An Algorithm Portfolio for the Sub-graph Isomorphism Problem

  • Roberto Battiti
  • Franco Mascia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4638)

Abstract

This work presents an algorithm for the sub-graph isomorphism problem based on a new pruning technique for directed graphs. During the tree search, the method checks if a new association between two vertices is compatible by considering the structure of their local neighborhoods, represented as the number of limited-length paths of different type originating from each vertex. In addition, randomized versions of the algorithms are studied experimentally by deriving their run-time distributions. Finally, algorithm portfolios consisting of multiple instances of the same randomized algorithm are proposed and analyzed. The experimental results on benchmark graphs demonstrate that the new pruning method is competitive w.r.t. recently proposed techniques. Significantly better results are obtained on sparse graphs. Furthermore, even better results are obtained by the portfolios, when both the average and standard deviation of solution times are considered.

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References

  1. 1.
    Ullmann, J.: An Algorithm for Subgraph Isomorphism. Journal of the ACM (JACM) 23(1), 31–42 (1976)CrossRefGoogle Scholar
  2. 2.
    Bunke, H., Messmer, B.T.: Recent advances in graph matching. IJPRAI 11(1), 169–203 (1997)Google Scholar
  3. 3.
    Larrosa, J., Valiente, G.: Constraint satisfaction algorithms for graph pattern matching. Mathematical Structures in Computer Science 12(4), 403–422 (2002)MATHCrossRefGoogle Scholar
  4. 4.
    Cordella, L.P., Pasquale Foggia, C.S., Vento, M.: A (sub)graph isomorphism algorithm for matching large graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(10), 1367–1372 (2004)CrossRefGoogle Scholar
  5. 5.
    Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co, New York, USA (1990)Google Scholar
  6. 6.
    McKay, B.: Practical graph isomorphism. In: Numerical mathematics and computing. In: Proc. 10th Manitoba Conf. Winnipeg/Manitoba, pp. 45–87 (1980)Google Scholar
  7. 7.
  8. 8.
    Huberman, B.A., Lukose, R.M., Hogg, T.: An economics approach to hard computational problems. Science 275, 51–54 (1997)CrossRefGoogle Scholar
  9. 9.
    Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1-2), 43–62 (2001)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Roberto Battiti
    • 1
  • Franco Mascia
    • 1
  1. 1.Università degli Studi di Trento, TrentoItaly

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