### Citations

1486 |
Introduction to Parallel Algorithms and Architectures,
- Leighton
- 1992
(Show Context)
Citation Context ...onnection networks; Cycle embedding; Faulty elements. I. INTRODUCTION HYPERCUBES are a powerful network that is able to perform various kinds of parallel computations and simulate many other networks =-=[14]-=-, [15]. Hypercubes have been widely studied in interconnection networks [6], [7], [8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. Th... |

277 |
Topological properties of hypercubes.
- Saad, Schultz
- 1988
(Show Context)
Citation Context ...ion networks; Cycle embedding; Faulty elements. I. INTRODUCTION HYPERCUBES are a powerful network that is able to perform various kinds of parallel computations and simulate many other networks [14], =-=[15]-=-. Hypercubes have been widely studied in interconnection networks [6], [7], [8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There ar... |

82 |
Dynamic fault-tree models for fault-tolerant computer systems,”
- Dugan, Bavuso, et al.
- 1992
(Show Context)
Citation Context ...[20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], [3], =-=[5]-=-, [13], [16]. One of the most popular variants is the folded hypercube, which is an extension of the hypercube and can be constructed by adding a link to every pair of nodes with complementary address... |

50 |
A variation on the hypercube with lower diameter.
- Efe
- 1991
(Show Context)
Citation Context ...are a powerful network that is able to perform various kinds of parallel computations and simulate many other networks [14], [15]. Hypercubes have been widely studied in interconnection networks [6], =-=[7]-=-, [8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2]... |

43 |
Rh: a versatile family of reduced hypercube interconnection networks
- Ziavras
- 1994
(Show Context)
Citation Context ...rful network that is able to perform various kinds of parallel computations and simulate many other networks [14], [15]. Hypercubes have been widely studied in interconnection networks [6], [7], [8], =-=[20]-=-. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], [3], [5],... |

30 |
Abraham Algorithm-based fault tolerance on a hypercube multiprocessor.
- Banerjee, Rahmeh, et al.
- 1990
(Show Context)
Citation Context ...[7], [8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link =-=[2]-=-, [3], [5], [13], [16]. One of the most popular variants is the folded hypercube, which is an extension of the hypercube and can be constructed by adding a link to every pair of nodes with complementa... |

26 |
The Twisted N-Cube with Application to Multiprocessing,"
- Esfahanian, Ni, et al.
- 1991
(Show Context)
Citation Context ... powerful network that is able to perform various kinds of parallel computations and simulate many other networks [14], [15]. Hypercubes have been widely studied in interconnection networks [6], [7], =-=[8]-=-, [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], [3]... |

24 |
Algorithms and Properties of a New Two-Level Network with Folded Hypercubes as Basic Modeles
- Duh, Chen, et al.
- 1995
(Show Context)
Citation Context ...UBES are a powerful network that is able to perform various kinds of parallel computations and simulate many other networks [14], [15]. Hypercubes have been widely studied in interconnection networks =-=[6]-=-, [7], [8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or lin... |

18 | On reliability of the folded hypercubes,
- Zhu, Xu, et al.
- 2007
(Show Context)
Citation Context ...e) is fault-free if it contains neither faulty nodes nor faulty links. Previously, the problem of faulttolerant embedding on an n-dimensional folded hypercube FQn has been studied in [9], [10], [17], =-=[18]-=-, [19]. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. [12] have shown that FQn − FFv − FFe for This work wa... |

16 |
Efficient Fault-Tolerant Mesh and Hypercube Architectures
- Bruck, Cypher, et al.
- 1992
(Show Context)
Citation Context ...[8], [20]. A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], =-=[3]-=-, [5], [13], [16]. One of the most popular variants is the folded hypercube, which is an extension of the hypercube and can be constructed by adding a link to every pair of nodes with complementary ad... |

10 |
Long paths in hypercubes with conditional node-faults. Information Sciences,
- -L, Liang, et al.
- 2009
(Show Context)
Citation Context ... A number of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], [3], [5], =-=[13]-=-, [16]. One of the most popular variants is the folded hypercube, which is an extension of the hypercube and can be constructed by adding a link to every pair of nodes with complementary address. The ... |

10 |
Embedding Hamiltonian cycles into folded hypercubes with faulty links
- Wang
- 2001
(Show Context)
Citation Context ... adding a link to every pair of nodes with complementary address. The folded hypercube has been shown to be able to improve the system’s performance over a regular hypercube in many measurements [1], =-=[17]-=-. Since faults may happen on both nodes and edges in a network, it is practically meaningful and important to consider faulty networks. A node is fault-free if it is not faulty. A link is fault-free i... |

8 |
Edge-fault-tolerant properties of hypercubes and folded hypercubes
- Xu, Ma, et al.
(Show Context)
Citation Context ...fault-free if it contains neither faulty nodes nor faulty links. Previously, the problem of faulttolerant embedding on an n-dimensional folded hypercube FQn has been studied in [9], [10], [17], [18], =-=[19]-=-. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. [12] have shown that FQn − FFv − FFe for This work was supp... |

5 |
Conditional faulttolerant edge-bipancyclicity of hypercubes
- Tsai, Lai
- 2007
(Show Context)
Citation Context ...ber of other topologies, such as paths, trees, rings, and meshes, can be embedded into a hypercube. There are also many related results in hypercubes with faulty vertices or link [2], [3], [5], [13], =-=[16]-=-. One of the most popular variants is the folded hypercube, which is an extension of the hypercube and can be constructed by adding a link to every pair of nodes with complementary address. The folded... |

4 |
EI-Amawy and Shahram Latifi, Properties and performance of folded hypercubes
- Ahmed
- 1991
(Show Context)
Citation Context ...ed by adding a link to every pair of nodes with complementary address. The folded hypercube has been shown to be able to improve the system’s performance over a regular hypercube in many measurements =-=[1]-=-, [17]. Since faults may happen on both nodes and edges in a network, it is practically meaningful and important to consider faulty networks. A node is fault-free if it is not faulty. A link is fault-... |

3 |
Cycle embedding in hypercubes with faulty vertices and edges
- Du, Jin, et al.
(Show Context)
Citation Context ...dimensional faulty hypercube Qn, let Fv and Fe be the sets of faulty nodes and faulty links of Qn, respectively. On the problem of finding the lower bound of longest fault-free cycle in Qn, Du et al. =-=[4]-=- have shown the result as Lemma 3. Lemma 3 ([4]). Qn − Fv − Fe for n ≥ 3 contains a fault-free cycle of length at least 2n − 2|Fv| if (1) |Fv| + |Fe| ≤2n − 4 and |Fe| ≤2n − 5 and (2) every node in Qn ... |

3 |
Fault-free cycles in folded hypercubes with more faulty elements
- Fu
- 2008
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Citation Context ...lty. A path (cycle) is fault-free if it contains neither faulty nodes nor faulty links. Previously, the problem of faulttolerant embedding on an n-dimensional folded hypercube FQn has been studied in =-=[9]-=-, [10], [17], [18], [19]. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. [12] have shown that FQn − FFv − FF... |

3 |
Some edge-fault-tolerant properties of the folded hypercube
- Hsieh
- 2008
(Show Context)
Citation Context ...A path (cycle) is fault-free if it contains neither faulty nodes nor faulty links. Previously, the problem of faulttolerant embedding on an n-dimensional folded hypercube FQn has been studied in [9], =-=[10]-=-, [17], [18], [19]. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. [12] have shown that FQn − FFv − FFe for ... |

3 |
A further result on faultfree cycles in faulty folded hypercubes
- Hsieh, Kuo, et al.
- 2009
(Show Context)
Citation Context ...percube FQn has been studied in [9], [10], [17], [18], [19]. Let FFv (respectively, FFe) be the set of faulty nodes (respectively, faulty links) in an n-dimensional folded hypercube FQn. Hsieh et al. =-=[12]-=- have shown that FQn − FFv − FFe for This work was supported in part by the National Science Council of Republic of China under contracts NSC 100-2221-E-128-003-. Jia-Jie Liu is with the Department of... |

2 |
and Tzu-Hsiung Shen, Edge-bipancyclicity of a hypercube with faulty vertices and edges
- Hsieh
(Show Context)
Citation Context ...Fv − Fe for n ≥ 3 contains a fault-free cycle of length at least 2n − 2|Fv| if (1) |Fv| + |Fe| ≤2n − 4 and |Fe| ≤2n − 5 and (2) every node in Qn is incident to at least two fault-free links. Lemma 4 (=-=[11]-=-). Every edge of Qn − Fv − Fe lies on a cycle of every length from 4 to 2n−2|Fv| even if |Fv|+|Fe| ≤n−2, where n ≥ 3. III. FAULT-FREE CYCLE IN THE FAULTY FOLDED HYPERCUBES In this section, we present ... |