Analysis of chemical graphs is becoming a major research topic in computational molecular biology due to its potential applications to drug design. One of the major approaches in such a study is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR) analysis, which is to infer chemical structures from given chemical activities/properties. Recently, a novel two-phase framework has been proposed for inverse QSAR/QSPR, where in the first phase an artificial neural network (ANN) is used to construct a prediction function. In the second phase, a mixed integer linear program (MILP) formulated on the trained ANN and a graph search algorithm are used to infer desired chemical structures. The framework has been applied to the case of chemical compounds with cycle index up to 2 so far. The computational results conducted on instances with n non-hydrogen atoms show that a feature vector can be inferred by solving an MILP for up to $$n=40$$ , whereas graphs can be enumerated for up to $$n=15$$ . When applied to the case of chemical acyclic graphs, the maximum computable diameter of a chemical structure was up to 8. In this paper, we introduce a new characterization of graph structure, called “branch-height” based on which a new MILP formulation and a new graph search algorithm are designed for chemical acyclic graphs. The results of computational experiments using such chemical properties as octanol/water partition coefficient, boiling point and heat of combustion suggest that the proposed method can infer chemical acyclic graphs with around $$n=50$$ and diameter 30.

中文翻译：

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一种基于人工神经网络和整数规划的具有有界分支高度的非环状化合物推断新方法

由于其在药物设计中的潜在应用，化学图分析正成为计算分子生物学的主要研究课题。这种研究的主要方法之一是逆定量结构活性/性质关系（逆 QSAR/QSPR）分析，即从给定的化学活性/性质推断化学结构。最近，针对逆 QSAR/QSPR 提出了一种新颖的两阶段框架，其中在第一阶段使用人工神经网络 (ANN) 来构建预测函数。在第二阶段，在经过训练的 ANN 上制定的混合整数线性程序 (MILP) 和图搜索算法用于推断所需的化学结构。到目前为止，该框架已应用于循环指数高达2的化合物的情况。对具有 n 个非氢原子的实例进行的计算结果表明，可以通过求解高达 $$n=40$$ 的 MILP 来推断特征向量，而可以枚举高达 $$n=15$$ 的图. 当应用于化学无环图的情况时，化学结构的最大可计算直径可达 8。在本文中，我们引入了一种新的图结构表征，称为“分支高度”，基于它，一个新的 MILP 公式和为化学无环图设计了一种新的图搜索算法。使用辛醇/水分配系数、沸点和燃烧热等化学性质的计算实验结果表明，所提出的方法可以推断出大约 $$n=50$$ 和直径 30 的化学无环图。