License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.12
URN: urn:nbn:de:0030-drops-140819
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14081/
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Akmal, Shyan ; Jin, Ce

Faster Algorithms for Bounded Tree Edit Distance

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LIPIcs-ICALP-2021-12.pdf (0.8 MB)

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}.

BibTeX - Entry

@InProceedings{akmal_et_al:LIPIcs.ICALP.2021.12,
  author =	{Akmal, Shyan and Jin, Ce},
  title =	{{Faster Algorithms for Bounded Tree Edit Distance}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{12:1--12:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14081},
  URN =		{urn:nbn:de:0030-drops-140819},
  doi =		{10.4230/LIPIcs.ICALP.2021.12},
  annote =	{Keywords: tree edit distance, edit distance, dynamic programming}
}

Keywords: tree edit distance, edit distance, dynamic programming
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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