Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Is complexity theory of use to AI?
Proc. of the international NATO symposium on Artificial and human intelligence
Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
Coordinating Pebble Motion On Graphs, The Diameter Of Permutation Groups, And Applications
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Planning and learning in permutation groups
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
IJCAI'73 Proceedings of the 3rd international joint conference on Artificial intelligence
Rush Hour is PSAPCE-complete, or "Why you should generously tip parking lot attendants"
Theoretical Computer Science
Playing Games with Algorithms: Algorithmic Combinatorial Game Theory
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Finding Optimal Solutions to Atomix
KI '01 Proceedings of the Joint German/Austrian Conference on AI: Advances in Artificial Intelligence
Controlling the learning process of real-time heuristic search
Artificial Intelligence
Assembling molecules in ATOMIX is hard
Theoretical Computer Science - Algorithmic combinatorial game theory
Information Processing Letters
Scaling Search with Pattern Databases
Model Checking and Artificial Intelligence
Weighted A∗ search -- unifying view and application
Artificial Intelligence
A selective macro-learning algorithm and its application to the N × N sliding-tile puzzle
Journal of Artificial Intelligence Research
Algorithms for solving Rubik's cubes
ESA'11 Proceedings of the 19th European conference on Algorithms
Heuristics for puzzle-based storage systems driven by a limited set of automated guided vehicles
Journal of Intelligent Manufacturing
The time complexity of A* with approximate heuristics on multiple-solution search spaces
Journal of Artificial Intelligence Research
Computational complexity of string puzzles
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
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The 8-puzzle and the 15-puzzle have been used for many years as a domain for testing heuristic search techniques. From experience it is known that these puzzles are ''difficult'' and therefore useful for testing search techniques. In this paper we give strong evidence that these puzzles are indeed good test problems. We extend the 8-puzzle and the 15-puzzle to an nxn board and show that finding a shortest solution for the extended puzzle is NP-hard and is thus believed to be computationally infeasible. We also sketch an approximation algorithm for transforming boards that is guaranteed to use no more than a constant times the minimum number of moves, where the constant is independent of the given boards and their side length n. The studied puzzles are instances of planar relocation problems where the reachability question is polynomial but efficient relocation is NP-hard. Such problems are natural robotics problems: A robot needs to efficiently relocate packages in the plane. Our research encourages the study of polynomial approximation algorithms for related robotics problems.