COMPLEXITY RESULTS FOR SAS⁺ PLANNING

Abstract

We have previously reported a number of tractable planning problems defined in the SAS+ formalism. This article complements these results by providing a complete map over the complexity of SAS+ planning under all combinations of the previously considered restrictions. We analyze the complexity of both finding a minimal plan and finding any plan. In contrast to other complexity surveys of planning, we study not only the complexity of the decision problems but also the complexity of the generation problems. We prove that the SAS+-PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS+-US problem, which we prove to be the maximal tractable problem in this case.

Refining complexity analyses in planning by exploiting the exponential time hypothesis

“…In particular, we will use propositional STRIPS with negative goals (PSN) [8], which can alternatively be viewed as SAS + [6] restricted to boolean (i.e. two-valued) variable domains.…”

Identifying and Exploiting Features for Effective Plan Retrieval in Case-Based Planning

“…The features that Fawcett et al exploited come from a number of different sources. They computed features by (a) considering different encodings of a planning problem (PDDL, SAT, SAS+) (Bäckström and Nebel 1995), (b) extracting pre-processing statistics, (c) analysing the search space topology (Hoffmann 2011b;2011a), and (d) considering probing features -brief runs of a planner on the considered problem, in order to extract information from its search trajectories. Their computation can take up to few minutes, according to the domain and the size of the considered problem.…”

Portfolio-based planning: State of the art, common practice and open challenges

“…For generating the predictive models they extracted a large set of features, derived from the SAS+ formulation [3]. They compared the performance of a number of strategies for configuring a portfolio, and evaluated them on planners and benchmarks of IPC 2011.…”