Bounded treewidth is one of the most cited combinatorial invariants in the literature. It was also applied for solving several counting problems efficiently. A canonical counting problem is #Sat, which asks to count the satisfying assignments of a Boolean formula. Recent work shows that benchmarking instances for #Sat often have reasonably small treewidth. This paper deals with counting problems for instances of small treewidth. We introduce a general framework to solve counting questions based on state-of-the-art database management systems (DBMSs). Our framework takes explicitly advantage of small treewidth by solving instances using dynamic programming (DP) on tree decompositions (TD). Therefore, we implement the concept of DP into a DBMS (PostgreSQL), since DP algorithms are already often given in terms of table manipulations in theory. This allows for elegant specifications of DP algorithms and the use of SQL to manipulate records and tables, which gives us a natural approach to bring DP algorithms into practice. To the best of our knowledge, we present the first approach to employ a DBMS for algorithms on TDs. A key advantage of our approach is that DBMSs naturally allow for dealing with huge tables with a limited amount of main memory (RAM).

中文翻译：

---

利用数据库管理系统和树宽进行计数

有界树宽是文献中引用最多的组合不变量之一。它也被应用于有效地解决几个计数问题。一个典型的计数问题是#Sat，它要求计算布尔公式的令人满意的分配。最近的工作表明，#Sat 的基准测试实例通常具有相当小的树宽。本文处理小树宽实例的计数问题。我们引入了一个通用框架来解决基于最先进的数据库管理系统 (DBMS) 的计数问题。我们的框架通过在树分解 (TD) 上使用动态规划 (DP) 解决实例，显式地利用了小树宽。因此，我们在 DBMS (PostgreSQL) 中实现了 DP 的概念，因为理论上已经经常根据表操作给出 DP 算法。这允许 DP 算法的优雅规范和使用 SQL 来操作记录和表，这为我们提供了一种将 DP 算法付诸实践的自然方法。据我们所知，我们提出了第一种将 DBMS 用于 TD 算法的方法。我们的方法的一个关键优势是 DBMS 自然允许处理具有有限主存 (RAM) 数量的大型表。