Evaluating Optimal Safe Flows Decomposition for RNA Assembly

In Bioinformatics, the applications of flow decomposition in directed acyclic graphs are highlighted in RNA Assembly problem. However, it admits multiple solutions where exactly one solution correctly represents the underlying transcripts. The problem was addressed by Safe and Complete framework~[RECOMB16], which reports all the parts of the solution that are present in every possible solution. Khan et al.~[RECOMB22] first studied flow decomposition in the safe and complete framework. Their algorithm showed superior performance ($\approx20\%$) over the popular heuristic (greedy-width) on sufficiently complex graphs for a unified metric of precision and coverage (F-score). They presented the solution in multiple representations using simple but suboptimal algorithms, which were later optimized by Khan and Tomescu~[ESA22], who also presented an optimal representation. In this paper, we evaluate the practical significance of the optimal algorithms by Khan and Tomescu~[ESA22]. Our work highlights the significance of the theoretically optimal algorithms improving time (up to $60-70\%$) and memory (up to $76-85\%$), and the optimal representations improving output size (up to $135-170\%$) significantly. However, the impact of optimal algorithms was limited due to a large number of extremely short safe paths. We propose heuristics to improve these representations further, resulting in further improvement in time (up to $10\%$) and output size ($10-25\%$). However, in absolute terms, these improvements were limited to a few seconds on real datasets involved due to the smaller size of the graphs. We thus generated large random graphs, to demonstrate the scalability of the above results. The older algorithms [RECOMB22] were not practical on moderately large graphs ($\geq 1M$ nodes), while optimal algorithms [ESA22] were linearly scalable for much larger graphs ($\geq 100M$ nodes).