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Search Strategies for Subgraph Isomorphism Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8321))

Abstract

Searching for subgraph isomorphisms is an essential problem in pattern matching. Most of the algorithms use a branch-and-bound method to sequentially assign pattern nodes to compatible nodes in the target graph. It is well known that the order in which nodes are assigned, a so-called search strategy, influences drastically the size of the search space. In this article we investigate the impact of various search strategies on the efficiency of two algorithms, the first being the Ullmann’s algorithm and the second one the recently proposed improvement of Ullmann’s algorithm. From the large set of proposed orders we find the most successful ones by thorough testing on a large database of graphs.

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References

  1. Balaban, A.T.: Applications of graph theory in chemistry. Journal of Chemical Information and Computer Sciences 25(3), 334–343 (1985)

    MathSciNet  Google Scholar 

  2. Carrington, P.J., Scott, J., Wasserman, S.: Models and methods in social network analysis. Cambridge University Press (2005)

    Google Scholar 

  3. Cordella, L.P., Foggia, P., Sansone, C., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Trans. Pattern Analysis and Machine Intelligence 26(10), 1367–1372 (2004)

    Article  Google Scholar 

  4. De Santo, M., Foggia, P., Sansone, C., Vento, M.: A large database of graphs and its use for benchmarking graph isomorphism algorithms. Pattern Recognition Letters 24(8), 1067–1079 (2003)

    Article  MATH  Google Scholar 

  5. Foggia, P., Sansone, C.: A performance comparison of five algorithms for graph isomorphism. In: TC-15 Workshop on Graph-based Representations in Pattern Recognition (2001)

    Google Scholar 

  6. Foggia, P., Sansone, C., Vento, M.: A database of graphs for isomorphism and sub-graph isomorphism benchmarking. In: Proc. of the 3rd IAPR TC-15 International Workshop on Graph-based Representations (2001)

    Google Scholar 

  7. Foggia, P., Sansone, C., Vento, M.: A Performance Comparison of Five Algorithm for Graph Isomorphism. In: 3rd IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition (2001)

    Google Scholar 

  8. Fürer, M., Prasad Kasiviswanathan, S.: Approximately counting embeddings into random graphs. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 416–429. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Gupta, A., Nishimura, N.: The complexity of subgraph isomorphism for classes of partial k-trees. Theoretical Computer Science 164(1), 287–298 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. He, Y., Evans, A.: Graph theoretical modeling of brain connectivity. Current Opinion in Neurology 23(4), 341–350 (2010)

    Google Scholar 

  11. Krahmer, E., Van Erk, S., Verleg, A.: Graph-based generation of referring expressions. Computational Linguistics 29(1), 53–72 (2003)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. Mihelič, J., Čibej, U.: Improvements of ullmann’s algorithm for subgraph isomorphism (submitted for publication, 2013)

    Google Scholar 

  14. Solnon, C.: All Different-based filtering for subgraph isomorphism. Artificial Intelligence 174(12-13), 850–864 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ullmann, J.R.: An Algorithm for Subgraph Isomorphism. J. Assoc. for Computing Machinery 23, 31–42 (1976)

    Article  MathSciNet  Google Scholar 

  16. Valiente, G.: Algorithms on Trees and Graphs. Springer (2002)

    Google Scholar 

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Čibej, U., Mihelič, J. (2014). Search Strategies for Subgraph Isomorphism Algorithms. In: Gupta, P., Zaroliagis, C. (eds) Applied Algorithms. ICAA 2014. Lecture Notes in Computer Science, vol 8321. Springer, Cham. https://doi.org/10.1007/978-3-319-04126-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-04126-1_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04125-4

  • Online ISBN: 978-3-319-04126-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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