No. 12, (1979) 757–768.zbMATHCrossRefGoogle Scholar
  15. 15-.
    Schoning U.,: Graph Isomorphism is in the Low Hierarchy, J. of Computer and System Sciences, No. 37, (1988) 312–323.Google Scholar
  16. 16-.
    You, M., Wong, A. K. C.: An Algorithm for Graph Optimal Isomorphism, in Proc. 1984 ICPR, (1984) 316–319.Google Scholar
  17. 17-.
    Stacey D. A., Wong, A. K. C.:A Largest Common Subgraph Isomorphism Algorithm for Attributed Graphs, Tech. Report, Dept. of System Design Eng., U. of Waterloo, Waterloo, ONT, June 1988.Google Scholar
  18. 18-.
    Shoukry A., Aboutabl M.: Neural Network Approach for Solving the Maximal Common Subgraph Problem, IEEE Trans, on Sys., Man, and Cyber., Vol. 26, No. 5, (Oct. 1996).Google Scholar
  19. 19-.
    Bayada D. M., Simpson R. W., Johnson A. P.: An Algorithm for the Multiple Common Subgraph Problem, J. Chem. Inf. Comput. Sci., Vol. 32, (1992) 680–685.CrossRefGoogle Scholar
  20. 20-.
    Lowe, A.: Three Dimension Object Recognition from Single Two Dimension Images, Artificial Int., Vol. 31,(1987) 335–395.Google Scholar
  21. 21-.
    Schalkoff R.: Pattern Recognition: Statistical, Structural and Neural Approaches, John Wiley & Sons Inc., (1992).Google Scholar
  22. 22-.
    Shaw A. C.: A Formal Picture Description Scheme or a Basis for Picture Processing Systems, Information and Control, Vol. 14, (1969) 9–52.zbMATHGoogle Scholar
  23. 23-.
    Pavilidis T.: Linear and Context-Free Graph Grammars, JACM, Vol. 19, (1972) 11–22.CrossRefGoogle Scholar
  24. 24-.
    Tanaka E.: Theoretical Aspects of Syntactic Pattern Recognition, Pattern Recognition, Vol. 28, No. 7, (1995) 1053–1061.CrossRefGoogle Scholar
  25. 25-.
    Kajitani Y., Sakurai H.,: On Distance of Graphs Defined by Use of Orthogonality Between Circuits and Cutsets Rep. CT-73-30, The Inst. of Elect, and Comm., Engineers of Japan, (1973).Google Scholar
  26. 26-.
    Tanaka E.: A Metric on Graphs and its Applications, IEE Japan ip-77-55, OCT. 31, (1977).Google Scholar
  27. 27-.
    Eshera M. A., Fu K. S.: An Image Understanding System Using Attributed Symbolic Representation and Inexact Graph Matching, PAMI, Vol. 8, No. 5, (1986) 604–617.Google Scholar
  28. 28-.
    Eshera M. A., Fu K. S.: A Graph Distance Measure for Image Analysis, IEEE Tran, on Sys., Man and Cybernetics, Vol. 14, No. 3, (1984) 398–408.zbMATHGoogle Scholar
  29. 29-.
    Shapiro L., Haralick R.: A Metric for Relational Descriptions, IEEE Trans. Pattern Analysis 4and Mach. Int., 7, (1985) 90–94.CrossRefGoogle Scholar
  30. 30-.
    Cinque L., Yasuda D., Shapiro L. G., Tanimoto S., Allen B.: An Improved Algorithm for Relational Distance Graph Matching, Pattern Recognition, Vol. 29, No. 2, (1996) 349–359.CrossRefGoogle Scholar
  31. 31-.
    Kuhn, H. W.: The Hungarian Method for the Assignment Problem, Naval Res. Log. Quart., No. 12, (1955) 83–97.Google Scholar
  32. 32-.
    Karp, R. M.: An Algorithm to Solve the m*n Assignment Problem in expected time O(mn log n), Networks, No. 10, (1980) 143–152.Google Scholar
  33. 33-.
    Yamada, S., Kasai, T.: An Efficient Algorithm for the Linear Assignment Problem, Elect, and Comm. in Japan, Part 3, Vol. 73, No. 12, (1990) 28–36.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Yasser El-Sonbaty
    • 1
  • M. A. Ismail
    • 2
  1. 1.Dept. of Computer Eng.Arab Academy for Science & Tech.AlexandriaEgypt
  2. 2.Dept. of Computer Sc.Faculty of EngineeringAlexandriaEgypt

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