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3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time

Authors Masoud Seddighin, Saeed Seddighin

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Author Details

Masoud Seddighin
  • Institute for Research in Fundamental Sciences (IPM), School of Computer Science, Tehran, Iran
Saeed Seddighin
  • Toyota Technological Institute at Chicago, IL, USA


We would like to thank Amir Abboud for very helpful discussions. The second author was supported by a Google Research Gift.

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Masoud Seddighin and Saeed Seddighin. 3+ε Approximation of Tree Edit Distance in Truly Subquadratic Time. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 115:1-115:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


Tree edit distance is a well-known generalization of the edit distance problem to rooted trees. In this problem, the goal is to transform a rooted tree into another rooted tree via (i) node addition, (ii) node deletion, and (iii) node relabel. In this work, we give a truly subquadratic time algorithm that approximates tree edit distance within a factor 3+ε. Our result is obtained through a novel extension of a 3-step framework that approximates edit distance in truly subquadratic time. This framework has also been previously used to approximate longest common subsequence in subquadratic time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • tree edit distance
  • approximation
  • subquadratic
  • edit distance


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