Alignment distance of regular tree languages

Yo Sub Han, Sang Ki Ko

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We consider the tree alignment distance problem between a tree and a regular tree language. The tree alignment distance is an alternative of the tree edit-distance, in which we construct an optimal alignment between two trees and compute its cost instead of directly computing the minimum cost of tree edits. The alignment distance is crucial for understanding the structural similarity between trees. We, in particular, consider the following problem: given a tree t and a tree automaton recognizing a regular tree language L, find the most similar tree from L with respect to t under the tree alignment metric. Regular tree languages are commonly used in practice such as XML schema or bioinformatics. We propose an O(mn) time algorithm for computing the (ordered) alignment distance between t and L when the maximum degree of t and trees in L is bounded by a constant, and O(mn2) time algorithm when the maximum degree of trees in L is not bounded, where m is the size of t and n is the size of finite tree automaton for L. We also study the case where a tree is not necessarily ordered, and show that the time complexity remains O(mn) if the maximum degree is bounded and MAX SNP-hard otherwise.

Original languageEnglish
Title of host publicationImplementation and Application of Automata - 22nd International Conference, CIAA 2017, Proceedings
EditorsArnaud Carayol, Cyril Nicaud
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783319601335
StatePublished - 2017
Event22nd International Conference on Implementation and Application of Automata, CIAA 2017 - Marne-la-Vallee, France
Duration: 27 Jun 201730 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10329 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Conference on Implementation and Application of Automata, CIAA 2017


  • Alignment edit-distance
  • Regular tree languages
  • Tree alignment
  • Tree automata


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