## 13 Citations

Gray codes and symmetric chains

- Computer Science, MathematicsICALP
- 2018

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

- Computer ScienceSODA
- 2017

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 $\mathcal{O}(1)$ on average, and the required space is $\math Cal O(n)$.

Combinatorial Gray codes-an updated survey

- Computer Science
- 2022

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

- Computer ScienceESA
- 2018

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 ∗

- Computer Science
- 2018

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

- Computer ScienceICALP
- 2020

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.

- Computer Science
- 2017

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

- MathematicsArXiv
- 2017

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?

- Computer ScienceArXiv
- 2017

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

- Mathematics, Computer ScienceGASCom
- 2018

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 64 REFERENCES

A constant-time algorithm for middle levels Gray codes

- Computer ScienceSODA
- 2017

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 $\mathcal{O}(1)$ on average, and the required space is $\math Cal O(n)$.

Efficient Computation of Middle Levels Gray Codes

- Computer Science, MathematicsACM Trans. Algorithms
- 2018

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).

Bipartite Kneser Graphs are Hamiltonian

- MathematicsComb.
- 2017

It is established the existence of cycles that visit almost all vertices in Kneser graphs K(n,k) when n=2k+o(k), generalizing and improving upon previous results on this problem.

Colorings of diagrams of interval orders and alpha-sequences of sets

- MathematicsDiscret. Math.
- 1995

The Coolest Way to Generate Binary Strings

- Computer ScienceTheory of Computing Systems
- 2013

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

- Computer ScienceSIAM Rev.
- 1997

The area of combinatorial Gray codes is surveyed, recent results, variations, and trends are described, and some open problems are highlighted.