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

Bertrand Marchand 1, 2 yann Ponty 1 Laurent Bulteau 2 
1 AMIBIO - Algorithms and Models for Integrative BIOlogy
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
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.
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Submitted on : Monday, May 2, 2022 - 5:51:09 PM
Last modification on : Tuesday, May 10, 2022 - 7:47:13 PM

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Bertrand Marchand, yann Ponty, Laurent Bulteau. Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics. Algorithms for Molecular Biology, BioMed Central, 2022. ⟨hal-03608412v2⟩

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