# Answer Set Solving with Bounded Treewidth Revisited

## TL;DR

This paper introduces new parameterized algorithms for answer set programming that leverage graph representations and treewidth to improve efficiency, especially for counting answer sets in low-treewidth instances.

## Contribution

It presents the first dynamic programming algorithms for ASP that handle full syntax and exploit treewidth as a parameter.

## Key findings

- Algorithms run in linear time for bounded treewidth and weights.
- Empirical results show good performance on low-treewidth benchmarks.
- Effective for counting answer sets in practical instances.

## Abstract

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two kinds of graph representations of programs to exploit their treewidth as a parameter. Treewidth roughly measures to which extent the internal structure of a program resembles a tree. Our main contribution is the design of parameterized dynamic programming algorithms, which run in linear time if the treewidth and weights of the given program are bounded. Compared to previous work, our algorithms handle the full syntax of ASP. Finally, we report on an empirical evaluation that shows good runtime behaviour for benchmark instances of low treewidth, especially for counting answer sets.