Exploiting Database Management Systems and Treewidth for Counting
This work addresses the challenge of scaling counting algorithms in computational complexity and AI, offering a novel integration of DBMS with treewidth-based methods, though it is incremental in applying existing DP techniques to a new system.
The paper tackles the problem of efficiently solving counting problems like #SAT for instances with small treewidth by introducing a framework that uses database management systems (DBMS) to implement dynamic programming on tree decompositions, resulting in practical advantages such as handling large tables with limited RAM, parallelization, and suspendable computation.
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.