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The ignoring delete lists relaxation is of paramount importance for bothsatisficing and optimal planning. In earlier work, it was observed that theoptimal relaxation heuristic h+ has amazing qualities in many classicalplanning benchmarks, in particular pertaining to the complete absence of localminima. The proofs of this are hand-made, raising the question whether suchproofs can be lead automatically by domain analysis techniques. In contrast toearlier disappointing results -- the analysis method has exponential runtimeand succeeds only in two extremely simple benchmark domains -- we herein answerthis question in the affirmative. We establish connections between causal graphstructure and h+ topology. This results in low-order polynomial time analysismethods, implemented in a tool we call TorchLight. Of the 12 domains where theabsence of local minima has been proved, TorchLight gives strong successguarantees in 8 domains. Empirically, its analysis exhibits strong performancein a further 2 of these domains, plus in 4 more domains where local minima mayexist but are rare. In this way, TorchLight can distinguish easy domains fromhard ones. By summarizing structural reasons for analysis failure, TorchLightalso provides diagnostic output indicating domain aspects that may cause localminima.

Analyzing Search Topology Without Running Any Search: On the Connection Between Causal Graphs and h+