Some Fixed Parameter Tractability Results for Planning with Non-Acyclic Domain-Transition Graphs

Abstract

Bäckström studied the parameterised complexity of planning when the domain-transition graphs (DTGs) are acyclic. He used the parameters d (domain size), k (number of paths in the DTGs) and w (treewidth of the causal graph), and showed that planning is fixed-parameter tractable (fpt) in these parameters, and fpt in only parameter k 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 d and k, reinterpreting this as the number of paths in the condensation of a DTG, and the two new parameters c (the number of contracted cycles along a path) and pmax (an upper bound for walking around cycles, when not unbounded).