State-dependent Cost Partitionings for Cartesian Abstractions in Classical Planning

Abstraction heuristics are a popular method to guide optimal search algorithms in classical planning. Cost partitionings allow to sum heuristic estimates admissibly by distributing action costs among the heuristics. We introduce state-dependent cost partitionings which take context information of actions into account, and show that an optimal state-dependent cost partitioning dominates its state-independent counterpart. We demonstrate the potential of our idea with a state-dependent variant of the recently proposed saturated cost partitioning, and show that it has the potential to improve not only over its state-independent counterpart, but even over the optimal state-independent cost partitioning. Our empirical results give evidence that ignoring the context of actions in the computation of a cost partitioning leads to a significant loss of information

Structural Patterns of Tractable Sequentially-Optimal Planning

We study the complexity of sequentially-optimal classical planning, and discover new problem classes for whose such optimization is tractable. The results are based on exploiting numerous structural characteristics of planning problems, and a constructive proof technique that connects between certain tools from planning and tractable constraint optimization. In particular, we believe that structure-based tractability results of this kind may help devising new admissible search heuristics. We discuss the prospects of this direction along a principled extension of pattern-database heuristics to “structural patterns ” of unlimited dimensionality