# 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
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