Domain-independent planning: representation and plan generation
Artificial Intelligence
Planning as search: a quantitative approach
Artificial Intelligence
Inheritance in automated planning
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Steps toward artificial intelligence
Computers & thought
Human Problem Solving
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 2
An expected-cost analysis of backtracking and non-backtracking algorithms
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
The downward refinement property
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Searching for an optimal path in a tree with random costs
Artificial Intelligence
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In the best case using an abstraction hierarchy in problem-solving can yield an exponential speed-up in search efficiency. Such a speed-up is predicted by various analytical models developed in the literature, and efficiency gains of this order have been confirmed empirically. However, these models assume that the Downward Refinement Property (DRP) holds. When this property holds, backtracking never need occur across abstraction levels. When it fails, search may have to consider many different abstract solutions before finding one that can be refined to a concrete solution. In this paper we provide an analysis of the expected search complexity without assuming the DRP. We find that our model predicts a phase boundary where abstraction provides no benefit: if the probability that an abstract solution can be refined is very low or very high, search with abstraction yields significant speed up. However, in the phase boundary area where the probability takes on an intermediate value search efficiency is not necessarily improved. The phenomenon of a phase boundary where search is hardest agrees with recent empirical studies of Cheeseman et al. [CKT91].