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Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics

Authors Bertrand Marchand , Yann Ponty , Laurent Bulteau

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Author Details

Bertrand Marchand
  • LIX CNRS UMR 7161, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
  • LIGM, CNRS, Univ Gustave Eiffel, F77454 Marne-la-vallée, France
Yann Ponty
  • LIX CNRS UMR 7161, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
Laurent Bulteau
  • LIGM, CNRS, Univ Gustave Eiffel, F77454 Marne-la-vallée, France

Funding

This work was supported by the French Agence Nationale de la Recherche through the Decrypted collaborative project (ANR-19-CE30-0021).

Acknowledgements

The authors would like to thank Julien Baste for pointing out prior work on treewidth modulators, and providing valuable input regarding vertex deletion problems.

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Bertrand Marchand, Yann Ponty, and Laurent Bulteau. Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 7:1-7:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.WABI.2021.7

Abstract

Hard graph problems are ubiquitous in Bioinformatics, inspiring the design of specialized Fixed-Parameter Tractable algorithms, many of which rely on a combination of tree-decomposition and dynamic programming. The time/space complexities of such approaches hinge critically on low values for the treewidth tw of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, i.e. the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth tw'. Our rationale is that the time gained thanks to a smaller treewidth in a parameterized algorithm compensates the extra post-processing needed to take deleted edges into account. Our core result is an FPT dynamic programming algorithm for Tree-Diet, using 2^{O(tw)}n time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when tw' or tw-tw' is constant). We propose a prototype implementation for our approach which we apply on difficult instances of selected RNA-based problems: RNA design, sequence-structure alignment, and search of pseudoknotted RNAs in genomes, revealing very encouraging results. This work paves the way for a wider adoption of tree-decomposition-based algorithms in Bioinformatics.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic programming
  • Theory of computation → Parameterized complexity and exact algorithms
  • Applied computing → Bioinformatics
Keywords
  • RNA
  • treewidth
  • FPT algorithms
  • RNA design
  • structure-sequence alignment

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