On an infinite family of solvable Hanoi graphs

Dany Azriel*, Noam Solomon, Shay Solomon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Tower of Hanoi problem is generalized by placing pegs on the vertices of a given directed graph G with two distinguished vertices, S and D, and allowing moves only along arcs of this graph. An optimal solution for such a graph G is an algorithm that completes the task of moving a tower of any given number of disks from S to D in a minimal number of disk moves. In this article we present an algorithm which solves the problem for two infinite families of graphs, and prove its optimality. To the best of our knowledge, this is the first optimality proof for an infinite family of graphs. Furthermore, we present a unified algorithm that solves the problem for a wider family of graphs and conjecture its optimality.

Original languageEnglish
Article number13
JournalACM Transactions on Algorithms
Issue number1
StatePublished - 1 Nov 2008
Externally publishedYes


  • Optimality proofs
  • Tower of Hanoi


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