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Computationally tractable planning problems reported in the literature so far have almost exclusively been deened by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying state-transition graph. The exponential size of this graph, though, makes such… (More)

We present a class of planning instances such that the plan existence problem is tractable while plan generation is prov-ably intractable for instances of this class. The class is deened by simple structural restrictions, all of them testable in polynomial-time. Furthermore, we show that plan generation can be carried out in solution-polynomial time, that… (More)

- Magnus Wahlström, Vilhelm Dahllöf, Peter Jonsson, Magnus Wahlström Count
- 2007

The topic of exact, exponential-time algorithms for NP-hard problems has received a lot of attention, particularly with the focus of producing algorithms with stronger theoretical guarantees, e.g. upper bounds on the running time on the form O (c n) for some c. Better methods of analysis may have an impact not only on these bounds, but on the nature of the… (More)

Allen's interval algebra is one of the best established formalisms for temporal reasoning. This article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra. When the constraints are chosen from the full Allen's algebra, this form of satisfiability problem is known to be… (More)

Classical propositional STRIPS planning is nothing but the search for a path in the state-transition graph induced by the operators in the planning problem. What makes the problem hard is the size and the sometimes adverse structure of this graph. We conjecture that the search for a plan would be more efficient if there were only a small number of paths… (More)

There has been a tremendous advance in domain-independent planning over the past decades, and planners have become increasingly efficient at finding plans. However, this has not been paired by any corresponding improvement in detecting unsolvable instances. Such instances are obviously important but largely neglected in planning. In other areas, such as… (More)

We i n vestigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satissability problem for RCC-5 is known to be NP-complete but not much i s k n o wn about its approximately four billion subclasses. We provide a complete classiication of satissability for all these… (More)