### Abstract

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(mn^{2}) 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 language | English |
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Title of host publication | Implementation and Application of Automata - 22nd International Conference, CIAA 2017, Proceedings |

Editors | Arnaud Carayol, Cyril Nicaud |

Publisher | Springer Verlag |

Pages | 126-137 |

Number of pages | 12 |

ISBN (Print) | 9783319601335 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

Event | 22nd International Conference on Implementation and Application of Automata, CIAA 2017 - Marne-la-Vallee, France Duration: 2017 Jun 27 → 2017 Jun 30 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10329 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 22nd International Conference on Implementation and Application of Automata, CIAA 2017 |
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Country | France |

City | Marne-la-Vallee |

Period | 17/6/27 → 17/6/30 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Implementation and Application of Automata - 22nd International Conference, CIAA 2017, Proceedings*(pp. 126-137). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10329 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-60134-2_11