Counting, generating and sampling tree alignments

Cedric Chauve 1 Julien Courtiel 1 Yann Ponty 2, 3
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 uninforma-tive, 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 :
Communication dans un congrès
ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 2016, 〈http://grammars.grlmc.com/AlCoB2016/〉
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https://hal.inria.fr/hal-01154030
Contributeur : Yann Ponty <>
Soumis le : samedi 12 décembre 2015 - 10:53:28
Dernière modification le : jeudi 11 janvier 2018 - 06:23:08
Document(s) archivé(s) le : samedi 29 avril 2017 - 11:44:23

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Distributed under a Creative Commons Paternité 4.0 International License

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  • HAL Id : hal-01154030, version 2
  • ARXIV : 1505.05983

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Cedric Chauve, Julien Courtiel, Yann Ponty. Counting, generating and sampling tree alignments. ALCOB - 3rd International Conference on Algorithms for Computational Biology - 2016, Jun 2016, Trujillo, Spain. 2016, 〈http://grammars.grlmc.com/AlCoB2016/〉. 〈hal-01154030v2〉

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