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={Dan 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… Expand
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