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On the Complexity of Tree Edit Distance with Variables

Authors Tatsuya Akutsu , Tomoya Mori, Naotoshi Nakamura, Satoshi Kozawa, Yuhei Ueno, Thomas N. Sato



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Author Details

Tatsuya Akutsu
  • Bioinformatics Center, Institute for Chemical Research, Kyoto University, Japan
Tomoya Mori
  • Bioinformatics Center, Institute for Chemical Research, Kyoto University, Japan
Naotoshi Nakamura
  • The Thomas N. Sato BioMEC-X Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan
  • Karydo TherapeutiX, Inc., Tokyo, Japan
  • Interdisciplinary Biology Laboratory (iBLab), Division of Natural Science, Graduate School of Science, Nagoya University, Japan
Satoshi Kozawa
  • The Thomas N. Sato BioMEC-X Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan
  • Karydo TherapeutiX, Inc., Tokyo, Japan
Yuhei Ueno
  • The Thomas N. Sato BioMEC-X Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan
  • Karydo TherapeutiX, Inc., Tokyo, Japan
  • V-iCliniX Laboratory, Nara Medical University, Japan
Thomas N. Sato
  • The Thomas N. Sato BioMEC-X Laboratories, Advanced Telecommunications Research Institute International (ATR), Kyoto, Japan
  • Karydo TherapeutiX, Inc., Tokyo, Japan
  • V-iCliniX Laboratory, Nara Medical University, Japan

Acknowledgements

We are grateful to the members of Sato lab at ATR and Karydo TherapeutiX, Inc. for advice and discussion throughout the course of this work.

Cite AsGet BibTex

Tatsuya Akutsu, Tomoya Mori, Naotoshi Nakamura, Satoshi Kozawa, Yuhei Ueno, and Thomas N. Sato. On the Complexity of Tree Edit Distance with Variables. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 44:1-44:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ISAAC.2022.44

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • Tree edit distance
  • unification
  • parameterized algorithms

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