Affiliation:
1. Ben-Gurion University of the Negev, Beer-Sheva, Israel
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Reference9 articles.
1. Benditkis S. and Safro I. 1998. Generalizations of the Tower of Hanoi problem. Final project report supervised by D. Berend. Dept. of Mathematics and Computer Science Ben-Gurion University Israel. Benditkis S. and Safro I. 1998. Generalizations of the Tower of Hanoi problem. Final project report supervised by D. Berend. Dept. of Mathematics and Computer Science Ben-Gurion University Israel.
2. Chen X. Tian B. and Wang L. 2007. Santa Claus' Towers of Hanoi. Graphs and Combinatorics 23{Supplement} 153--167. 10.1007/s00373-007-0705-4 Chen X. Tian B. and Wang L. 2007. Santa Claus' Towers of Hanoi. Graphs and Combinatorics 23{Supplement} 153--167. 10.1007/s00373-007-0705-4
3. Optimal Algorithms for Tower of Hanoi Problems with Relaxed Placement Rules
4. On Optimal Solutions for the Bottleneck Tower of Hanoi Problem
5. The bottleneck Towers of Hanoi problem;Poole D.;J. Recreat. Math.,1992
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