## Abstract

The generalized Tower of Hanoi problem with h<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.

Original language | English |
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Pages (from-to) | 1465-1483 |

Number of pages | 19 |

Journal | Discrete Applied Mathematics |

Volume | 160 |

Issue number | 10-11 |

DOIs | |

State | Published - Jul 2012 |

Externally published | Yes |

### Funding

Funders | Funder number |
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Sapir Academic College, Israel |

## Keywords

- Analysis of algorithms
- Path graphs
- Subexponential growth rate
- Tower of Hanoi

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