# Edit distance between unlabeled ordered trees

Anne Micheli; Dominique Rossin

RAIRO - Theoretical Informatics and Applications (2006)

- Volume: 40, Issue: 4, page 593-609
- ISSN: 0988-3754

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topMicheli, Anne, and Rossin, Dominique. "Edit distance between unlabeled ordered trees." RAIRO - Theoretical Informatics and Applications 40.4 (2006): 593-609. <http://eudml.org/doc/249700>.

@article{Micheli2006,

abstract = {
There exists a bijection between one-stack sortable permutations (permutations which avoid the pattern (231)) and rooted plane trees. We define an edit distance between permutations which is consistent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for (231) pattern-avoiding permutations.
Moreover, we obtain the generating function of the edit distance between ordered unlabeled trees and some special ones.
For the general case we show that the mean edit distance between a rooted plane tree and all other rooted plane trees is at least n/ln(n).
Some results can be extended to labeled trees considering colored
Dyck paths or, equivalently, colored one-stack sortable permutations.
},

author = {Micheli, Anne, Rossin, Dominique},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Edit distance; trees.; one-stack sortable permutation; pattern avoidance},

language = {eng},

month = {11},

number = {4},

pages = {593-609},

publisher = {EDP Sciences},

title = {Edit distance between unlabeled ordered trees},

url = {http://eudml.org/doc/249700},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Micheli, Anne

AU - Rossin, Dominique

TI - Edit distance between unlabeled ordered trees

JO - RAIRO - Theoretical Informatics and Applications

DA - 2006/11//

PB - EDP Sciences

VL - 40

IS - 4

SP - 593

EP - 609

AB -
There exists a bijection between one-stack sortable permutations (permutations which avoid the pattern (231)) and rooted plane trees. We define an edit distance between permutations which is consistent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for (231) pattern-avoiding permutations.
Moreover, we obtain the generating function of the edit distance between ordered unlabeled trees and some special ones.
For the general case we show that the mean edit distance between a rooted plane tree and all other rooted plane trees is at least n/ln(n).
Some results can be extended to labeled trees considering colored
Dyck paths or, equivalently, colored one-stack sortable permutations.

LA - eng

KW - Edit distance; trees.; one-stack sortable permutation; pattern avoidance

UR - http://eudml.org/doc/249700

ER -

## References

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