通过ILP实现快速、灵活和精确的最小流分解
Fast, Flexible, and Exact Minimum Flow Decompositions via ILP
摘要：
最小流分解（MFD）（寻找完美分解流的最小路径集的问题）是计算机科学中的经典问题，它的变体是生物信息学中多组装问题（例如RNA组装）的强大模型。然而，由于这个问题及其变体是NP难的，实际的多装配工具要么使用算法，要么解决更简单的多项式时间可解版本的问题，这可能会产生解决方案，不是最小的或不完美的分解流。许多RNA汇编器也使用这种实际变体的整数线性规划（ILP）公式，它们需要编码所有潜在的指数级解决方案路径。此外，MFD的唯一精确求解器不能扩展到大型实例，并且不能有效地推广到实际的MFD变体。在这项工作中，我们提供了第一个实用的ILP制定MFD（因此，第一个快速和精确的求解MFD），编码的基础上，所有的指数许多解决方案的路径，只使用一个二次变量。在模拟和真实的流图上，我们的方法在13秒内解决了任何实例。我们还表明，我们的ILP配方可以很容易地和有效地适应许多实际的变化，如纳入较长或双端读取或最大限度地减少流错误。我们希望我们的研究结果可以消除当前多组装模型的复杂性和易处理性之间的权衡，并成为未来实用RNA组装工具的核心。
英文摘要：
Minimum flow decomposition (MFD) (the problem of finding a minimum set of paths that perfectly decomposes a flow) is a classical problem in Computer Science, and variants of it are powerful models in multiassembly problems in Bioinformatics (e.g. RNA assembly). However, because this problem and its variants are NP-hard, practical multiassembly tools either use heuristics or solve simpler, polynomial-time solvable versions of the problem, which may yield solutions that are not mini-mal or do not perfectly decompose the flow. Many RNA assemblers also use integer linear programming(ILP) formulations of such practical variants, having the major limitation they need to encode all the potentially exponentially many solution paths. Moreover, the only exact solver for MFD does not scale to large instances and cannot be efficiently generalized to practical MFD variants. In this work, we provide the first practical ILP formulation for MFD (and thus the first fast and exact solver for MFD), based on encoding all of the exponentially many solution paths using only a quadratic number of variables. On both simulated and real flow graphs, our approach solves any instance in under 13 seconds. We also show that our ILP formulation can be easily and efficiently adapted for many practical variants, such as incorporating longer or paired-end reads or minimizing flow errors. We hope that our results can remove the current tradeoff between the complexity of a multi assembly model and its tractability and can lie at the core of future practical RNA assembly tools.
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