@article{Bäckström_2015, title={Some Fixed Parameter Tractability Results for Planning with Non-Acyclic Domain-Transition Graphs}, volume={29}, url={https://ojs.aaai.org/index.php/AAAI/article/view/9648}, DOI={10.1609/aaai.v29i1.9648}, abstractNote={ <p> Bäckström studied the parameterised complexity of planning when the domain-transition graphs (DTGs) are acyclic. He used the parameters <em>d </em>(domain size), <em>k</em> (number of paths in the DTGs) and <em>w</em> (treewidth of the causal graph), and showed that planning is fixed-parameter tractable (fpt) in these parameters, and fpt in only parameter <em>k </em>if the causal graph is a polytree. We continue this work by considering some additional cases of non-acyclic DTGs. In particular, we consider the case where each strongly connected component (SCC) in a DTG must be a simple cycle, and we show that planning is fpt for this case if the causal graph is a polytree. This is done by first preprocessing the instance to construct an equivalent abstraction and then apply Bäckströms technique to this abstraction. We use the parameters<em> d </em>and <em>k</em>, reinterpreting this as the number of paths in the condensation of a DTG, and the two new parameters <em>c </em>(the number of contracted cycles along a path) and <em>p</em>max (an upper bound for walking around cycles, when not unbounded). </p> }, number={1}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Bäckström, Christer}, year={2015}, month={Mar.} }