利用数据库管理系统和树宽进行计数
Exploiting Database Management Systems and Treewidth for Counting
AI总结：
本文提出利用数据库管理系统（PostgreSQL）在树分解上实现动态规划，以高效求解小树宽实例的计数问题（如#SAT），首次将DBMS用于树分解算法，并利用其处理大表、并行化和挂起计算的优势。
摘要：
有界树宽是最常被引用的组合不变量之一，文献中已将其应用于高效解决多个计数问题。一个典型的计数问题是#SAT，它要求计算布尔公式满足赋值的数量。近期工作表明，#SAT的基准实例通常具有相当小的树宽。本文研究小树宽实例的计数问题。我们引入一个基于最先进的数据库管理系统（DBMS）的通用框架来解决计数问题。我们的框架通过使用树分解（TD）上的动态规划（DP）来显式利用小树宽。因此，我们将DP概念实现到数据库管理系统（PostgreSQL）中，因为DP算法在理论上通常已经以表操作的形式给出。这允许对DP算法进行优雅的规格说明，并使用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，我们提出了首个在树分解算法中采用数据库管理系统的方法。我们方法的一个关键优势是，数据库管理系统天然允许在有限的主内存（RAM）下处理大型表、并行化以及挂起计算。
英文摘要：
Bounded treewidth is one of the most cited combinatorial invariants, which was applied in the literature 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 (DBMS). 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 DBMS naturally allow to deal with huge tables with a limited amount of main memory (RAM), parallelization, as well as suspending computation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
