## 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.

Original language | English |
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Article number | 25 |

Journal | ACM Transactions on Algorithms |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - 1 Jun 2008 |

## Keywords

- Optimality proofs
- Tower of Hanoi

## ASJC Scopus subject areas

- Mathematics (miscellaneous)