Shortest paths in the Tower of Hanoi graph and finite automata

@article{Romik2006ShortestPI,
  title={Shortest paths in the Tower of Hanoi graph and finite automata},
  author={D. Romik},
  journal={SIAM J. Discret. Math.},
  year={2006},
  volume={20},
  pages={610-622}
}
  • D. Romik
  • Published 2006
  • Mathematics, Computer Science
  • SIAM J. Discret. Math.
  • We present efficient algorithms for constructing a shortest path between two configurations in the Tower of Hanoi graph and for computing the length of the shortest path. The key element is a finite-state machine which decides, after examining on the average only a small number of the largest discs (asymptotically, $\frac{63}{38} \approx 1.66$), whether the largest disc will be moved once or twice. This solves a problem raised by Andreas Hinz and results in a better understanding of how the… CONTINUE READING
    68 Citations
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    • PDF
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    • 7
    Distances and automatic sequences in distinguished variants of Hanoi graphs
    • 2
    • Highly Influenced
    • PDF
    On The Average-Case Complexity of the Bottleneck Tower of Hanoi Problem
    • PDF
    Shortest paths in Sierpiński graphs
    • 14
    Twin Towers of Hanoi
    • Z. Sunic
    • Mathematics, Computer Science
    • Eur. J. Comb.
    • 2012
    • 3
    • PDF
    Independent sets on the Towers of Hanoi graphs
    • 4
    • PDF
    Extrema property of the k-ranking of directed paths and cycles
    • 2
    • Highly Influenced
    • PDF

    References

    SHOWING 1-10 OF 18 REFERENCES
    An analysis of the generalized Towers of Hanoi problem
    • M. Er
    • Mathematics, Computer Science
    • BIT Comput. Sci. Sect.
    • 1983
    • 13
    Shortest paths between regular states of the Tower of Hanoi
    • A. Hinz
    • Mathematics, Computer Science
    • Inf. Sci.
    • 1992
    • 41
    • Highly Influential
    A statistical analysis of the towers of hanoi problem
    • 32
    • Highly Influential
    The average distance on the Sierpiński gasket
    • 57
    • Highly Influential
    On the Frame-Stewart algorithm for the multi-peg Tower of Hanoi problem
    • 42
    • PDF
    The Tower of Hanoi: A historical survey and bibliography
    • version 0.2. Preprint
    • 2001
    The Tower of Hanoi. Algebras and Combinatorics (ICAC'97, Hong Kong)
    • The Tower of Hanoi. Algebras and Combinatorics (ICAC'97, Hong Kong)
    • 1999
    Graphs S(n
    • k) and a variant of the Tower of Hanoi problem. Czechoslovak Math. J. 47 (122), 95–104
    • 1997