Optimality of an algorithm solving the Bottleneck Tower of Hanoi problem

Yefim Dinitz, Shay Solomon

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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 languageEnglish
Article number25
JournalACM Transactions on Algorithms
Volume4
Issue number3
DOIs
StatePublished - 1 Jun 2008

Keywords

  • Optimality proofs
  • Tower of Hanoi

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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