Open AccessProceedings Article
Finding optimal solutions to the twenty-four puzzle
Richard E. Korf,Larry A. Taylor +1 more
- pp 1202-1207
TLDR
A general theory for the automatic discovery of heuristics based on considering multiple subgoals simultaneously is presented, and it is observed that as heuristic search problems are scaled up, more powerful heuristic functions become both necessary and cost-effective.Abstract:
We have found the first optimal solutions to random instances of the Twenty-Four Puzzle, the 5 × 5 version of the well-known sliding-tile puzzles. Our new contribution to this problem is a more powerful admissible heuristic function. We present a general theory for the automatic discovery of such heuristics, which is based on considering multiple subgoals simultaneously. In addition, we apply a technique for pruning duplicate nodes in depth-first search using a finitestate machine. Finally, we observe that as heuristic search problems are scaled up, more powerful heuristic functions become both necessary and cost-effective.read more
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References
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Journal ArticleDOI
A Formal Basis for the Heuristic Determination of Minimum Cost Paths
TL;DR: How heuristic information from the problem domain can be incorporated into a formal mathematical theory of graph searching is described and an optimality property of a class of search strategies is demonstrated.
Journal ArticleDOI
Combinatorial optimization: algorithms and complexity
TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.
Journal ArticleDOI
Depth-first iterative-deepening: an optimal admissible tree search
TL;DR: This heuristic depth-first iterative-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifteen Puzzle within practical resource limits.
An Optimal Admissible Tree Search
TL;DR: This heuristic depth-first iteratiw-deepening algorithm is the only known algorithm that is capable of finding optimal solutions to randomly generated instances of the Fifeen Puzzle within practical resource limits.
Proceedings Article
Pruning duplicate nodes in depth-first search
Larry A. Taylor,Richard E. Korf +1 more
TL;DR: This work presents a technique for reducing the asymptotic complexity of depth-first search by eliminating the generation of duplicate nodes, and implements and tests the technique on a grid, the Fifteen Puzzle, the Twenty-Four Puzzle, and two versions of Rubik's Cube.