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. Discrete Math.},
  year={2006},
  volume={20},
  pages={610-622}
}
Abstract. 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, 63 38 ≈ 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
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