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Developing Heuristic for Subgraph Isomorphism Problem

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 306))

Abstract

Subgraph isomorphism problem is an NP-hard problem and the available algorithms are of exponential time complexity. Hence these are not efficient for real world applications. A number of heuristic methods are proposed in the literature in this field. Ullmann[6] proposed a solution for subgraph isomorphism problem in 1976, which is being referred till today. Ullmann’s algorithm is refined to get better algorithms in current literature. Cordella et al.[7] proposed an algorithm VF2, that improves Ullmann’s refinement. In this project, we propose a heuristic to be applied to Ullmann’s algorithm in order to reduce the search space. We show that the proposed heuristic performs better than both Ullmann’s and VF2 algorithm. The testing is done using a graph generation software[12]. Further the heuristic algorithm is tested on the benchmark data set [4]. Both the experiments show that our proposed heuristics perform better for all type of graphs given in the benchmark data set.

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References

  1. Corneil, D.G., Gotlieb, C.C.: An Efficient Algorithm for Graph Isomorphism. Journal of the ACM (JACM) 17(1) (1970)

    Google Scholar 

  2. Qiu, M., Hu, H., Jiang, Q., Hu, H.: A New Approach of Graph Isomorphism Detection based on Decision Tree. In: Second International Workshop on Education Technology and Computer Science, vol. 2, pp. 32–35 (2010)

    Google Scholar 

  3. Zager, L.A., Verghese, G.C.: Graph Similarity Scoring and Matching. Applied Mathematics Letters 21(1), 86–94 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Foggia, P.: A Database of Graphs for Isomorphism and Sub-Graph Isomorphism, http://amalfi.dis.unina.it/graph/

  5. Lipets, V., Vanetik, N., Gudes, E.: Subsea: an efficient heuristic algorithm for subgraph isomorphism. In: Data Mining and Knowledge Discovery, vol. 19(3), pp. 320–350 (2009)

    Google Scholar 

  6. Ullmann, J.R.: An Algorithm for Subgraph Isomorphism. Journal of the ACM 23(1) (1976)

    Google Scholar 

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

    Article  Google Scholar 

  8. Randi, M.: On Canonical Numbering of Atoms in a Molecule and Graph Isomorphism. Journal of Chemical Information and Computer Sciences, 171–180 (1977)

    Google Scholar 

  9. Kuramochi, M., Karypis, G.: An Efficient Algorithm for Discovering Frequent Subgraphs. IEEE Transactions on Knowledge and Data Engineering 16(9) (2004)

    Google Scholar 

  10. Messmer, B.T., Bunke, H.: A Decision Tree Approach to Graph and Subgraph Isomorphism Detection. Pattern Recognition 32(12), 1979–1998 (1999)

    Article  Google Scholar 

  11. Battiti, R., Mascia, F.: An Algorithm Portfolio for the Sub-graph Isomorphism Problem. In: Stützle, T., Birattari, M., Hoos, H.H. (eds.) SLS 2007. LNCS, vol. 4638, pp. 106–120. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. Viger, F., Latapy, M.: Efficient and Simple Generation of Random Simple Connected Graphs with Prescribed Degree Sequence. In: Computing and Combinatorics Conference (2005), http://www-rp.lip6.fr/~latapy/FV/generation.html

  13. Blondel, V.D., Gajardo, A., Heymans, M., Senellart, P., Van Dooren, P.: A Measure of Similarity between Graph Vertices: Applications to Synonym Extraction and Web Searching. Applications to Synonym Extraction and Web Searching. SIAM Review 46, 647–666 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Kaijar, S., Bhavani, S.D. (2012). Developing Heuristic for Subgraph Isomorphism Problem. In: Parashar, M., Kaushik, D., Rana, O.F., Samtaney, R., Yang, Y., Zomaya, A. (eds) Contemporary Computing. IC3 2012. Communications in Computer and Information Science, vol 306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32129-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-32129-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32128-3

  • Online ISBN: 978-3-642-32129-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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