Skip to main content
Springer Nature Link
Log in

Efficient Method to Perform Isomorphism Testing of Labeled Graphs

  • Conference paper
Computational Science and Its Applications - ICCSA 2006 (ICCSA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3984))

Included in the following conference series:

Abstract

The need to perform isomorphism testing is emerging recently in many application domains such as graph-based data mining for discovering frequent common patterns in a graph database. Due to the complex nature of graph representations, the isomorphism testing between labeled graphs is one of the most time-consuming phases during the mining process. The canonical form of a graph that serves as the isomorphism certificate needs O(n!) to produce for a graph of order n, or Θ(Π i = 1 c(|π i |!)) if vertex invariants are employed to divide n vertices into c equivalence classes with |π i | vertices in each class i. In this paper, we propose a new algorithm to perform isomorphism testing of labeled graphs with worst case time complexity O(Σ i = 1 c(|π i |!)), in which the product of all |π i |! terms is replaced by the sum of the terms and the asymptotic notation is changed from big theta to big oh. To the best of our knowledge, this proposed model is the latest work that focuses on the dealing of the isomorphism testing of labeled graphs. The result of this algorithm is directly applicable to the fields of graph isomorphism testing for labeled graphs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Artymiuk, P., Poirrette, A., Grindley, H., Rice, D., Willett, P.: A Graph-thoeretic Approach to the Identification of Three-dimensional Patterns of Amino Acid Side-chains in Protein Structures. Journal of Molecular Biology 243(2), 327–344 (1994)

    Article  Google Scholar 

  2. Chartrand, G., Zhang, P. (eds.): Introduction to Graph Theory. McGraw Hill, New York (2002)

    Google Scholar 

  3. Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty Years of Graph Matching in Pattern Recognition. Int’l Journal of Pattern Recognition and Artificial Intelligence 18(3), 265–298 (2004)

    Article  Google Scholar 

  4. Cordella, L., Foggia, P., Sansone, C., Vento, M.: A (Sub)Graph Isomorphism Algorithm for Matching Large Graphs. IEEE Tran. Pattern Analysis and Machine Intelligence 26(10), 1367–1372 (2004)

    Article  Google Scholar 

  5. Foggia, P., Sansone, C., Vento, M.: A Performance Comparison of Five Algorithms for Graph Isomorphism. In: Proc. of the 3rd IAPR-TC15 Workshop on Graph-based Representation (2001)

    Google Scholar 

  6. Gross, J., Yellen, J. (eds.): Handbook of Graph Theory. CRC Press, Florida (2004)

    MATH  Google Scholar 

  7. Hsieh, S.M., Hsu, C.C.: New Method for Similarity Retrieval of Iconic Image Database. In: Proceedings of 2005 SPIE-IS&T Symposium on Electronic Imaging: Conference on Storage and Retrieval Methods and Applications for Multimedia, vol. 5682, pp. 247–257 (2005)

    Google Scholar 

  8. Hong, P., Huang, T.: Mining Inexact Spatial Patterns. In: Workshop on Discrete Mathematics and Data Mining (2002)

    Google Scholar 

  9. Huan, J., Wang, W., Prims, J.: Efficient Mining of Frequent Subgraph in the Presence of Isomorphism, University of North Carolina Computer Science Technical Report (2003)

    Google Scholar 

  10. Kim, N., Shiffeldrim, N., Gan, H., Schlick, T.: Candidates for Novel RNA Topologies. Journal of Molecular Biology 34(1), 1129–1144 (2004)

    Article  Google Scholar 

  11. Kuramochi, M., Karypis, G.: An Efficient Algorithm for Discovering Frequent Subgraphs. IEEE Trans. Knowledge and Data Engineering 16(9), 1038–1051 (2004)

    Article  Google Scholar 

  12. McKay, B.D.: Nauty Users Guide (2003), http://cs.anu.edu.au/~bdm/nauty

  13. McKay, B.D.: Practical Graph Isomorphism. Congressus Numerantium, 30, 45–87 (1981)

    Google Scholar 

  14. Neapolitan, R., Naimipour, K.: Foundations of Algorithms. D. C. Heath and Company, Massachusetts (1996)

    Google Scholar 

  15. Petrakis, E., Faloutsos, C., Lin, K.: ImageMap: An Image Indexing Method Based on Spatial Similarity. IEEE Trans. Knowledge and Data Engineering 14(5), 979–987 (2002)

    Article  Google Scholar 

  16. Theobald, D.: Topology revisited: representing spatial relations. Int’l Journal of Geographical Information Science 15(8), 689–705 (2001)

    Article  Google Scholar 

  17. Valiente, G.: Trading uninitialized space for time. Information Processing Letters 92, 9–13 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Washio, T., Motoda, H.: State of the Art of Graph-Based Data Mining. ACM SIGKDD Exploration Newsletters 5(1), 59–68 (2003)

    Article  Google Scholar 

  19. Yan, X., Han, J.: gSpan: Graph-Based Substructure Pattern Mining. In: Proceedings of 2002 IEEE Int’l Conference on Data Mining (2002)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep. Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan

    Shu-Ming Hsieh, Chiun-Chieh Hsu & Li-Fu Hsu

Authors
  1. Shu-Ming Hsieh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chiun-Chieh Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Li-Fu Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Calgary,, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. OptimaNumerics Ltd.,, Cathedral House 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  5. Clayton School of IT, Monash University, 3800, Clayton, Australia

    David Taniar

  6. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  7. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  8. School of Information and Communication Engineering, Sungkyunkwan University, Korea

    Hyunseung Choo

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hsieh, SM., Hsu, CC., Hsu, LF. (2006). Efficient Method to Perform Isomorphism Testing of Labeled Graphs. In: Gavrilova, M.L., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751649_46

Download citation

  • DOI: https://doi.org/10.1007/11751649_46

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34079-9

  • Online ISBN: 978-3-540-34080-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics