This Article 
 Bibliographic References 
 Add to: 
A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection
May 1998 (vol. 20 no. 5)
pp. 493-504

Abstract—In this paper, we propose a new algorithm for error-correcting subgraph isomorphism detection from a set of model graphs to an unknown input graph. The algorithm is based on a compact representation of the model graphs. This representation is derived from the set of model graphs in an off-line preprocessing step. The main advantage of the proposed representation is that common subgraphs of different model graphs are represented only once. Therefore, at run time, given an unknown input graph, the computational effort of matching the common subgraphs for each model graph onto the input graph is done only once. Consequently, the new algorithm is only sublinearly dependent on the number of model graphs. Furthermore, the new algorithm can be combined with a future cost estimation method that greatly improves its run-time performance.

[1] H. Bunke and G. Allerman, "Inexact Graph Matching for Structural Pattern Recognition," Pattern Recognition Letters, vol. 1, no. 4, pp. 245-253, 1983.
[2] J. Ben-Arie and A.Z. Meiri, "3D-Object Recognition by Optimal Matching Search of Multinary Relation Graphs," Computer Vision, Graphics, and Image Processing, vol. 37, pp. 345-361, 1987.
[3] W.J. Christmas, J. Kittler, and M. Petrou, “Structural Matching in Computer Vision Using Probabilistic Relaxation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 749–764, Aug. 1995.
[4] M.S. Costa and L.G. Shapiro, "Analysis of Scenes Containing Multiple Non-Polyhedral 3D Objects," C. Braccini, L. DeFloriani, and G. Vernazza, eds., Lectures Notes in Computer Science 974: Image Analysis and Processing. Springer Verlag, 1995.
[5] M.A. Eshera and K.S. Fu, "A Graph Distance Measure for Image Analysis," IEEE Trans. Systems, Man, and Cybernetics, vol. 14, no. 3, pp. 398-408, May 1984.
[6] J. Feng, M. Laumy, and M. Dhome, "Inexact Matching Using Neural Networks," E.S. Gelsema and L.N. Kanal, eds., Pattern Recognition in Practice IV: Multiple Paradigms, Comparative Studies, and Hybrid Systems, pp. 177-184. North-Holland, 1994.
[7] C.L. Forgy, "Rete, A Fast Algorithm for the Many Pattern/Many Object Pattern Match Problem," Artificial Intelligence, vol. 19, pp. 17-37. Elvesier, 1982.
[8] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman and Company, 1979.
[9] J. Kittler, W.J. Christmas, and M. Petrou, "Probabilistic Relaxation for Matching of Symbolic Structures," H. Bunke, ed., Advances in Structural and Syntactic Pattern Recognition, pp. 471-480. World Scientific, 1992.
[10] S.W. Lee, J.H. Kim, and F.C.A. Groen, "Translation- Rotation- and Scale Invariant Recognition of Hand-Drawn Symbols in Schematic Diagrams," Int'l J. Pattern Recognition and Artificial Intelligence, vol. 4, no. 1, pp. 1-15, 1990.
[11] S.W. Lu, Y. Ren, and C.Y. Suen, "Hierarchical Attributed Graph Representation and Recognition of Handwritten Chinese Characters," Pattern Recognition, vol. 24, pp. 617-632, 1991.
[12] H.S. Lee and M.I. Schor, "Match Algorithms for Generalized Rete Networks," Artificial Intelligence, pp. 255-270, 1992.
[13] B.T. Messmer and H. Bunke, "Automatic Learning and Recognition of Graphical Symbols in Engineering Drawings," K. Tombre and R. Kasturi, eds., Graphics Recognition, Lecture Notes in Computer Science, vol. 1,072, pp. 123-134. Springer Verlag, 1996.
[14] B.T. Messmer, "Efficient Graph Matching Algorithms for Preprocessed Model Graphs," PhD thesis, Institut für Informatik und angewandte Mathematik, Universität Bern, Switzerland, 1995.
[15] N.J. Nilsson, Principles of Artificial Intelligence.Palo Alto, Calif.: Tioga, 1980.
[16] K. Sengupta and K.L. Boyer, “Organizing Large Structural Modelbases,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 4, pp. 321-332, Apr. 1995.
[17] A. Sanfeliu and K.S. Fu, "A Distance Measure Between Attributed Relational Graphs for Pattern Recognition," IEEE Trans. Systems, Man, and Cybernetics, vol. 13, pp. 353-363, 1983.
[18] L.G. Shapiro and R.M. Haralick, "Structural Descriptions and Inexact Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 3, pp. 504-519, 1981.
[19] L.G. Shapiro and R.M. Haralick, "Organization of Relational Models for Scene Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, pp. 595-602, 1982.
[20] H. Sossa and R. Horaud, Model Indexing: The Graph-Hashing Approach Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 811-815, 1992.
[21] D.S. Seong, H.S. Kim, and K.H. Park, "Incremental Clustering of Attributed Graphs," IEEE Trans. Systems, Man, and Cybernetics, vol. 23, no. 5, pp. 1,399-1,411, 1993.
[22] W.H. Tsai and K.S Fu, "Error-Correcting Isomorphisms of Attributed Relational Graphs for Pattern Recognition," IEEE Trans. Systems, Man, and Cybernetics, vol. 9, pp. 757-768, 1979.
[23] R.A. Wagner and M.J. Fischer, "The String-to-String Correction Problem," J. Assoc. Computing Machinery, vol. 21, no. 1, pp. 168-173, 1974.
[24] E.K. Wong, "Three-Dimensional Object Recognition by Attributed Graphs," H. Bunke and A. Sanfeliu, eds., Syntactic and Structural Pattern Recognition-Theory and Applications, pp. 381-414. World Scientific, 1990.
[25] A.K.C Wong, M. You, and S.C. Chan, “An Algorithm for Graph Optimal Monomorphism,” IEEE Trans. Systems, Man and Cybernetics, vol. 20, no. 3, pp. 628-636, May/June 1990.
[26] L. Xu and E. Oja, "Improved Simulated Annealing, Boltzmann Machine, and Attributed Graph Matching," L. Almeida, ed., Lecture Notes in Computer Science, vol. 412, pp. 151-161. Springer Verlag, 1990.

Index Terms:
Graphs, subgraph isomorphism, graph matching, error-correcting graph matching, search, graph algorithms, graph decomposition.
Bruno T. Messmer, Horst Bunke, "A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 493-504, May 1998, doi:10.1109/34.682179
Usage of this product signifies your acceptance of the Terms of Use.