Yefim Dinitz
Abstract
We study the Bottleneck Tower of Hanoi puzzle posed by D. Wood in 1981. There, a relaxed placement rule allows a larger disk to be placed higher than a smaller one if their size difference is less than a pregiven value k. A shortest sequence of moves (optimal algorithm) transferring all the disks placed on some peg in decreasing order of size, to another peg in the same order is in question. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, and computed the length of the shortest move sequence under its framework. However, other strategies were overlooked, so the lower bound/optimality question remained open. In 1998, Benditkis, Berend, and Safro proved the optimality of Poole's algorithm for the first nontrivial case k = 2. We prove Poole's algorithm to be optimal in the general case.
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- Dinitz, Y., and Solomon, S. 2007. On optimal solutions for the Bottleneck Tower of Hanoi problem. In Proceedings of the 33rd International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM'2007), J. van Leeuwen, J. Italiano, W. van der Hoek, C. Meinel, H. Sack, and F. Plášil, Eds. Lecture Notes in Computer Science, vol. 4362 Springer-Verlag, Berlin-Heidelberg, Germany, 248--259. Google ScholarDigital Library
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Index Terms
- Optimality of an algorithm solving the Bottleneck Tower of Hanoi problem
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