*J. Hoffmann*

Between 1998 and 2004, the planning community has seen vast progress in terms of the sizes of benchmark examples that domain-independent planners can tackle successfully. The key technique behind this progress is the use of heuristic functions based on relaxing the planning task at hand, where the relaxation is to assume that all delete lists are empty. The unprecedented success of such methods, in many commonly used benchmark examples, calls for an understanding of what classes of domains these methods are well suited for.

In the investigation at hand, we derive a formal background to such an understanding. We perform a case study covering a range of 30 commonly used STRIPS and ADL benchmark domains, including all examples used in the first four international planning competitions. We *prove* connections between domain structure and local search topology -- heuristic cost surface properties — under an idealized version of the heuristic functions used in modern planners. The idealized heuristic function is called h^{+}, and differs from the practically used functions in that it returns the length of an *optimal* relaxed plan, which is NP-hard to compute. We identify several key characteristics of the topology under h^{+}, concerning the existence/non-existence of unrecognized dead ends, as well as the existence/non-existence of constant upper bounds on the difficulty of escaping local minima and benches. These distinctions divide the (set of all) planning domains into a taxonomy of classes of varying h^+ topology. As it turns out, many of the 30 investigated domains lie in classes with a relatively easy topology. Most particularly, 12 of the domains lie in classes where FF's search algorithm, provided with h^{+}, is a polynomial solving mechanism.

We also present results relating h^{+} to its approximation as implemented in FF. The behavior regarding dead ends is provably the same. We summarize the results of an empirical investigation showing that, in many domains, the topological qualities of h^{+} are largely inherited by the approximation. The overall investigation gives a rare example of a successful analysis of the connections between typical-case problem structure, and search performance. The theoretical investigation also gives hints on how the topological phenomena might be automatically recognizable by domain analysis techniques. We outline some preliminary steps we made into that direction.

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