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Efficient Method to Perform Isomorphism Testing of Labeled Graphs

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Computational Science and Its Applications - ICCSA 2006 (ICCSA 2006)

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

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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.

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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
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  2. Chiun-Chieh Hsu
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  3. Li-Fu Hsu
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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

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© 2006 Springer-Verlag Berlin Heidelberg

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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

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  • 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)

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