Many important problems in Bioinformatics (e.g., assembly or multi-assembly) admit multiple solutions, while the final objective is to report only one. A common approach to deal with this uncertainty is finding safe partial solutions (e.g., contigs) which are common to all solutions. Previous research on safety has focused on polynomially-time solvable problems, whereas many successful and natural models are NP-hard to solve, leaving a lack of "safety tools" for such problems. We propose the first method for computing all safe solutions for an NP-hard problem, minimum flow decomposition. We obtain our results by developing a "safety test" for paths based on a general Integer Linear Programming (ILP) formulation. Moreover, we provide implementations with practical optimizations aimed to reduce the total ILP time, the most efficient of these being based on a recursive group-testing procedure. Results: Experimental results on the transcriptome datasets of Shao and Kingsford (TCBB, 2017) show that all safe paths for minimum flow decompositions correctly recover up to 90% of the full RNA transcripts, which is at least 25% more than previously known safe paths, such as (Caceres et al. TCBB, 2021), (Zheng et al., RECOMB 2021), (Khan et al., RECOMB 2022, ESA 2022). Moreover, despite the NP-hardness of the problem, we can report all safe paths for 99.8% of the over 27,000 non-trivial graphs of this dataset in only 1.5 hours. Our results suggest that, on perfect data, there is less ambiguity than thought in the notoriously hard RNA assembly problem. Availability: https://github.com/algbio/mfd-safety

翻译：生物信息学中的许多重要问题（例如组装或多组装）通常存在多种解，而最终目标往往仅需报告其中一个。处理这种不确定性的常见方法是寻找所有解共有的安全局部解（如重叠群）。先前关于安全性的研究主要聚焦于多项式时间可解问题，然而许多成功且自然的模型实际上是NP难问题，导致此类问题缺乏“安全工具”。我们首次提出针对NP难问题——最小流分解——计算所有安全解的方法。通过基于通用整数线性规划（ILP）公式的路径“安全测试”获得结果。此外，我们提供了包含实际优化策略的实现，旨在减少总ILP求解时间，其中最有效的优化基于递归分组测试流程。结果：在Shao和Kingsford（TCBB, 2017）的转录组数据集上的实验表明，最小流分解的所有安全路径可正确恢复多达90%的全长RNA转录本，这比先前已知的安全路径（如Caceres等，TCBB 2021；Zheng等，RECOMB 2021；Khan等，RECOMB 2022, ESA 2022）至少高出25%。尽管问题具有NP难度，我们仍能在1.5小时内报告该数据集中超过27,000个非平凡图的99.8%的所有安全路径。结果表明，在完美数据条件下，著名的RNA组装难题中存在的模糊性比此前认为的更少。可用性：https://github.com/algbio/mfd-safety