Representation Selection for Constraint Satisfaction: A Case Study Using n-Queens
IEEE Expert: Intelligent Systems and Their Applications
Human Problem Solving
Where the really hard problems are
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Minimal assumption distribution propagation in belief networks
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
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We present a method for approximating the expected number of steps required by a heuristic search algorithm to reach a goal from any initial state in a problem space. The method is based on a mapping from the original state space to an abstract space in which states are characterized only by a syntactic "distance" from the nearest goal. Modeling the search algorithm as a Markov process in the abstract space yields a simple system of equations for the solution time for each state. We derive some insight into the behavior of search algorithms by examining some closed form solutions for these equations; we also show that many problem spaces have a clearly delineated "easy zone", inside which problems are trivial and outside which problems are impossible. The theory is borne out by experiments with both Markov and non-Markov search algorithms. Our results also bear on recent experimental data suggesting that heuristic repair algorithms can solve large constraint satisfaction problems easily, given a preprocessor that generates a sufficiently good initial state.