Complexity of the path multi-peg Tower of Hanoi

Daniel Berend; Amir Sapir

Complexity of the path multi-peg Tower of Hanoi

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

The Tower of Hanoi problem with h ≥ 4 pegs is long known to require a sub-exponential number of moves in order to transfer a pile of n disks from one peg to another. In this paper we discuss the Path;, 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 bi-directional interconnections among pegs, here there are only h -1 of them. Despite the significant reduction in the number of interconnections, the task of moving n disks between any two pegs is still shown to grow sub-exponentially as a function of the number of disks.

Original language	English
Title of host publication	Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics
Editors	C. Demetrescu, R. Sedgewick, R. Tamassia
Pages	212-215
Number of pages	4
State	Published - 1 Dec 2005
Event	Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics - Vancouver, BC, Canada Duration: 22 Jan 2005 → 22 Jan 2005

Publication series

Name	Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics

Conference

Conference	Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics
Country/Territory	Canada
City	Vancouver, BC
Period	22/01/05 → 22/01/05

ASJC Scopus subject areas

General Engineering

Cite this

Berend, D., & Sapir, A. (2005). Complexity of the path multi-peg Tower of Hanoi. In C. Demetrescu, R. Sedgewick, & R. Tamassia (Eds.), Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics (pp. 212-215). (Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics).

Berend, Daniel ; Sapir, Amir. / Complexity of the path multi-peg Tower of Hanoi. Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics. editor / C. Demetrescu ; R. Sedgewick ; R. Tamassia. 2005. pp. 212-215 (Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics).

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title = "Complexity of the path multi-peg Tower of Hanoi",

abstract = "The Tower of Hanoi problem with h ≥ 4 pegs is long known to require a sub-exponential number of moves in order to transfer a pile of n disks from one peg to another. In this paper we discuss the Path;, 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 bi-directional interconnections among pegs, here there are only h -1 of them. Despite the significant reduction in the number of interconnections, the task of moving n disks between any two pegs is still shown to grow sub-exponentially as a function of the number of disks.",

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booktitle = "Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics",

note = "Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics ; Conference date: 22-01-2005 Through 22-01-2005",

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Berend, D & Sapir, A 2005, Complexity of the path multi-peg Tower of Hanoi. in C Demetrescu, R Sedgewick & R Tamassia (eds), Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics. Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics, pp. 212-215, Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics, Vancouver, BC, Canada, 22/01/05.

Complexity of the path multi-peg Tower of Hanoi. / Berend, Daniel; Sapir, Amir.
Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics. ed. / C. Demetrescu; R. Sedgewick; R. Tamassia. 2005. p. 212-215 (Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - The Tower of Hanoi problem with h ≥ 4 pegs is long known to require a sub-exponential number of moves in order to transfer a pile of n disks from one peg to another. In this paper we discuss the Path;, 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 bi-directional interconnections among pegs, here there are only h -1 of them. Despite the significant reduction in the number of interconnections, the task of moving n disks between any two pegs is still shown to grow sub-exponentially as a function of the number of disks.

AB - The Tower of Hanoi problem with h ≥ 4 pegs is long known to require a sub-exponential number of moves in order to transfer a pile of n disks from one peg to another. In this paper we discuss the Path;, 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 bi-directional interconnections among pegs, here there are only h -1 of them. Despite the significant reduction in the number of interconnections, the task of moving n disks between any two pegs is still shown to grow sub-exponentially as a function of the number of disks.

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Berend D, Sapir A. Complexity of the path multi-peg Tower of Hanoi. In Demetrescu C, Sedgewick R, Tamassia R, editors, Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics. 2005. p. 212-215. (Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithms and Combinatorics).

Complexity of the path multi-peg Tower of Hanoi

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