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arXiv · 1706.07851

A practical fpt algorithm for Flow Decomposition and transcript assembly

Kyle Kloster·Philipp Kuinke·Michael P. O'Brien·Felix Reidl·Fernando Sánchez Villaamil·Blair D. Sullivan·Andrew van der Poel
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Abstract

The Flow Decomposition problem, which asks for the smallest set of weighted paths that "covers" a flow on a DAG, has recently been used as an important computational step in transcript assembly. We prove the problem is in FPT when parameterized by the number of paths by giving a practical linear fpt algorithm. Further, we implement and engineer a Flow Decomposition solver based on this algorithm, and evaluate its performance on RNA-sequence data. Crucially, our solver finds exact solutions while achieving runtimes competitive with a state-of-the-art heuristic. Finally, we contextualize our design choices with two hardness results related to preprocessing and weight recovery. Specifically, $k$-Flow Decomposition does not admit polynomial kernels under standard complexity assumptions, and the related problem of assigning (known) weights to a given set of paths is NP-hard.

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Kyle Kloster, Philipp Kuinke, Michael P. O'Brien, Felix Reidl, Fernando Sánchez Villaamil, Blair D. Sullivan, Andrew van der Poel. 2017-06-23. A practical fpt algorithm for Flow Decomposition and transcript assembly. https://arxiv.org/abs/1706.07851

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