Safety and Completeness in Flow Decompositions for RNA Assembly

Flow decomposition has numerous applications, ranging from networking to bioinformatics. Some applications require any valid decomposition that optimizes some property as number of paths, robustness, or path lengths. Many bioinformatic applications require the specific decomposition which relates to the underlying data that generated the flow. Thus, no optimization criteria guarantees to identify the correct decomposition for real inputs. We propose to instead report the safe paths, which are subpaths of at least one path in every flow decomposition. Ma et al. [WABI 2020] addressed the existence of multiple optimal solutions in a probabilistic framework, which is referred to as non-identifiability. Later, they gave a quadratic-time algorithm [RECOMB 2021] based on a global criterion for solving a problem called AND-Quant, which generalizes the problem of reporting whether a given path is safe. We present the first local characterization of safe paths for flow decompositions in directed acyclic graphs, giving a practical algorithm for finding the complete set of safe paths. We also evaluated our algorithm against the trivial safe algorithms (unitigs, extended unitigs) and a popular heuristic (greedy-width) for flow decomposition on RNA transcripts datasets. Despite maintaining perfect precision our algorithm reports ≈ 50% higher coverage over trivial safe algorithms. Though greedy-width reports better coverage, it has significantly lower precision on complex graphs. On a unified metric (F-Score) of coverage and precision, our algorithm outperforms greedy-width by ≈ 20%, when the evaluated dataset has significant number of complex graphs. Also, it has superior time (3–5 × ) and space efficiency (1.2–2.2 × ), resulting in a better and more practical approach for bioinformatics applications of flow decomposition.