Three edge-disjoint Hamiltonian cycles in crossed cubes with applications to fault-tolerant data broadcasting

Pai, Kung-Jui; Wu, Ro-Yu; Peng, Sheng‐Lung; Chang, Jou–Ming

doi:10.1007/s11227-022-04825-5

Cited by 3 publications

(2 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For n ≥ 6, there exist three edge-disjoint Hamiltonian cycles in CQn. In the research direction of EDHCs, briefly summarize the solution methods in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Most of the articles use the method of recursive construction.…”

Section: Theorem 2 ([23]mentioning

confidence: 99%

“…In addition, some articles will go out of the cycle along the edge of a specific direction or a specific dimension. Then, by exchanging some edges, multiple cycles are connected to In the research direction of EDHCs, briefly summarize the solution methods in [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Most of the articles use the method of recursive construction.…”

Section: Theorem 2 ([23]mentioning

confidence: 99%

See 1 more Smart Citation

Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting

Pai

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

All-to-all broadcasting means to distribute the exclusive message of each node in the network to all other nodes. It can be handled by rings, and a Hamiltonian cycle is a ring that visits each vertex exactly once. Multiple edge-disjoint Hamiltonian cycles, abbreviated as EDHCs, have two application advantages: (1) parallel data broadcast and (2) edge fault-tolerance in network communications. There are three edge-disjoint Hamiltonian cycles on n-dimensional locally twisted cubes and n-dimensional crossed cubes while n ≥ 6, respectively. Locally twisted cubes, crossed cubes, folded locally twisted cubes (denoted as FLTQn), and folded crossed cubes (denoted as FCQn) are among the hypercube-variant network. The topology of hypercube-variant network has more wealth than normal hypercubes in network properties. Then, the following results are presented in this paper: (1) Using the technique of edge exchange, three EDHCs are constructed in FLTQ5 and FCQ5, respectively. (2) According to the recursive structure of FLTQn and FCQn, there are three EDHCs in FLTQn and FCQn while n ≥ 6. (3) Considering that multiple faulty edges will occur randomly, the data broadcast performance of three EDHCs in FLTQn and FCQn is evaluated by simulation when 5 ≤ n ≤ 9.

show abstract

Section: Theorem 2 ([23]mentioning

confidence: 99%

Section: Theorem 2 ([23]mentioning

confidence: 99%

Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting

Pai

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

Hamiltonian cycle embedding with fault-tolerant edges and adaptive diagnosis in half hypercube

Fan,

Liu,

2023

J Supercomput

View full text Add to dashboard Cite

Interconnection network directly affects the efficiency of parallel and distributed systems. Hypercube is one of the most important interconnection networks in parallel computing systems. As a significant variant of hypercube, half hypercube has the same number of vertices as hypercube while its degree is only half that of hypercube, which indicates that it has lower network overhead than hypercube. In this paper, we study the fault-tolerant embedding of Hamiltonian cycles and design an adaptive diagnosis algorithm for the half hypercube. Firstly, we prove that the half hypercube is Hamiltonian and propose an algorithm to construct a Hamiltonian cycle in the network. Furthermore, we prove that half hypercube is Hamiltonian with no more than (⌈n/2⌉−1) faulty edges. Finally, we present a parallel adaptive diagnosis scheme under PMC model, which can identify almost all faulty vertices in five rounds.

show abstract

One-to-one node disjoint paths on divide-and-swap cubes

Zhang,

You,

Han

et al. 2024

International Journal of Computer Mathematics: Computer Systems

View full text Add to dashboard Cite

Three edge-disjoint Hamiltonian cycles in crossed cubes with applications to fault-tolerant data broadcasting

Cited by 3 publications

References 38 publications

Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting

Three Edge-Disjoint Hamiltonian Cycles in Folded Locally Twisted Cubes and Folded Crossed Cubes with Applications to All-to-All Broadcasting

Hamiltonian cycle embedding with fault-tolerant edges and adaptive diagnosis in half hypercube

One-to-one node disjoint paths on divide-and-swap cubes

Contact Info

Product

Resources

About