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A vibrant theoretical research area are efficient exact parameterizedalgorithms. Very recent solving competitions such as the PACE challenge showthat there is also increasing practical interest in the parameterizedalgorithms community. An important research question is whether dedicatedparameterized exact algorithms exhibit certain practical relevance and one caneven beat well-established problem solvers. We consider the logic-baseddeclarative modeling language and problem solving framework Answer SetProgramming (ASP). State-of-the-art ASP solvers rely considerably on Sat-basedalgorithms. An ASP solver (DynASP2), which is based on a classical dynamicprogramming on tree decompositions, has been published very recently.Unfortunately, DynASP2 can outperform modern ASP solvers on programs of smalltreewidth only if the question of interest is to count the number of solutions.In this paper, we describe underlying concepts of our new implementation(DynASP2.5) that shows competitive behavior to state-of-the-art ASP solverseven for finding just one solution when solving problems as the Steiner treeproblem that have been modeled in ASP on graphs with low treewidth. Ourimplementation is based on a novel approach that we call multi-pass dynamicprogramming (M-DPSINC).

DynASP2.5: Dynamic Programming on Tree Decompositions in Action