Gray codes generation algorithm and theoretical evaluation of random walks in \(N\)-cubes

DOI10.3390/math6060098zbMath1454.94007OpenAlexW2805683563MaRDI QIDQ1634365

Jean-François Couchot, Pierre-Cyrille Héam, Sylvain Contassot-Vivier

Publication date: 18 December 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math6060098

zbMATH Keywords

Hamiltonian cyclesmixing timeGray codesPRNG\(N\)-cube

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41) Eulerian and Hamiltonian graphs (05C45) Communication theory (94A05)

Uses Software

• TestU01
• Diehard
• CIPRNG

Cites Work

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• Exact solution for a class of random walk on the hypercube
• Handbook of computational statistics. Concepts and methods.
• A construction of Gray codes inducing complete graphs
• Generating all cycles, chordless cycles, and Hamiltonian cycles with the principle of exclusion
• Explicit definition of the binary reflected Gray codes
• Balanced Gray codes
• Canonical form of Gray codes in \(N\)-cubes
• On binary reflected Gray codes and functions
• Random Walk in a N-Cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
• On the Link between Strongly Connected Iteration Graphs and Chaotic Boolean Discrete-Time Dynamical Systems
• On locally balanced gray codes
• Asymptotic analysis of a random walk on a hypercube with many dimensions
• TestU01
• Random Walk: A Modern Introduction
• Counting sequences
• Markov Chains