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.ISAAC.2022.44
URN: urn:nbn:de:0030-drops-173295
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Akutsu, Tatsuya ; Mori, Tomoya ; Nakamura, Naotoshi ; Kozawa, Satoshi ; Ueno, Yuhei ; Sato, Thomas N.

On the Complexity of Tree Edit Distance with Variables

LIPIcs-ISAAC-2022-44.pdf (0.7 MB)


In this paper, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas. We analyze the computational complexity of several variants of this model. In particular, we show that the problem is NP-complete for ordered trees. We also show for unordered trees that the problem of deciding whether or not the distance is 0 is graph isomorphism complete but can be solved in polynomial time if the maximum outdegree of input trees is bounded by a constant. We also present parameterized and exponential-time algorithms for ordered and unordered cases, respectively.

BibTeX - Entry

  author =	{Akutsu, Tatsuya and Mori, Tomoya and Nakamura, Naotoshi and Kozawa, Satoshi and Ueno, Yuhei and Sato, Thomas N.},
  title =	{{On the Complexity of Tree Edit Distance with Variables}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{44:1--44:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-173295},
  doi =		{10.4230/LIPIcs.ISAAC.2022.44},
  annote =	{Keywords: Tree edit distance, unification, parameterized algorithms}

Keywords: Tree edit distance, unification, parameterized algorithms
Collection: 33rd International Symposium on Algorithms and Computation (ISAAC 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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