We have developed efficient parameterized algorithms for the enumeration problems of graphs arising in chemistry. In particular, we have focused on the following problems: enumeration of Kekul\'e structures, computation of Hosoya index, computation of Merrifield-Simmons index, and computation of graph entropy based on matchings and independent sets. All these problems are known to be $\# P$-complete. We have developed FPT algorithms for bounded treewidth and bounded pathwidth for these problems with a better time complexity than the known state-of-the-art in the literature. We have also conducted experiments on the entire PubChem database of chemical compounds and tested our algorithms. We also provide a comparison with naive baseline algorithms for these problems, along with a distribution of treewidth for the chemical compounds available in the PubChem database.

翻译：针对化学中出现的图枚举问题，我们开发了高效的参数化算法。具体聚焦于以下问题：Kekulé结构枚举、Hosoya指数计算、Merrifield-Simmons指数计算，以及基于匹配与独立集的图熵计算。已知这些问题均为$\# P$-完全问题。我们提出了针对有界树宽和有界路径宽的FPT算法，其时间复杂度优于现有文献中的最优方法。我们还在整个PubChem化合物数据库上进行了实验，测试了算法的性能。同时，针对这些问题提供了与朴素基线算法的对比分析，并给出了PubChem数据库中化合物树宽的分布统计。