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Covering Tree with Stars

  • Jan Baumbach
  • Jiong Guo
  • Rashid Ibragimov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7936)

Abstract

We study the tree edit distance problem with edge deletions and edge insertions as edit operations. We reformulate a special case of this problem as Covering Tree with Stars (CTS): given a tree T and a set \(\cal{S}\) of stars, can we connect the stars in \(\cal{S}\) by adding edges between them such that the resulting tree is isomorphic to T? We prove that in the general setting, CST is NP-complete, which implies that the tree edit distance considered here is also NP-hard, even when both input trees having diameters bounded by 10. We also show that, when the number of distinct stars is bounded by a constant k, CTS can be solved in polynomial time by presenting a dynamic programming algorithm running in \(O(|V(T)|^2\cdot k\cdot |V({\cal S})|^{2k})\) time.

Keywords

graph algorithms tree edit distance NP-completeness dynamic programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jan Baumbach
    • 1
    • 3
  • Jiong Guo
    • 2
  • Rashid Ibragimov
    • 1
  1. 1.Max Planck Institute für InformatikSaarbrückenGermany
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.University of Southern DenmarkOdense MDenmark

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