基于整数线性规划的流分解问题的安全框架
A Safety Framework for Flow Decomposition Problems via Integer Linear Programming
摘要：
生物信息学中的许多重要问题（例如，组装或多组装）允许多个解决方案，而最终目标是只报告一个。处理这种不确定性的常见方法是找到安全的部分解决方案（例如，重叠群），这是所有解决方案所共有的。以往的安全性研究主要集中在多项式时间可解问题上，而许多成功的自然模型都是NP难问题，因此缺乏解决此类问题的“安全工具”。我们提出了第一种方法来计算所有的安全解决方案的NP-难问题，最小流分解。我们得到我们的结果，通过开发一个“安全测试”的基础上，一般的线性规划（ILP）制定的路径。此外，我们提供了实际的优化实现，旨在减少总的ILP时间，其中最有效的是基于递归组测试过程。结果如下：Shao和Kingsford（TCBB，2017）的转录组数据集的实验结果表明，最小流分解的所有安全路径正确恢复了高达90%的完整RNA转录物，这比先前已知的安全路径至少多25%，例如（Caceres et al. TCBB，2021），（Zheng et al.，RECOMB 2021），（Khan等人，RECOMB 2022，ESA 2022）。此外，尽管这个问题是NP困难的，但我们可以在1.5小时内报告这个数据集中超过27，000个非平凡图中99.8%的所有安全路径。我们的研究结果表明，在完美的数据，有更少的模糊性比想象中的臭名昭著的困难RNA组装问题。可用性：https://github.com/algbio/mfd-safety
英文摘要：
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
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