Trimming and gluing Gray codes

@inproceedings{Gregor2018TrimmingAG,
  title={Trimming and gluing Gray codes},
  author={Petr Gregor and Torsten M{\"u}tze},
  booktitle={Theor. Comput. Sci.},
  year={2018}
}

Figures from this paper

Gray codes and symmetric chains
TLDR
This work provides a solution for the case $\ell=2$ and solves a relaxed version of the problem for general values of $\ell$, by constructing cycle factors for those instances.
A constant-time algorithm for middle levels Gray codes
TLDR
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 ) .
Combinatorial Gray codes-an updated survey
TLDR
This survey provides a comprehensive picture of the state-of-the-art of the research on combinatorial Gray codes and gives an update on Savage’s influential survey, incorporating many more recent developments.
Space-Optimal Quasi-Gray Codes with Logarithmic Read Complexity
TLDR
This paper presents construction of quasi-Gray codes of dimension n and length 3^n over the ternary alphabet with worst-case read complexity O(log n) and write complexity 2 and significantly improves on previously known constructions and breaks the Omega(n) worst- case barrier for space-optimal (non-redundant) quasi- Gray codes.
I T ] 1 7 Ju l 2 01 8 Optimal Quasi-Gray Codes : The Alphabet Matters ∗
TLDR
The results significantly improve on previously known constructions and for the odd-size alphabets the authors break the Ω(n) worst-case barrier for space-optimal (non-redundant) quasiGray codes with constant number of writes.
On the central levels problem
TLDR
A Hamilton cycle is constructed through the $n$-dimensional hypercube that contains the symmetric chain decomposition constructed by Greene and Kleitman in the 1970s, and a loopless algorithm is provided for computing the corresponding Gray code.
Optimal Quasi-Gray Codes: The Alphabet Matters.
TLDR
The results significantly improve on previously known constructions and for the odd-size alphabets the authors break the $\Omega(n)$ worst-case barrier for space-optimal (non-redundant) quasi-Gray codes with constant number of writes.
A short proof of the middle levels theorem
TLDR
A new proof of the well-known middle levels conjecture is presented, which is much shorter and more accessible than the original proof.
Optimal Quasi-Gray Codes: Does the Alphabet Matter?
TLDR
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.
On Hamilton cycles in highly symmetric graphs
TLDR
Some of the recent results on Hamilton cycles in various families of highly symmetric graphs are surveyed, including the solution of the well-known middle levels conjecture, and several far-ranging generalizations of it that were proved subsequently.
...
...

References

SHOWING 1-10 OF 63 REFERENCES
Monotone Gray Codes and the Middle Levels Problem
Efficient Computation of Middle Levels Gray Codes
TLDR
This work provides the first efficient algorithm to compute a middle levels Gray code and computes the next ℓ bitstrings in the Gray code in time O(n+n/ℓ), which is O( n) on average per bitstring provided that �« = Ω (n).
A constant-time algorithm for middle levels Gray codes
TLDR
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 ) .
Bipartite Kneser graphs are Hamiltonian
TLDR
It is established the existence of long cycles in Kneser graphs (visiting almost all vertices), generalizing and improving upon previous results on this problem.
On generalized middle-level problem
The Coolest Way to Generate Binary Strings
TLDR
A loopless algorithm for generating binary strings with any weight range in which successive strings have Levenshtein distance two is given and the recursive structure of the order is investigated and it is shown that it shares certain sublist properties with lexicographic order.
A Survey of Combinatorial Gray Codes
TLDR
The area of combinatorial Gray codes is surveyed, recent results, variations, and trends are described, and some open problems are highlighted.
...
...