On optimal solutions for the bottleneck tower of hanoi problem

Yefim Dinitz, Shay Solomon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study two aspects of a generalization of the Tower of Hanoi puzzle. In 1981, D. Wood suggested its variant, where a bigger disk may be placed higher than a smaller one if their size difference is less than k. In 1992, D. Poole suggested a natural disk-moving strategy for this problem, but only in 2005, the authors proved it be optimal in the general case. We describe the family of all optimal solutions to this problem and present a closed formula for their number, as a function of the number of disks and k. Besides, we prove a tight bound for the diameter of the configuration graph of the problem suggested by Wood. Finally, we prove that the average length of shortest sequence of moves, over all pairs of initial and final configurations, is the same as the above diameter, up to a constant factor.

Original languageEnglish
Title of host publicationSOFSEM 2007
Subtitle of host publicationTheory and Practice of Computer Science - 33rd Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
PublisherSpringer Verlag
Pages248-259
Number of pages12
ISBN (Print)9783540695066
DOIs
StatePublished - 2007
Externally publishedYes
Event33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007 - Harrachov, Czech Republic
Duration: 20 Jan 200726 Jan 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4362 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference33rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2007
Country/TerritoryCzech Republic
CityHarrachov
Period20/01/0726/01/07

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