Johanna Groven

Yasir Mahmood, Markus Hecher, Johanna Groven et al.

Structural measures of graphs, such as treewidth, are central tools in computational complexity resulting in efficient algorithms when exploiting the parameter. It is even known that modern SAT solvers work efficiently on instances of small treewidth. Since these solvers are widely applied, research interests in compact encodings into (Q)SAT for solving and to understand encoding limitations. Even more general is the graph parameter clique-width, which unlike treewidth can be small for dense graphs. Although algorithms are available for clique-width, little is known about encodings. We initiate the quest to understand encoding capabilities with clique-width by considering abstract argumentation, which is a robust framework for reasoning with conflicting arguments. It is based on directed graphs and asks for computationally challenging properties, making it a natural candidate to study computational properties. We design novel reductions from argumentation problems to (Q)SAT. Our reductions linearly preserve the clique-width, resulting in directed decomposition-guided (DDG) reductions. We establish novel results for all argumentation semantics, including counting. Notably, the overhead caused by our DDG reductions cannot be significantly improved under reasonable assumptions.

Victor Lagerkvist, Johanna Groven, Leif Eriksson

The region connection calculus ($RCC$) and Allen's interval algebra ($IA$) are two well-known NP-hard spatial-temporal qualitative reasoning problems. They are solvable in $2^{O(n \log n)}$ time, where $n$ is the number of variables, and $IA$ is additionally known to be solvable in $o(n)^n$ time. However, no improvement over exhaustive search is known for $RCC$, and if they are also solvable in single exponential time $2^{O(n)}$ is unknown. We investigate multiple avenues towards reaching such bounds. First, we show that branching is insufficient since there are too many non-redundant constraints. Concretely, we classify the maximum number of non-redundant constraints in $RCC$ and $IA$. Algorithmically, we make two significant contributions based on dynamic programming (DP). The first algorithm runs in $4^n$ time and is applicable to a non-trivial, NP-hard fragment of $IA$, which includes the well-known interval graph sandwich problem of Golumbic and Shamir (1993). For the richer $RCC$ problem with 8 basic relations we use a more sophisticated approach which asymptotically matches the $o(n)^n$ bound for $IA$.