Journal of Combinatorial Optimization

, Volume 29, Issue 1, pp 141–152 | Cite as

Covering tree with stars

Article
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Abstract

We study the tree edit distance (TED) 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 \(\mathcal {S}\) of stars, can we connect the stars in \(\mathcal {S}\) 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 TED considered here is also NP-hard, even when both input trees have 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 \(O(|V(T)|^2\cdot k\cdot |V(\mathcal{S})|^{2k})\) time.

Keywords

Graph algorithms Tree edit distance NP-completeness  Dynamic programming 

Notes

Acknowledgments

Partially supported by the DFG Excellence Cluster MMCI and International Max Planck Research School.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.University of Southern DenmarkOdense MDenmark
  2. 2.Universität des SaarlandesSaarbrückenGermany
  3. 3.Max Planck Institute für InformatikSaarbrückenGermany

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