Implicit abstraction heuristics for cost-optimal planning

State-space search with explicit abstraction heuristics is a state of the art approach to cost-optimal planning. These heuristics, however, have the limitation that the size of the abstract space must be bounded by some constant. We therefore introduce the notion of (additive) implicit abstractions, in which the planning task is abstracted by instances of tractable fragments of cost-optimal planning. We show that the fork-decomposition, a concrete instance of this framework based on two novel such fragments, compares favorably to the state of the art in cost-optimal planning. Additive ensembles of admissible heuristics are used in cost-optimal planning to exploit the individual strengths of different admissible heuristics. Continuing our focus on abstraction heuristics, we describe a procedure that takes a planning problem, a search state, and a set of admissible heuristics, and derives an optimal additive composition of these heuristics with respect to the given state. We show that this procedure is polynomial-time for arbitrary sets of abstraction heuristics.