# Exploiting Database Management Systems and Treewidth for Counting

arXiv: https://arxiv.org/abs/2001.04191 · HTML: https://mlsanity.com/paper/2001.04191/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2020.

## Built on by (most cited first, 7 of 7)

- [Rushing and Strolling among Answer Sets -- Navigation Made Easy](https://mlsanity.com/paper/2112.07596/) (2021)
- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [A Quantitative Symbolic Approach to Individual Human Reasoning](https://mlsanity.com/paper/2205.05030/) (2022)
- [IASCAR: Incremental Answer Set Counting by Anytime Refinement](https://mlsanity.com/paper/2311.07233/) (2023)
- [DPO: Dynamic-Programming Optimization on Hybrid Constraints](https://mlsanity.com/paper/2205.08632/) (2022)
- [Solving Projected Model Counting by Utilizing Treewidth and its Limits](https://mlsanity.com/paper/2305.19212/) (2023)
- [DPER: Dynamic Programming for Exist-Random Stochastic SAT](https://mlsanity.com/paper/2205.09826/) (2022)

## Abstract (arXiv)

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.