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arXiv · 1102.4885

The Tower of Hanoi problem on Path_h graphs

Daniel Berend·Amir Sapir·Shay Solomon
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Abstract

The generalized Tower of Hanoi problem with h \ge 4 pegs is known to require a sub-exponentially fast growing number of moves in order to transfer a pile of n disks from one peg to another. In this paper we study the Path_h variant, where the pegs are placed along a line, and disks can be moved from a peg to its nearest neighbor(s) only. Whereas in the simple variant there are h(h-1)/2 possible bi-directional interconnections among pegs, here there are only h-1 of them. Despite the significant reduction in the number of interconnections, the number of moves needed to transfer a pile of n disks between any two pegs also grows sub-exponentially as a function of n. We study these graphs, identify sets of mutually recursive tasks, and obtain a relatively tight upper bound for the number of moves, depending on h, n and the source and destination pegs.

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Daniel Berend, Amir Sapir, Shay Solomon. 2011-02-24. The Tower of Hanoi problem on Path_h graphs. https://arxiv.org/abs/1102.4885

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