Tree Diet: Reducing the Treewidth to Unlock FPT Algorithms in RNA Bioinformatics release_ovpvupwbfbftzb5radjf2iriri

by Bertrand Marchand, Yann Ponty, Laurent Bulteau

Released as a post by Cold Spring Harbor Laboratory.

2021  

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 <jats:italic>tw</jats:italic> of the input graph. In order to extend their scope of applicability, we introduce the Tree-Diet problem, <jats:italic>i.e.</jats:italic> the removal of a minimal set of edges such that a given tree-decomposition can be slimmed down to a prescribed treewidth <jats:italic>tw′</jats:italic>. 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<jats:italic><jats:sup>O(tw)</jats:sup>n</jats:italic> time and space. We complement this result with parameterized complexity lower-bounds for stronger variants (e.g., NP-hardness when <jats:italic>tw′</jats:italic> or <jats:italic>tw–tw′</jats:italic> 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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Date   2021-05-04
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