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Faster Algorithms for Bounded Tree Edit Distance

Authors Shyan Akmal , Ce Jin

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ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • tree edit distance
  • edit distance
  • dynamic programming

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Abstract

Tree edit distance is a well-studied measure of dissimilarity between rooted trees with node labels. It can be computed in O(n³) time [Demaine, Mozes, Rossman, and Weimann, ICALP 2007], and fine-grained hardness results suggest that the weighted version of this problem cannot be solved in truly subcubic time unless the APSP conjecture is false [Bringmann, Gawrychowski, Mozes, and Weimann, SODA 2018].
We consider the unweighted version of tree edit distance, where every insertion, deletion, or relabeling operation has unit cost. Given a parameter k as an upper bound on the distance, the previous fastest algorithm for this problem runs in O(nk³) time [Touzet, CPM 2005], which improves upon the cubic-time algorithm for k≪ n^{2/3}. In this paper, we give a faster algorithm taking O(nk² log n) time, improving both of the previous results for almost the full range of log n ≪ k≪ n/√{log n}.

Cite As Get BibTex

Shyan Akmal and Ce Jin. Faster Algorithms for Bounded Tree Edit Distance. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 12:1-12:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ICALP.2021.12

Author Details

Shyan Akmal
  • MIT, EECS and CSAIL, Cambridge, MA, USA
Ce Jin
  • MIT, EECS and CSAIL, Cambridge, MA, USA

Funding

  • Akmal, Shyan: Supported by NSF Grant CCF-1909429.
  • Jin, Ce: Supported by an MIT Akamai Presidential Fellowship.

Acknowledgements

We thank Virginia Vassilevska Williams for several helpful discussions.

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