On a question of Leiss regarding the Hanoi Tower problem

D. Azriel, D. Berend

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The Tower of Hanoi problem is generalized in such a way that the pegs are located at the vertices of a directed graph G, and moves of disks may be made only along edges of G. Leiss obtained a complete characterization of graphs in which arbitrarily many disks can be moved from the source vertex S to the destination vertex D. Here we consider graphs which do not satisfy this characterization; hence, there is a bound on the number of disks which can be handled. Denote by gn the maximal such number as G varies over all such graphs with n vertices and S, D vary over the vertices. Answering a question of Leiss [Finite Hanoi problems: How many discs can be handled? Congr. Numer. 44 (1984) 221-229], we prove that gn grows sub-exponentially fast. Moreover, there exists a constant C such that gn ≤ Cn1 / 2 log2 n for each n. On the other hand, for each ε > 0 there exists a constant Cε > 0 such that gn ≥ Cε n(1 / 2 - ε) log2 n for each n.

Original languageEnglish
Pages (from-to)377-383
Number of pages7
JournalTheoretical Computer Science
Volume369
Issue number1-3
DOIs
StatePublished - 15 Dec 2006

Keywords

  • Digraph
  • Graphs
  • Hanoi Tower problem
  • Recurrence equation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

Fingerprint

Dive into the research topics of 'On a question of Leiss regarding the Hanoi Tower problem'. Together they form a unique fingerprint.

Cite this