Edit Distance between Unlabeled Ordered Trees

Abstract : There exists a bijection between one stack sortable permutations --permutations which avoid the pattern $231$-- and planar trees. We define an edit distance between permutations which is coherent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for $(231)$ avoiding permutations. Moreover, we obtain the generating function of the edit distance between ordered trees and some special ones. For the general case we show that the mean edit distance between a planar tree and all other planar 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.
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RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2006, 40, pp.593-609
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https://hal.archives-ouvertes.fr/hal-00005569
Contributeur : Dominique Rossin <>
Soumis le : lundi 27 juin 2005 - 11:31:54
Dernière modification le : jeudi 15 novembre 2018 - 20:26:55
Document(s) archivé(s) le : jeudi 1 avril 2010 - 21:46:16

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Anne Micheli, Dominique Rossin. Edit Distance between Unlabeled Ordered Trees. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2006, 40, pp.593-609. 〈hal-00005569〉

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