Flowtigs: Safety in flow decompositions for assembly graphs

A <i>decomposition</i> of a network flow is a set of weighted walks whose superposition equals the flow. In this article, we give a simple and linear-time-verifiable complete characterization (<i>flowtigs</i>) of walks that are <i>safe</i> in such general flow decompositions, i.e., that are subwalks of any possible flow decomposition. We provide an <i>O</i>(<i>mn</i>)-time algorithm that identifies all maximal flowtigs and represents them inside a compact structure. On the practical side, we study flowtigs in the use-case of metagenomic assembly. By using the species abundances as flow values of the metagenomic assembly graph, we can model the possible assembly solutions as flow decompositions into weighted closed walks. On simulated data, compared to reporting unitigs or maximal safe walks based only on the graph structure, reporting flowtigs results in a notably more contiguous assembly. On real data, we frame flowtigs as a heuristic and provide an algorithm that is guided by this heuristic.