Edit distance between unlabeled ordered trees
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 4, pp. 593-609.

There exists a bijection between one-stack sortable permutations (permutations which avoid the pattern $\left(231\right)$) 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 $\left(231\right)$ 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 $n/ln\left(n\right)$. Some results can be extended to labeled trees considering colored Dyck paths or, equivalently, colored one-stack sortable permutations.

DOI: 10.1051/ita:2006043
Classification: 05C12,  05C05,  05A05,  05A15
Keywords: edit distance, trees
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author = {Micheli, Anne and Rossin, Dominique},
title = {Edit distance between unlabeled ordered trees},
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Micheli, Anne; Rossin, Dominique. Edit distance between unlabeled ordered trees. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 40 (2006) no. 4, pp. 593-609. doi : 10.1051/ita:2006043. http://www.numdam.org/articles/10.1051/ita:2006043/

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