Counting, generating, analyzing and sampling tree alignments

Cedric Chauve 1 Julien Courtiel 2 Yann Ponty 3, 4
3 AMIB - Algorithms and Models for Integrative Biology
CNRS - Centre National de la Recherche Scientifique : UMR8623, Polytechnique - X, Inria Saclay - Ile de France, UP11 - Université Paris-Sud - Paris 11, LRI - Laboratoire de Recherche en Informatique, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : Pairwise ordered tree alignment are combinatorial objects that appear in important applications , such as RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical sets of matches between identical pairs of trees. This ambiguity is uninformative, and detrimental to any probabilistic analysis. In this work, we consider tree alignments up to equivalence. Our first result is a precise asymptotic enumeration of tree alignments, obtained from a context-free grammar by mean of basic analytic combinatorics. Our second result focuses on alignments between two given ordered trees S and T. By refining our grammar to align specific trees, we obtain a decomposition scheme for the space of alignments, and use it to design an efficient dynamic programming algorithm for sampling alignments under the Gibbs-Boltzmann probability distribution. This generalizes existing tree alignment algorithms, and opens the door for a probabilistic analysis of the space of suboptimal alignments.
Type de document :
Pré-publication, Document de travail
Submitted to IJFCS. 2017
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  • HAL Id : hal-01500116, version 1

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Cedric Chauve, Julien Courtiel, Yann Ponty. Counting, generating, analyzing and sampling tree alignments. Submitted to IJFCS. 2017. 〈hal-01500116〉

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