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Covering Tree with Stars

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Computing and Combinatorics (COCOON 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7936))

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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.

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Baumbach, J., Guo, J., Ibragimov, R. (2013). Covering Tree with Stars. In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_34

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  • DOI: https://doi.org/10.1007/978-3-642-38768-5_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38767-8

  • Online ISBN: 978-3-642-38768-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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