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On the Complexity of Frequent Subtree Mining in Very Simple Structures

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Inductive Logic Programming

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9046))

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Abstract

We study the complexity of frequent subtree mining in very simple graphs beyond forests. We show for d-tenuous outerplanar graphs that frequent subtrees can be listed with polynomial delay if the cycle degree, i.e., the maximum number of blocks that share a common vertex, is bounded by some constant. The crucial step in the proof of this positive result is a polynomial time algorithm deciding subgraph isomorphism from trees into d-tenuous outerplanar graphs of bounded cycle degree. We obtain this algorithm by generalizing the algorithm of Shamir and Tsur that decides subgraph isomorphism between trees. Our results may also be of some interest to algorithmic graph theory, as they indicate that even for very simple structures, the cycle degree is a crucial parameter for the tractability of subgraph isomorphism. We also discuss some interesting problems towards generalizing the positive result of this work.

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Notes

  1. 1.

    http://cactus.nci.nih.gov/download/nci, Release 4 File Series.

  2. 2.

    We recall that by condition, G contains at least one edge.

  3. 3.

    Though the terminology below follows that of [8] (which, in turn, is based on the concepts in [16]), the definitions of iso-triples and characteristics in this paper are entirely different from those in [8].

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bonn, Bonn, Germany

    Pascal Welke, Tamás Horváth & Stefan Wrobel

  2. Fraunhofer IAIS, Schloss Birlinghoven, Sankt Augustin, Germany

    Tamás Horváth & Stefan Wrobel

Authors
  1. Pascal Welke
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  2. Tamás Horváth
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  3. Stefan Wrobel
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Corresponding author

Correspondence to Pascal Welke .

Editor information

Editors and Affiliations

  1. Department of Computer Science, KU Leuven, Leuven, Belgium

    Jesse Davis

  2. Department of Computer Science, KU Leuven, Leuven, Belgium

    Jan Ramon

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Welke, P., Horváth, T., Wrobel, S. (2015). On the Complexity of Frequent Subtree Mining in Very Simple Structures. In: Davis, J., Ramon, J. (eds) Inductive Logic Programming. Lecture Notes in Computer Science(), vol 9046. Springer, Cham. https://doi.org/10.1007/978-3-319-23708-4_14

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  • DOI: https://doi.org/10.1007/978-3-319-23708-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23707-7

  • Online ISBN: 978-3-319-23708-4

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