Gaifman Graphs in Lifted Planning

We introduce the metric induced by Gaifman graphs into lifted planning. We analyze what kind of information this metric carries and how it can be utilized for constructing lifted delete-free relaxation heuristics. In particular, we prove how the action dynamics influence the distances between objects. As a corollary, we derive a lower bound on the length of any plan. Finally, we apply our theoretical findings on the Gaifman graphs to improve the delete-free relaxation heuristics induced by PDDL homomorphisms.