Answer Set Solving with Bounded Treewidth Revisited
This work provides incremental improvements for researchers and practitioners in computational logic and AI by extending full ASP syntax handling compared to prior methods.
The paper tackled the problem of efficiently solving answer set programming (ASP) problems by exploiting bounded treewidth as a parameter, resulting in algorithms that run in linear time under bounded conditions and show good runtime behavior for low-treewidth benchmark instances, especially in counting answer sets.
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.