# Loopless Gray Code Enumeration and the Tower of Bucharest

@inproceedings{Herter2016LooplessGC, title={Loopless Gray Code Enumeration and the Tower of Bucharest}, author={Felix Herter and G. Rote}, booktitle={FUN}, year={2016} }

We give new algorithms for generating all n-tuples over an alphabet of m letters, changing only one letter at a time (Gray codes). These algorithms are based on the connection with variations of the Towers of Hanoi game. Our algorithms are loopless, in the sense that the next change can be determined in a constant number of steps, and they can be implemented in hardware. We also give another family of loopless algorithms that is based on the idea of working ahead and saving the work in a buffer… Expand

#### 7 Citations

Loopless Gray code enumeration and the Tower of Bucharest

- Computer Science, Mathematics
- Theor. Comput. Sci.
- 2018

New algorithms for generating all n -tuples over an alphabet of m letters, changing only one letter at a time (Gray codes) are given, based on the connection with variations of the Tower of Hanoi game. Expand

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A constant-time algorithm for middle levels Gray codes

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A semi-automatic way as a kind of "dominant eigenvalue" of a bilinear operation on sixtuples that is derived from the dynamic-programming recursion for computing the number of minimal dominating sets of a tree is obtained. Expand

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The results significantly improve on previously known constructions and for the odd-size alphabets the worst-case barrier for space-optimal (non-redundant) quasi-Gray codes with constant number of writes is broken. Expand

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A linear algorithm is proposed to layout incomplete ternary n‐cube network onto torus NoC, and theoretical analysis demonstrates that the proposed algorithm can reduce the network cost and wirelength, which be conducive to estimate the wire length and chip area. Expand

A Constant-Time Algorithm for Middle Levels Gray Codes

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This work presents an algorithm for computing a middle levels Gray code in optimal time and space: each new set in the Gray code is generated in time $${{\mathcal {O}}}(1)$$ O ( 1 ) on average, and the required space is $${{\ mathcal { O}}}(n)$ O ( n ) . Expand

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Loopless Gray code enumeration and the Tower of Bucharest

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New algorithms for generating all n -tuples over an alphabet of m letters, changing only one letter at a time (Gray codes) are given, based on the connection with variations of the Tower of Hanoi game. Expand

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