Summary: State space search is a basic method for analyzing reachability in discrete transition systems. To tackle large compactly described transition systems – the state space explosion – a wealth of techniques (e.g., partial-order reduction) have been developed that reduce the search space without affecting the existence of (optimal) solution paths. Focusing on classical AI planning, where the compact description is in terms of a vector of state variables, an initial state, a goal condition, and a set of actions, we add another technique, that we baptize star-topology decoupling, into this arsenal. A star topology partitions the state variables into components so that a single center component directly interacts with several leaf components, but the leaves interact only via the center. Many applications explicitly come with such structure; any classical planning task can be viewed in this way by selecting the center as a subset of state variables separating connected leaf components.
Our key observation is that, given such a star topology, the leaves are conditionally independent given the center, in the sense that, given a fixed path of transitions by the center, the possible center-compliant paths are independent across the leaves. Our decoupled search hence branches over center transitions only, and maintains the center-compliant paths for each leaf separately. As we show, this method has exponential separations to all previous search reduction techniques, i.e., examples where it results in exponentially less effort. One can, in principle, prune duplicates in a way so that the decoupled state space can never be larger than the original one. Standard search algorithms remain applicable using simple transformations. Our experiments exhibit large improvements on standard AI planning benchmarks with a pronounced star topology.