The problem of computing the Elementary Flux Modes (EFMs) and Minimal Cut Sets (MCSs) of metabolic network is a fundamental one in metabolic networks. A key insight is that they can be understood as a dual pair of monotone Boolean functions (MBFs). Using this insight, this computation reduces to the question of generating from an oracle a dual pair of MBFs. If one of the two sets (functions) is known, then the other can be computed through a process known as dualization. Fredman and Khachiyan provided two algorithms, which they called simply A and B that can serve as an engine for oracle-based generation or dualization of MBFs. We look at efficiencies available in implementing their algorithm B, which we will refer to as FK-B. Like their algorithm A, FK-B certifies whether two given MBFs in the form of Conjunctive Normal Form and Disjunctive Normal Form are dual or not, and in case of not being dual it returns a conflicting assignment (CA), that is, an assignment that makes one of the given Boolean functions True and the other one False. The FK-B algorithm is a recursive algorithm that searches through the tree of assignments to find a CA. If it does not find any CA, it means that the given Boolean functions are dual. In this article, we propose six techniques applicable to the FK-B and hence to the dualization process. Although these techniques do not reduce the time complexity, they considerably reduce the running time in practice. We evaluate the proposed improvements by applying them to compute the MCSs from the EFMs in the 19 small- and medium-sized models from the BioModels database along with 4 models of biomass synthesis in Escherichia coli that were used in an earlier computational survey Haus et al. (2008).

中文翻译：

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使用 Fredman-Khachiyan 算法加速代谢网络模型的结构分析 B.


计算代谢网络的基本通量模式（EFM）和最小割集（MCS）问题是代谢网络中的一个基本问题。一个关键的见解是它们可以被理解为一对单调布尔函数（MBF）。利用这一见解，该计算可简化为从预言机生成一对 MBF 的问题。如果两个集合（函数）中的一个已知，则可以通过称为对偶化的过程来计算另一个。 Fredman 和 Khachiyan 提供了两种算法，他们简称为 A 和 B，可以作为基于预言的生成或 MBF 对偶化的引擎。我们着眼于实现算法 B 的效率，我们将其称为 FK-B。与他们的算法 A 一样，FK-B 证明两个给定的合取范式和析取范式形式的 MBF 是否对偶，如果不是对偶，则返回一个冲突赋值 (CA)，即赋值这使得给定的布尔函数之一为 True，另一为 False。 FK-B 算法是一种递归算法，通过搜索分配树来查找 CA。如果没有找到任何CA，则意味着给定的布尔函数是对偶的。在本文中，我们提出了六种适用于 FK-B 以及二元化过程的技术。尽管这些技术并没有降低时间复杂度，但它们在实践中大大减少了运行时间。我们通过应用这些改进来计算 BioModels 数据库中 19 个中小型模型中的 EFM 的 MCS，以及早期计算调查 Haus 等人中使用的 4 个大肠杆菌生物质合成模型，从而评估所提出的改进。 （2008）。